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

Percentage Accurate: 98.2% → 98.6%

Time: 8.0s

Alternatives: 13

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq 4 \cdot 10^{+269}:\\ \;\;\;\;x + t_1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 4e+269) (+ x (* t_1 y)) (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 4e+269) {
		tmp = x + (t_1 * y);
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= 4d+269) then
        tmp = x + (t_1 * y)
    else
        tmp = 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 t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 4e+269) {
		tmp = x + (t_1 * y);
	} else {
		tmp = z * (y / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= 4e+269:
		tmp = x + (t_1 * y)
	else:
		tmp = z * (y / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= 4e+269)
		tmp = Float64(x + Float64(t_1 * y));
	else
		tmp = Float64(z * Float64(y / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= 4e+269)
		tmp = x + (t_1 * y);
	else
		tmp = z * (y / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+269], N[(x + N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 4.0000000000000002e269

   1. Initial program 99.5%

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

   if 4.0000000000000002e269 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 37.9%

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

      1. associate-*r/ 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-/l* 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in z around inf 99.5%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*r/ 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 4 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 2: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+137}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-84}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-36}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.6e+137)
   (+ x y)
   (if (<= t -2.4e-84)
     (- x (* y (/ z t)))
     (if (<= t 9e-98)
       (+ x (/ (* z y) a))
       (if (<= t 1.15e-36) (* (- t z) (/ y (- t a))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+137) {
		tmp = x + y;
	} else if (t <= -2.4e-84) {
		tmp = x - (y * (z / t));
	} else if (t <= 9e-98) {
		tmp = x + ((z * y) / a);
	} else if (t <= 1.15e-36) {
		tmp = (t - z) * (y / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.6d+137)) then
        tmp = x + y
    else if (t <= (-2.4d-84)) then
        tmp = x - (y * (z / t))
    else if (t <= 9d-98) then
        tmp = x + ((z * y) / a)
    else if (t <= 1.15d-36) then
        tmp = (t - z) * (y / (t - a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.6e+137) {
		tmp = x + y;
	} else if (t <= -2.4e-84) {
		tmp = x - (y * (z / t));
	} else if (t <= 9e-98) {
		tmp = x + ((z * y) / a);
	} else if (t <= 1.15e-36) {
		tmp = (t - z) * (y / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.6e+137:
		tmp = x + y
	elif t <= -2.4e-84:
		tmp = x - (y * (z / t))
	elif t <= 9e-98:
		tmp = x + ((z * y) / a)
	elif t <= 1.15e-36:
		tmp = (t - z) * (y / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.6e+137)
		tmp = Float64(x + y);
	elseif (t <= -2.4e-84)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 9e-98)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	elseif (t <= 1.15e-36)
		tmp = Float64(Float64(t - z) * Float64(y / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.6e+137)
		tmp = x + y;
	elseif (t <= -2.4e-84)
		tmp = x - (y * (z / t));
	elseif (t <= 9e-98)
		tmp = x + ((z * y) / a);
	elseif (t <= 1.15e-36)
		tmp = (t - z) * (y / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.6e+137], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.4e-84], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-98], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-36], N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.59999999999999999e137 or 1.14999999999999998e-36 < t

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l/ 74.7%

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

      4. sub-neg 74.7%

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

      5. +-commutative 74.7%

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

      6. neg-sub0 74.7%

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

      7. associate-+l- 74.7%

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

      8. sub0-neg 74.7%

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

      9. neg-mul-1 74.7%

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

      10. times-frac 94.7%

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

      11. fma-def 94.7%

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

      12. sub-neg 94.7%

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

      13. +-commutative 94.7%

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

      14. neg-sub0 94.7%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 94.7%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 94.7%

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

      17. neg-mul-1 94.7%

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

      18. *-commutative 94.7%

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

      19. associate-/l* 94.7%

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

      20. metadata-eval 94.7%

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

      21. /-rgt-identity 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 84.4%

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

   if -4.59999999999999999e137 < t < -2.40000000000000017e-84

   1. Initial program 99.9%

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

      1. associate-*r/ 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-/l* 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 82.9%

