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

Percentage Accurate: 98.3% → 98.3%

Time: 8.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% 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: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

2. Final simplification 98.8%

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

Alternative 2: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= t -6.8e+57)
     (+ x y)
     (if (<= t -5.2e-298)
       x
       (if (<= t 1.28e-182)
         t_1
         (if (<= t 6.5e-131) x (if (<= t 5.5e-120) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (t <= -6.8e+57) {
		tmp = x + y;
	} else if (t <= -5.2e-298) {
		tmp = x;
	} else if (t <= 1.28e-182) {
		tmp = t_1;
	} else if (t <= 6.5e-131) {
		tmp = x;
	} else if (t <= 5.5e-120) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (a - t))
    if (t <= (-6.8d+57)) then
        tmp = x + y
    else if (t <= (-5.2d-298)) then
        tmp = x
    else if (t <= 1.28d-182) then
        tmp = t_1
    else if (t <= 6.5d-131) then
        tmp = x
    else if (t <= 5.5d-120) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (t <= -6.8e+57) {
		tmp = x + y;
	} else if (t <= -5.2e-298) {
		tmp = x;
	} else if (t <= 1.28e-182) {
		tmp = t_1;
	} else if (t <= 6.5e-131) {
		tmp = x;
	} else if (t <= 5.5e-120) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if t <= -6.8e+57:
		tmp = x + y
	elif t <= -5.2e-298:
		tmp = x
	elif t <= 1.28e-182:
		tmp = t_1
	elif t <= 6.5e-131:
		tmp = x
	elif t <= 5.5e-120:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t <= -6.8e+57)
		tmp = Float64(x + y);
	elseif (t <= -5.2e-298)
		tmp = x;
	elseif (t <= 1.28e-182)
		tmp = t_1;
	elseif (t <= 6.5e-131)
		tmp = x;
	elseif (t <= 5.5e-120)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (t <= -6.8e+57)
		tmp = x + y;
	elseif (t <= -5.2e-298)
		tmp = x;
	elseif (t <= 1.28e-182)
		tmp = t_1;
	elseif (t <= 6.5e-131)
		tmp = x;
	elseif (t <= 5.5e-120)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+57], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.2e-298], x, If[LessEqual[t, 1.28e-182], t$95$1, If[LessEqual[t, 6.5e-131], x, If[LessEqual[t, 5.5e-120], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.79999999999999984e57 or 5.5000000000000001e-120 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 70.1%

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

   if -6.79999999999999984e57 < t < -5.1999999999999998e-298 or 1.2800000000000001e-182 < t < 6.5000000000000002e-131

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf 64.2%

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

   if -5.1999999999999998e-298 < t < 1.2800000000000001e-182 or 6.5000000000000002e-131 < t < 5.5000000000000001e-120

   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/ 89.0%

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

      4. sub-neg 89.0%

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

      5. +-commutative 89.0%

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

      6. neg-sub0 89.0%

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

      7. associate-+l- 89.0%

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

      8. sub0-neg 89.0%

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

      9. neg-mul-1 89.0%

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

      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 z around inf 63.0%

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

      1. associate-*r/ 63.0%

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

      2. associate-*r* 63.0%

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

      3. neg-mul-1 63.0%

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

   6. Simplified 63.0%

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

      1. frac-2neg 63.0%

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

      2. div-inv 62.9%

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

      3. distribute-lft-neg-out 62.9%

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

      4. remove-double-neg 62.9%

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

   8. Applied egg-rr 62.9%

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

      1. associate-*l* 71.1%

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

      2. associate-*r/ 71.2%

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

      3. *-rgt-identity 71.2%

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

      4. neg-sub0 71.2%

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

      5. associate--r- 71.2%

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

      6. neg-sub0 71.2%

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

      7. +-commutative 71.2%

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

      8. sub-neg 71.2%

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

   10. Simplified 71.2%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-59}:\\ \;\;\;\;x + z \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+105}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.7e+94)
   (+ x y)
   (if (<= t -7e-59)
     (+ x (* z (/ y (- t))))
     (if (<= t 1.55e+105) (+ x (* y (/ (- z t) a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.7e+94) {
		tmp = x + y;
	} else if (t <= -7e-59) {
		tmp = x + (z * (y / -t));
	} else if (t <= 1.55e+105) {
		tmp = x + (y * ((z - 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 <= (-3.7d+94)) then
        tmp = x + y
    else if (t <= (-7d-59)) then
        tmp = x + (z * (y / -t))
    else if (t <= 1.55d+105) then
        tmp = x + (y * ((z - 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 <= -3.7e+94) {
		tmp = x + y;
	} else if (t <= -7e-59) {
		tmp = x + (z * (y / -t));
	} else if (t <= 1.55e+105) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.7e+94:
		tmp = x + y
	elif t <= -7e-59:
		tmp = x + (z * (y / -t))
	elif t <= 1.55e+105:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.7e+94)
		tmp = Float64(x + y);
	elseif (t <= -7e-59)
		tmp = Float64(x + Float64(z * Float64(y / Float64(-t))));
	elseif (t <= 1.55e+105)
		tmp = Float64(x + Float64(y * Float64(Float64(z - 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 <= -3.7e+94)
		tmp = x + y;
	elseif (t <= -7e-59)
		tmp = x + (z * (y / -t));
	elseif (t <= 1.55e+105)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.7e+94], N[(x + y), $MachinePrecision], If[LessEqual[t, -7e-59], N[(x + N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+105], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000001e94 or 1.55000000000000002e105 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 77.2%