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

   5. Taylor expanded in a around 0 73.9%

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

      1. +-commutative 73.9%

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

      2. mul-1-neg 73.9%

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

      3. associate-*r/ 77.6%

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

      4. unsub-neg 77.6%

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

   7. Simplified 77.6%

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

   if -2.40000000000000017e-84 < t < 8.99999999999999994e-98

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. *-commutative 93.4%

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

      3. associate-*l/ 98.2%

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

      4. sub-neg 98.2%

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

      5. +-commutative 98.2%

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

      6. neg-sub0 98.2%

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

      7. associate-+l- 98.2%

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

      8. sub0-neg 98.2%

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

      9. neg-mul-1 98.2%

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

      10. times-frac 96.1%

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

      11. fma-def 96.1%

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

      12. sub-neg 96.1%

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

      13. +-commutative 96.1%

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

      14. neg-sub0 96.1%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 96.1%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 96.1%

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

      17. neg-mul-1 96.1%

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

      18. *-commutative 96.1%

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

      19. associate-/l* 96.1%

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

      20. metadata-eval 96.1%

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

      21. /-rgt-identity 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in t around 0 81.5%

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

   if 8.99999999999999994e-98 < t < 1.14999999999999998e-36

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. *-commutative 85.2%

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

      3. associate-*l/ 85.0%

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

      4. sub-neg 85.0%

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

      5. +-commutative 85.0%

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

      6. neg-sub0 85.0%

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

      7. associate-+l- 85.0%

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

      8. sub0-neg 85.0%

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

      9. neg-mul-1 85.0%

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

      10. times-frac 99.5%

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

      11. fma-def 99.5%

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

      12. sub-neg 99.5%

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

      13. +-commutative 99.5%

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

      14. neg-sub0 99.5%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 99.5%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 99.5%

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

      17. neg-mul-1 99.5%

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

      18. *-commutative 99.5%

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

      19. associate-/l* 99.5%

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

      20. metadata-eval 99.5%

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

      21. /-rgt-identity 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around -inf 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*r/ 89.9%

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

   6. Simplified 89.9%

      \[\leadsto \color{blue}{\left(t - z\right) \cdot \frac{y}{t - a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+137}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-84}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-36}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+257} \lor \neg \left(z \leq -6.5 \cdot 10^{+213}\right) \land \left(z \leq -6.8 \cdot 10^{+138} \lor \neg \left(z \leq 6.6 \cdot 10^{+205}\right)\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.4e+257)
         (and (not (<= z -6.5e+213))
              (or (<= z -6.8e+138) (not (<= z 6.6e+205)))))
   (* z (/ y (- a t)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.4e+257) || (!(z <= -6.5e+213) && ((z <= -6.8e+138) || !(z <= 6.6e+205)))) {
		tmp = z * (y / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.4d+257)) .or. (.not. (z <= (-6.5d+213))) .and. (z <= (-6.8d+138)) .or. (.not. (z <= 6.6d+205))) then
        tmp = z * (y / (a - t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.4e+257) || (!(z <= -6.5e+213) && ((z <= -6.8e+138) || !(z <= 6.6e+205)))) {
		tmp = z * (y / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.4e+257) or (not (z <= -6.5e+213) and ((z <= -6.8e+138) or not (z <= 6.6e+205))):
		tmp = z * (y / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.4e+257) || (!(z <= -6.5e+213) && ((z <= -6.8e+138) || !(z <= 6.6e+205))))
		tmp = Float64(z * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.4e+257) || (~((z <= -6.5e+213)) && ((z <= -6.8e+138) || ~((z <= 6.6e+205)))))
		tmp = z * (y / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.4e+257], And[N[Not[LessEqual[z, -6.5e+213]], $MachinePrecision], Or[LessEqual[z, -6.8e+138], N[Not[LessEqual[z, 6.6e+205]], $MachinePrecision]]]], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.40000000000000052e257 or -6.49999999999999982e213 < z < -6.80000000000000022e138 or 6.6000000000000004e205 < z

   1. Initial program 88.6%

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

      1. associate-*r/ 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-/l* 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 79.1%

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

   5. Taylor expanded in x around 0 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-*r/ 75.1%

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

   7. Simplified 75.1%

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

   if -8.40000000000000052e257 < z < -6.49999999999999982e213 or -6.80000000000000022e138 < z < 6.6000000000000004e205