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

   if -3.7000000000000001e94 < t < -7.0000000000000002e-59

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. *-commutative 97.2%

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

      3. associate-*l/ 94.5%

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

      4. sub-neg 94.5%

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

      5. +-commutative 94.5%

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

      6. neg-sub0 94.5%

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

      7. associate-+l- 94.5%

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

      8. sub0-neg 94.5%

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

      9. neg-mul-1 94.5%

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

      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 a around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in t around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. mul-1-neg 77.8%

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

      3. distribute-rgt-neg-in 77.8%

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

      4. associate-*l/ 77.9%

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

      5. *-commutative 77.9%

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

      6. distribute-lft-neg-out 77.9%

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

      7. distribute-rgt-neg-in 77.9%

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

      8. mul-1-neg 77.9%

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

      9. metadata-eval 77.9%

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

      10. times-frac 77.9%

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

      11. *-lft-identity 77.9%

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

      12. neg-mul-1 77.9%

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

   9. Simplified 77.9%

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

   if -7.0000000000000002e-59 < t < 1.55000000000000002e105

   1. Initial program 98.6%

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

   2. Taylor expanded in a around inf 85.9%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+94}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-59}:\\ \;\;\;\;x + z \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+105}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-59}:\\ \;\;\;\;x + z \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+105}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e+100)
   (+ x y)
   (if (<= t -7e-59)
     (+ x (* z (/ y (- t))))
     (if (<= t 2.2e+105) (+ x (* z (/ y a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e+100) {
		tmp = x + y;
	} else if (t <= -7e-59) {
		tmp = x + (z * (y / -t));
	} else if (t <= 2.2e+105) {
		tmp = x + (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 (t <= (-2.8d+100)) then
        tmp = x + y
    else if (t <= (-7d-59)) then
        tmp = x + (z * (y / -t))
    else if (t <= 2.2d+105) then
        tmp = x + (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 (t <= -2.8e+100) {
		tmp = x + y;
	} else if (t <= -7e-59) {
		tmp = x + (z * (y / -t));
	} else if (t <= 2.2e+105) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e+100:
		tmp = x + y
	elif t <= -7e-59:
		tmp = x + (z * (y / -t))
	elif t <= 2.2e+105:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e+100)
		tmp = Float64(x + y);
	elseif (t <= -7e-59)
		tmp = Float64(x + Float64(z * Float64(y / Float64(-t))));
	elseif (t <= 2.2e+105)
		tmp = Float64(x + 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 (t <= -2.8e+100)
		tmp = x + y;
	elseif (t <= -7e-59)
		tmp = x + (z * (y / -t));
	elseif (t <= 2.2e+105)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e+100], N[(x + y), $MachinePrecision], If[LessEqual[t, -7e-59], N[(x + N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+105], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7999999999999998e100 or 2.20000000000000007e105 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 77.2%

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

   if -2.7999999999999998e100 < t < -7.0000000000000002e-59

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. *-commutative 97.2%

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

      3. associate-*l/ 94.5%

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

      4. sub-neg 94.5%

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

      5. +-commutative 94.5%

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

      6. neg-sub0 94.5%

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

      7. associate-+l- 94.5%

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

      8. sub0-neg 94.5%

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

      9. neg-mul-1 94.5%

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

      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 a around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in t around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. mul-1-neg 77.8%