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-*l/ 86.9%

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

      4. sub-neg 86.9%

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

      5. +-commutative 86.9%

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

      6. neg-sub0 86.9%

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

      7. associate-+l- 86.9%

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

      8. sub0-neg 86.9%

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

      9. neg-mul-1 86.9%

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

      10. times-frac 95.5%

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

      11. fma-def 95.5%

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

      12. sub-neg 95.5%

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

      13. +-commutative 95.5%

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

      14. neg-sub0 95.5%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 95.5%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 95.5%

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

      17. neg-mul-1 95.5%

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

      18. *-commutative 95.5%

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

      19. associate-/l* 95.5%

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

      20. metadata-eval 95.5%

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

      21. /-rgt-identity 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around inf 71.8%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+257} \lor \neg \left(z \leq -6.5 \cdot 10^{+213}\right) \land \left(z \leq -6.8 \cdot 10^{+138} \lor \neg \left(z \leq 6.6 \cdot 10^{+205}\right)\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+137}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-43}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.42e+137)
   (+ x y)
   (if (<= t -7.5e-43)
     (- x (* y (/ z t)))
     (if (<= t 4.4e-35) (+ x (/ y (/ a z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.42e+137) {
		tmp = x + y;
	} else if (t <= -7.5e-43) {
		tmp = x - (y * (z / t));
	} else if (t <= 4.4e-35) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.42d+137)) then
        tmp = x + y
    else if (t <= (-7.5d-43)) then
        tmp = x - (y * (z / t))
    else if (t <= 4.4d-35) then
        tmp = x + (y / (a / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.42e+137) {
		tmp = x + y;
	} else if (t <= -7.5e-43) {
		tmp = x - (y * (z / t));
	} else if (t <= 4.4e-35) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.42e+137:
		tmp = x + y
	elif t <= -7.5e-43:
		tmp = x - (y * (z / t))
	elif t <= 4.4e-35:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.42e+137)
		tmp = Float64(x + y);
	elseif (t <= -7.5e-43)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 4.4e-35)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.42e+137)
		tmp = x + y;
	elseif (t <= -7.5e-43)
		tmp = x - (y * (z / t));
	elseif (t <= 4.4e-35)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.42e+137], N[(x + y), $MachinePrecision], If[LessEqual[t, -7.5e-43], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-35], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.42e137 or 4.39999999999999987e-35 < t

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l/ 74.7%

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

      4. sub-neg 74.7%

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

      5. +-commutative 74.7%

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

      6. neg-sub0 74.7%

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

      7. associate-+l- 74.7%

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

      8. sub0-neg 74.7%

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

      9. neg-mul-1 74.7%

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

      10. times-frac 94.7%

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

      11. fma-def 94.7%

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

      12. sub-neg 94.7%

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

      13. +-commutative 94.7%

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

      14. neg-sub0 94.7%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 94.7%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 94.7%

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

      17. neg-mul-1 94.7%

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

      18. *-commutative 94.7%

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

      19. associate-/l* 94.7%

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

      20. metadata-eval 94.7%

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

      21. /-rgt-identity 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 84.4%

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

   if -1.42e137 < t < -7.50000000000000068e-43

   1. Initial program 99.8%

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

      1. associate-*r/ 93.1%

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

      2. *-commutative 93.1%

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

      3. associate-/l* 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around inf 81.5%

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

   5. Taylor expanded in a around 0 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. associate-*r/ 78.5%

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

      4. unsub-neg 78.5%

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

   7. Simplified 78.5%

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

   if -7.50000000000000068e-43 < t < 4.39999999999999987e-35

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. *-commutative 92.9%

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

      3. associate-*l/ 95.6%

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

      4. sub-neg 95.6%

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

      5. +-commutative 95.6%

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

      6. neg-sub0 95.6%

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

      7. associate-+l- 95.6%

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

      8. sub0-neg 95.6%

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

      9. neg-mul-1 95.6%

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

      10. times-frac 96.9%

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

      11. fma-def 96.9%

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

      12. sub-neg 96.9%

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

      13. +-commutative 96.9%

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

      14. neg-sub0 96.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 96.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 96.9%

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

      17. neg-mul-1 96.9%

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

      18. *-commutative 96.9%

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

      19. associate-/l* 96.9%

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

      20. metadata-eval 96.9%

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

      21. /-rgt-identity 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 74.9%

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

      1. associate-/l* 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+137}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-43}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-35}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 78.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-28} \lor \neg \left(x \leq 1.6 \cdot 10^{-99}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.45e-28) (not (<= x 1.6e-99)))
   (+ x (* y (/ z (- a t))))
   (* (- t z) (/ y (- t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e-28) || !(x <= 1.6e-99)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = (t - z) * (y / (t - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.45d-28)) .or. (.not. (x <= 1.6d-99))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = (t - z) * (y / (t - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e-28) || !(x <= 1.6e-99)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = (t - z) * (y / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.45e-28) or not (x <= 1.6e-99):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = (t - z) * (y / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.45e-28) || !(x <= 1.6e-99))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(Float64(t - z) * Float64(y / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.45e-28) || ~((x <= 1.6e-99)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = (t - z) * (y / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.45e-28], N[Not[LessEqual[x, 1.6e-99]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45000000000000006e-28 or 1.6e-99 < x

   1. Initial program 97.0%

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

   2. Taylor expanded in z around inf 87.5%

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

   if -1.45000000000000006e-28 < x < 1.6e-99

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-*l/ 75.1%

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

      4. sub-neg 75.1%

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

      5. +-commutative 75.1%

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

      6. neg-sub0 75.1%

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

      7. associate-+l- 75.1%

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

      8. sub0-neg 75.1%

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

      9. neg-mul-1 75.1%

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

      10. times-frac 92.5%

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

      11. fma-def 92.5%

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

      12. sub-neg 92.5%

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

      13. +-commutative 92.5%

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

      14. neg-sub0 92.5%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 92.5%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 92.5%

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

      17. neg-mul-1 92.5%

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

      18. *-commutative 92.5%

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

      19. associate-/l* 92.5%

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

      20. metadata-eval 92.5%

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

      21. /-rgt-identity 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around -inf 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-*r/ 81.1%

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

   6. Simplified 81.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-28} \lor \neg \left(x \leq 1.6 \cdot 10^{-99}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \end{array} \]

Alternative 6: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+20} \lor \neg \left(z \leq 7.6 \cdot 10^{-56}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.42e+20) (not (<= z 7.6e-56)))
   (+ x (* y (/ z (- a t))))
   (+ x (/ y (/ (- t a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.42e+20) || !(z <= 7.6e-56)) {
		tmp = x + (y * (z / (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 <= (-1.42d+20)) .or. (.not. (z <= 7.6d-56))) then
        tmp = x + (y * (z / (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 <= -1.42e+20) || !(z <= 7.6e-56)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (y / ((t - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.42e+20) or not (z <= 7.6e-56):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (y / ((t - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.42e+20) || !(z <= 7.6e-56))
		tmp = Float64(x + Float64(y * Float64(z / 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 <= -1.42e+20) || ~((z <= 7.6e-56)))
		tmp = x + (y * (z / (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, -1.42e+20], N[Not[LessEqual[z, 7.6e-56]], $MachinePrecision]], N[(x + N[(y * N[(z / 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 < -1.42e20 or 7.6000000000000004e-56 < z

   1. Initial program 95.0%

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

   2. Taylor expanded in z around inf 85.2%

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

   if -1.42e20 < z < 7.6000000000000004e-56

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l/ 85.5%

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

      4. sub-neg 85.5%

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

      5. +-commutative 85.5%

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

      6. neg-sub0 85.5%

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

      7. associate-+l- 85.5%

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

      8. sub0-neg 85.5%

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

      9. neg-mul-1 85.5%

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

      10. times-frac 94.7%

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

      11. fma-def 94.6%

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

      12. sub-neg 94.6%

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

      13. +-commutative 94.6%

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

      14. neg-sub0 94.6%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 94.6%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 94.6%

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

      17. neg-mul-1 94.6%

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

      18. *-commutative 94.6%

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

      19. associate-/l* 94.6%

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

      20. metadata-eval 94.6%

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

      21. /-rgt-identity 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 92.3%

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

   6. Simplified 92.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+20} \lor \neg \left(z \leq 7.6 \cdot 10^{-56}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t - a}{t}}\\ \end{array} \]