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

      3. distribute-rgt-neg-in 77.8%

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

      4. associate-*l/ 77.9%

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

      5. *-commutative 77.9%

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

      6. distribute-lft-neg-out 77.9%

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

      7. distribute-rgt-neg-in 77.9%

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

      8. mul-1-neg 77.9%

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

      9. metadata-eval 77.9%

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

      10. times-frac 77.9%

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

      11. *-lft-identity 77.9%

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

      12. neg-mul-1 77.9%

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

   9. Simplified 77.9%

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

   if -7.0000000000000002e-59 < t < 2.20000000000000007e105

   1. Initial program 98.6%

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

   2. Taylor expanded in t around 0 83.2%

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

      1. associate-/l* 85.1%

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

   4. Simplified 85.1%

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

      1. associate-/r/ 85.4%

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

   6. Applied egg-rr 85.4%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-59}:\\ \;\;\;\;x + z \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+105}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+35} \lor \neg \left(a \leq 170000000000\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.6e+35) (not (<= a 170000000000.0)))
   (+ x (* y (/ (- z t) a)))
   (+ x (/ y (/ t (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e+35) || !(a <= 170000000000.0)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + (y / (t / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.6d+35)) .or. (.not. (a <= 170000000000.0d0))) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = x + (y / (t / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e+35) || !(a <= 170000000000.0)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + (y / (t / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.6e+35) or not (a <= 170000000000.0):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + (y / (t / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.6e+35) || !(a <= 170000000000.0))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + Float64(y / Float64(t / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.6e+35) || ~((a <= 170000000000.0)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + (y / (t / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.6e+35], N[Not[LessEqual[a, 170000000000.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.60000000000000007e35 or 1.7e11 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 90.5%

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

   if -2.60000000000000007e35 < a < 1.7e11

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-*l/ 91.1%

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

      4. sub-neg 91.1%

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

      5. +-commutative 91.1%

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

      6. neg-sub0 91.1%

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

      7. associate-+l- 91.1%

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

      8. sub0-neg 91.1%

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

      9. neg-mul-1 91.1%

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

      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 a around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-/l* 81.4%

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

   6. Simplified 81.4%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+35} \lor \neg \left(a \leq 170000000000\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \end{array} \]

Alternative 6: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-65} \lor \neg \left(t \leq 7.8 \cdot 10^{+28}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.1e-65) (not (<= t 7.8e+28)))
   (- x (* t (/ y (- a t))))
   (+ x (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e-65) || !(t <= 7.8e+28)) {
		tmp = x - (t * (y / (a - t)));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.1d-65)) .or. (.not. (t <= 7.8d+28))) then
        tmp = x - (t * (y / (a - t)))
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e-65) || !(t <= 7.8e+28)) {
		tmp = x - (t * (y / (a - t)));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.1e-65) or not (t <= 7.8e+28):
		tmp = x - (t * (y / (a - t)))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.1e-65) || !(t <= 7.8e+28))
		tmp = Float64(x - Float64(t * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.1e-65) || ~((t <= 7.8e+28)))
		tmp = x - (t * (y / (a - t)));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.1e-65], N[Not[LessEqual[t, 7.8e+28]], $MachinePrecision]], N[(x - N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.10000000000000016e-65 or 7.7999999999999997e28 < t

   1. Initial program 99.2%

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

      1. associate-*r/ 81.7%

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

   3. Simplified 81.7%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in z around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. mul-1-neg 72.4%

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

      3. unsub-neg 72.4%

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

      4. associate-/l* 86.8%

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

      5. remove-double-neg 86.8%

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

      6. distribute-frac-neg 86.8%

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

      7. distribute-neg-frac 86.8%

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

      8. associate-/l* 72.4%

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

      9. distribute-neg-frac 72.4%

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

      10. *-commutative 72.4%

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

      11. distribute-lft-neg-out 72.4%

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

      12. associate-*r/ 85.2%

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

      13. distribute-lft-neg-out 85.2%

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

      14. distribute-rgt-neg-in 85.2%

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

      15. distribute-frac-neg 85.2%

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

      16. distribute-rgt-neg-out 85.2%

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

      17. distribute-frac-neg 85.2%

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

      18. remove-double-neg 85.2%

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

   8. Simplified 85.2%

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

   if -3.10000000000000016e-65 < t < 7.7999999999999997e28

   1. Initial program 98.4%

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

   2. Taylor expanded in a around inf 88.1%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-65} \lor \neg \left(t \leq 7.8 \cdot 10^{+28}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 7: 82.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-59} \lor \neg \left(t \leq 10^{+29}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.7e-59) (not (<= t 1e+29)))
   (- x (/ y (+ (/ a t) -1.0)))
   (+ x (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.7e-59) || !(t <= 1e+29)) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.7d-59)) .or. (.not. (t <= 1d+29))) then
        tmp = x - (y / ((a / t) + (-1.0d0)))
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.7e-59) || !(t <= 1e+29)) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.7e-59) or not (t <= 1e+29):
		tmp = x - (y / ((a / t) + -1.0))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.7e-59) || !(t <= 1e+29))
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.7e-59) || ~((t <= 1e+29)))
		tmp = x - (y / ((a / t) + -1.0));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.7e-59], N[Not[LessEqual[t, 1e+29]], $MachinePrecision]], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6999999999999999e-59 or 9.99999999999999914e28 < t