Alternative 7: 77.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-35}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e+39) (+ x y) (if (<= t 3.1e-35) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+39) {
		tmp = x + y;
	} else if (t <= 3.1e-35) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.5d+39)) then
        tmp = x + y
    else if (t <= 3.1d-35) then
        tmp = x + (y * (z / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+39) {
		tmp = x + y;
	} else if (t <= 3.1e-35) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e+39:
		tmp = x + y
	elif t <= 3.1e-35:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e+39)
		tmp = Float64(x + y);
	elseif (t <= 3.1e-35)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e+39)
		tmp = x + y;
	elseif (t <= 3.1e-35)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e+39], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.1e-35], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.50000000000000011e39 or 3.10000000000000012e-35 < t

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l/ 77.1%

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

      4. sub-neg 77.1%

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

      5. +-commutative 77.1%

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

      6. neg-sub0 77.1%

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

      7. associate-+l- 77.1%

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

      8. sub0-neg 77.1%

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

      9. neg-mul-1 77.1%

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

      10. times-frac 95.4%

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

      11. fma-def 95.4%

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

      12. sub-neg 95.4%

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

      13. +-commutative 95.4%

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

      14. neg-sub0 95.4%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 95.4%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 95.4%

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

      17. neg-mul-1 95.4%

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

      18. *-commutative 95.4%

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

      19. associate-/l* 95.4%

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

      20. metadata-eval 95.4%

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

      21. /-rgt-identity 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in t around inf 80.1%

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

   if -9.50000000000000011e39 < t < 3.10000000000000012e-35

   1. Initial program 94.1%

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

   2. Taylor expanded in t around 0 74.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+39}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-35}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 77.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+40)
   (+ x y)
   (if (<= t 1.75e-34) (+ x (/ y (/ a z))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+40) {
		tmp = x + y;
	} else if (t <= 1.75e-34) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d+40)) then
        tmp = x + y
    else if (t <= 1.75d-34) then
        tmp = x + (y / (a / z))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+40) {
		tmp = x + y;
	} else if (t <= 1.75e-34) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+40:
		tmp = x + y
	elif t <= 1.75e-34:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+40)
		tmp = Float64(x + y);
	elseif (t <= 1.75e-34)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e+40)
		tmp = x + y;
	elseif (t <= 1.75e-34)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+40], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.75e-34], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.14999999999999997e40 or 1.75e-34 < t

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l/ 77.1%

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

      4. sub-neg 77.1%

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

      5. +-commutative 77.1%

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

      6. neg-sub0 77.1%

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

      7. associate-+l- 77.1%

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

      8. sub0-neg 77.1%

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

      9. neg-mul-1 77.1%

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

      10. times-frac 95.4%

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

      11. fma-def 95.4%

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

      12. sub-neg 95.4%

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

      13. +-commutative 95.4%

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

      14. neg-sub0 95.4%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 95.4%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 95.4%

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

      17. neg-mul-1 95.4%

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

      18. *-commutative 95.4%

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

      19. associate-/l* 95.4%

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

      20. metadata-eval 95.4%

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

      21. /-rgt-identity 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in t around inf 80.1%

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

   if -1.14999999999999997e40 < t < 1.75e-34

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. *-commutative 94.1%

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

      3. associate-*l/ 95.5%

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

      4. sub-neg 95.5%

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

      5. +-commutative 95.5%

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

      6. neg-sub0 95.5%

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

      7. associate-+l- 95.5%

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

      8. sub0-neg 95.5%

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

      9. neg-mul-1 95.5%

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

      10. times-frac 97.4%

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

      11. fma-def 97.4%

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

      12. sub-neg 97.4%

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

      13. +-commutative 97.4%

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

      14. neg-sub0 97.4%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 97.4%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 97.4%

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

      17. neg-mul-1 97.4%

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

      18. *-commutative 97.4%

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

      19. associate-/l* 97.4%

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

      20. metadata-eval 97.4%

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

      21. /-rgt-identity 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. associate-/l* 74.9%

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

   6. Simplified 74.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 62.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{+281} \lor \neg \left(z \leq 2.5 \cdot 10^{+218}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.38e+281) (not (<= z 2.5e+218))) (* z (/ y a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.38e+281) || !(z <= 2.5e+218)) {
		tmp = z * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.38d+281)) .or. (.not. (z <= 2.5d+218))) then
        tmp = z * (y / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.38e+281) || !(z <= 2.5e+218)) {
		tmp = z * (y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.38e+281) or not (z <= 2.5e+218):
		tmp = z * (y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.38e+281) || !(z <= 2.5e+218))
		tmp = Float64(z * Float64(y / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.38e+281) || ~((z <= 2.5e+218)))
		tmp = z * (y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.38e+281], N[Not[LessEqual[z, 2.5e+218]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.38000000000000008e281 or 2.49999999999999991e218 < z

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. *-commutative 96.7%

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

      3. associate-*l/ 77.4%

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

      4. sub-neg 77.4%

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

      5. +-commutative 77.4%

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

      6. neg-sub0 77.4%

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

      7. associate-+l- 77.4%

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

      8. sub0-neg 77.4%

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

      9. neg-mul-1 77.4%

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

      10. times-frac 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. neg-sub0 99.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 99.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 99.9%

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

      17. neg-mul-1 99.9%

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

      18. *-commutative 99.9%

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

      19. associate-/l* 99.9%

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

      20. metadata-eval 99.9%

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

      21. /-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 67.2%

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

   5. Taylor expanded in y around inf 50.5%

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

      1. associate-*l/ 61.6%

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

      2. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   if -1.38000000000000008e281 < z < 2.49999999999999991e218

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. *-commutative 97.4%

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

      3. associate-*l/ 86.5%

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

      4. sub-neg 86.5%

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

      5. +-commutative 86.5%

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

      6. neg-sub0 86.5%

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

      7. associate-+l- 86.5%

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

      8. sub0-neg 86.5%

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

      9. neg-mul-1 86.5%

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

      10. times-frac 95.9%

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

      11. fma-def 95.9%

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

      12. sub-neg 95.9%

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

      13. +-commutative 95.9%

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

      14. neg-sub0 95.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 95.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 95.9%

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

      17. neg-mul-1 95.9%

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

      18. *-commutative 95.9%

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

      19. associate-/l* 95.9%

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

      20. metadata-eval 95.9%

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

      21. /-rgt-identity 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around inf 68.0%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{+281} \lor \neg \left(z \leq 2.5 \cdot 10^{+218}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 61.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.7 \cdot 10^{+218}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 2.7e+218) (+ x y) (* y (/ z a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 2.7e+218) {
		tmp = x + y;
	} else {
		tmp = 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 (z <= 2.7d+218) then
        tmp = x + y
    else
        tmp = 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 (z <= 2.7e+218) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 2.7e+218:
		tmp = x + y
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 2.7e+218)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 2.7e+218)
		tmp = x + y;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 2.7e+218], N[(x + y), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.70000000000000013e218

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l/ 85.7%

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

      4. sub-neg 85.7%

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

      5. +-commutative 85.7%

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

      6. neg-sub0 85.7%

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

      7. associate-+l- 85.7%

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

      8. sub0-neg 85.7%

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

      9. neg-mul-1 85.7%

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

      10. times-frac 96.0%

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

      11. fma-def 96.0%

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

      12. sub-neg 96.0%

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

      13. +-commutative 96.0%

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

      14. neg-sub0 96.0%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 96.0%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 96.0%

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

      17. neg-mul-1 96.0%

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

      18. *-commutative 96.0%

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

      19. associate-/l* 96.0%

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

      20. metadata-eval 96.0%

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

      21. /-rgt-identity 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in t around inf 66.5%

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

   if 2.70000000000000013e218 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l/ 83.0%

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

      4. sub-neg 83.0%

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

      5. +-commutative 83.0%

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

      6. neg-sub0 83.0%

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

      7. associate-+l- 83.0%

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

      8. sub0-neg 83.0%

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

      9. neg-mul-1 83.0%

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

      10. times-frac 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. neg-sub0 99.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 99.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 99.9%

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

      17. neg-mul-1 99.9%

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

      18. *-commutative 99.9%

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

      19. associate-/l* 99.9%

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

      20. metadata-eval 99.9%

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

      21. /-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 69.5%

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

   5. Taylor expanded in y around inf 51.8%

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

      1. associate-*r/ 53.6%

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

   7. Simplified 53.6%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.7 \cdot 10^{+218}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 11: 53.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.6e-76) x (if (<= x 2.9e-98) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.6e-76) {
		tmp = x;
	} else if (x <= 2.9e-98) {
		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 <= (-7.6d-76)) then
        tmp = x
    else if (x <= 2.9d-98) 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 <= -7.6e-76) {
		tmp = x;
	} else if (x <= 2.9e-98) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.6e-76:
		tmp = x
	elif x <= 2.9e-98:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.6e-76)
		tmp = x;
	elseif (x <= 2.9e-98)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.6e-76)
		tmp = x;
	elseif (x <= 2.9e-98)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.6e-76], x, If[LessEqual[x, 2.9e-98], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000004e-76 or 2.9e-98 < x