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. mul-1-neg 72.4%

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

      3. unsub-neg 72.4%

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

      4. associate-/l* 86.8%

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

      5. div-sub 86.8%

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

      6. *-inverses 86.8%

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

   4. Simplified 86.8%

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

   if -3.6999999999999999e-59 < t < 9.99999999999999914e28

   1. Initial program 98.4%

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

   2. Taylor expanded in a around inf 88.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-59} \lor \neg \left(t \leq 10^{+29}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 8: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+104}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+57) (+ x y) (if (<= t 8e+104) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+57) {
		tmp = x + y;
	} else if (t <= 8e+104) {
		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 <= (-7d+57)) then
        tmp = x + y
    else if (t <= 8d+104) 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 <= -7e+57) {
		tmp = x + y;
	} else if (t <= 8e+104) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+57:
		tmp = x + y
	elif t <= 8e+104:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+57)
		tmp = Float64(x + y);
	elseif (t <= 8e+104)
		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 <= -7e+57)
		tmp = x + y;
	elseif (t <= 8e+104)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+57], N[(x + y), $MachinePrecision], If[LessEqual[t, 8e+104], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.9999999999999995e57 or 8e104 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 75.5%

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

   if -6.9999999999999995e57 < t < 8e104

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 81.5%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+104}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+106}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.3e+59) (+ x y) (if (<= t 1.1e+106) (+ x (* z (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.3e+59) {
		tmp = x + y;
	} else if (t <= 1.1e+106) {
		tmp = x + (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 (t <= (-6.3d+59)) then
        tmp = x + y
    else if (t <= 1.1d+106) then
        tmp = x + (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 (t <= -6.3e+59) {
		tmp = x + y;
	} else if (t <= 1.1e+106) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.3e+59:
		tmp = x + y
	elif t <= 1.1e+106:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.3e+59)
		tmp = Float64(x + y);
	elseif (t <= 1.1e+106)
		tmp = Float64(x + 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 (t <= -6.3e+59)
		tmp = x + y;
	elseif (t <= 1.1e+106)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.3e+59], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.1e+106], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.3e59 or 1.09999999999999996e106 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 75.5%

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

   if -6.3e59 < t < 1.09999999999999996e106

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 79.9%

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

      1. associate-/l* 81.5%

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

   4. Simplified 81.5%

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

      1. associate-/r/ 82.2%

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

   6. Applied egg-rr 82.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+59}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+106}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 63.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+58) (+ x y) (if (<= t 1.2e-72) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+58) {
		tmp = x + y;
	} else if (t <= 1.2e-72) {
		tmp = x;
	} 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 <= (-2.6d+58)) then
        tmp = x + y
    else if (t <= 1.2d-72) then
        tmp = x
    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 <= -2.6e+58) {
		tmp = x + y;
	} else if (t <= 1.2e-72) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e+58:
		tmp = x + y
	elif t <= 1.2e-72:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+58)
		tmp = Float64(x + y);
	elseif (t <= 1.2e-72)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e+58)
		tmp = x + y;
	elseif (t <= 1.2e-72)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+58], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.2e-72], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.59999999999999988e58 or 1.2e-72 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 71.9%

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

   if -2.59999999999999988e58 < t < 1.2e-72

   1. Initial program 97.8%

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

   2. Taylor expanded in x around inf 53.2%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+58}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 52.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+126}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y -9.5e+126) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.5e+126) {
		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 (y <= (-9.5d+126)) 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 (y <= -9.5e+126) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9.5e+126:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9.5e+126)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9.5e+126)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9.5e+126], y, x]

Derivation

1. Split input into 2 regimes

2. if y < -9.49999999999999951e126

   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/ 66.3%

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

      4. sub-neg 66.3%

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

      5. +-commutative 66.3%

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

      6. neg-sub0 66.3%

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

      7. associate-+l- 66.3%

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

      8. sub0-neg 66.3%

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

      9. neg-mul-1 66.3%

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

      10. times-frac 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. +-commutative 99.8%

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

      14. neg-sub0 99.8%

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

      15. associate-+l- 99.8%

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

      16. sub0-neg 99.8%

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

      17. neg-mul-1 99.8%

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

      18. *-commutative 99.8%

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

      19. associate-/l* 99.8%

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

      20. metadata-eval 99.8%

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

      21. /-rgt-identity 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 46.3%

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

      1. +-commutative 46.3%

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

      2. associate-/l* 58.6%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in y around inf 55.6%

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

   8. Taylor expanded in z around 0 22.7%

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

   if -9.49999999999999951e126 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 58.9%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+126}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 51.0% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

2. Taylor expanded in x around inf 52.4%

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

3. Final simplification 52.4%

   \[\leadsto x \]

Developer target: 99.4% 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 2023240 
(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)))))