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l/ 89.5%

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

      4. sub-neg 89.5%

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

      5. +-commutative 89.5%

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

      6. neg-sub0 89.5%

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

      7. associate-+l- 89.5%

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

      8. sub0-neg 89.5%

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

      9. neg-mul-1 89.5%

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

      10. times-frac 98.6%

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

      11. fma-def 98.5%

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

      12. sub-neg 98.5%

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

      13. +-commutative 98.5%

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

      14. neg-sub0 98.5%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 98.5%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 98.5%

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

      17. neg-mul-1 98.5%

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

      18. *-commutative 98.5%

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

      19. associate-/l* 98.5%

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

      20. metadata-eval 98.5%

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

      21. /-rgt-identity 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 65.5%

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

   if -7.6000000000000004e-76 < x < 2.9e-98

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. *-commutative 97.7%

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

      3. associate-*l/ 77.4%

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

      4. sub-neg 77.4%

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

      5. +-commutative 77.4%

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

      6. neg-sub0 77.4%

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

      7. associate-+l- 77.4%

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

      8. sub0-neg 77.4%

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

      9. neg-mul-1 77.4%

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

      10. times-frac 91.9%

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

      11. fma-def 91.9%

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

      12. sub-neg 91.9%

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

      13. +-commutative 91.9%

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

      14. neg-sub0 91.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 91.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 91.9%

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

      17. neg-mul-1 91.9%

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

      18. *-commutative 91.9%

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

      19. associate-/l* 91.9%

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

      20. metadata-eval 91.9%

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

      21. /-rgt-identity 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around -inf 65.4%

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

      1. *-commutative 65.4%

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

      2. associate-*r/ 80.0%

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

   6. Simplified 80.0%

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

   7. Taylor expanded in z around 0 34.0%

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

      1. associate-*l/ 43.5%

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

      2. *-commutative 43.5%

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

   9. Simplified 43.5%

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

   10. Taylor expanded in t around inf 44.2%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 61.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. +-commutative 97.3%

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

   2. *-commutative 97.3%

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

   3. associate-*l/ 85.5%

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

   4. sub-neg 85.5%

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

   5. +-commutative 85.5%

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

   6. neg-sub0 85.5%

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

   7. associate-+l- 85.5%

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

   8. sub0-neg 85.5%

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

   9. neg-mul-1 85.5%

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

   10. times-frac 96.3%

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

   11. fma-def 96.3%

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

   12. sub-neg 96.3%

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

   13. +-commutative 96.3%

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

   14. neg-sub0 96.3%

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

   15. associate-+l- 96.3%

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

   16. sub0-neg 96.3%

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

   17. neg-mul-1 96.3%

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

   18. *-commutative 96.3%

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

   19. associate-/l* 96.3%

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

   20. metadata-eval 96.3%

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

   21. /-rgt-identity 96.3%

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

3. Simplified 96.3%

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

4. Taylor expanded in t around inf 63.0%

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

5. Final simplification 63.0%

   \[\leadsto x + y \]

Alternative 13: 51.9% 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 97.3%

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

   1. +-commutative 97.3%

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

   2. *-commutative 97.3%

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

   3. associate-*l/ 85.5%

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

   4. sub-neg 85.5%

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

   5. +-commutative 85.5%

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

   6. neg-sub0 85.5%

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

   7. associate-+l- 85.5%

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

   8. sub0-neg 85.5%

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

   9. neg-mul-1 85.5%

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

   10. times-frac 96.3%

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

   11. fma-def 96.3%

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

   12. sub-neg 96.3%

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

   13. +-commutative 96.3%

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

   14. neg-sub0 96.3%

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

   15. associate-+l- 96.3%

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

   16. sub0-neg 96.3%

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

   17. neg-mul-1 96.3%

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

   18. *-commutative 96.3%

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

   19. associate-/l* 96.3%

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

   20. metadata-eval 96.3%

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

   21. /-rgt-identity 96.3%

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

3. Simplified 96.3%

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

4. Taylor expanded in y around 0 48.5%

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

5. Final simplification 48.5%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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