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

Percentage Accurate: 98.3% → 98.6%

Time: 7.7s

Alternatives: 12

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: 98.3% 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: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+54}:\\ \;\;\;\;x + t_1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - z, \frac{y}{t - a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 5e+54) (+ x (* t_1 y)) (fma (- t z) (/ y (- t a)) x))))

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 <= 5e+54) {
		tmp = x + (t_1 * y);
	} else {
		tmp = fma((t - z), (y / (t - a)), x);
	}
	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 <= 5e+54)
		tmp = Float64(x + Float64(t_1 * y));
	else
		tmp = fma(Float64(t - z), Float64(y / Float64(t - a)), x);
	end
	return 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, 5e+54], N[(x + N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision], N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 5.00000000000000005e54

   1. Initial program 99.4%

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

   if 5.00000000000000005e54 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. *-commutative 83.7%

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

      3. associate-*l/ 96.7%

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

      4. sub-neg 96.7%

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

      5. +-commutative 96.7%

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

      6. neg-sub0 96.7%

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

      7. associate-+l- 96.7%

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

      8. sub0-neg 96.7%

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

      9. neg-mul-1 96.7%

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

      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%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 5 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - z, \frac{y}{t - a}, x\right)\\ \end{array} \]

Alternative 2: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-10}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-39}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) a)))))
   (if (<= t -2.15e+24)
     (+ x y)
     (if (<= t -9e-10)
       (* (- t z) (/ y (- t a)))
       (if (<= t 1e-80)
         t_1
         (if (<= t 6e-39)
           (- x (* z (/ y t)))
           (if (<= t 3.1e+103) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / a));
	double tmp;
	if (t <= -2.15e+24) {
		tmp = x + y;
	} else if (t <= -9e-10) {
		tmp = (t - z) * (y / (t - a));
	} else if (t <= 1e-80) {
		tmp = t_1;
	} else if (t <= 6e-39) {
		tmp = x - (z * (y / t));
	} else if (t <= 3.1e+103) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / a))
    if (t <= (-2.15d+24)) then
        tmp = x + y
    else if (t <= (-9d-10)) then
        tmp = (t - z) * (y / (t - a))
    else if (t <= 1d-80) then
        tmp = t_1
    else if (t <= 6d-39) then
        tmp = x - (z * (y / t))
    else if (t <= 3.1d+103) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / a));
	double tmp;
	if (t <= -2.15e+24) {
		tmp = x + y;
	} else if (t <= -9e-10) {
		tmp = (t - z) * (y / (t - a));
	} else if (t <= 1e-80) {
		tmp = t_1;
	} else if (t <= 6e-39) {
		tmp = x - (z * (y / t));
	} else if (t <= 3.1e+103) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / a))
	tmp = 0
	if t <= -2.15e+24:
		tmp = x + y
	elif t <= -9e-10:
		tmp = (t - z) * (y / (t - a))
	elif t <= 1e-80:
		tmp = t_1
	elif t <= 6e-39:
		tmp = x - (z * (y / t))
	elif t <= 3.1e+103:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (t <= -2.15e+24)
		tmp = Float64(x + y);
	elseif (t <= -9e-10)
		tmp = Float64(Float64(t - z) * Float64(y / Float64(t - a)));
	elseif (t <= 1e-80)
		tmp = t_1;
	elseif (t <= 6e-39)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= 3.1e+103)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / a));
	tmp = 0.0;
	if (t <= -2.15e+24)
		tmp = x + y;
	elseif (t <= -9e-10)
		tmp = (t - z) * (y / (t - a));
	elseif (t <= 1e-80)
		tmp = t_1;
	elseif (t <= 6e-39)
		tmp = x - (z * (y / t));
	elseif (t <= 3.1e+103)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e+24], N[(x + y), $MachinePrecision], If[LessEqual[t, -9e-10], N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-80], t$95$1, If[LessEqual[t, 6e-39], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+103], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.14999999999999994e24 or 3.1000000000000002e103 < t

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l/ 76.7%

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

      4. sub-neg 76.7%

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

      5. +-commutative 76.7%

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

      6. neg-sub0 76.7%

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

      7. associate-+l- 76.7%

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

      8. sub0-neg 76.7%

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

      9. neg-mul-1 76.7%

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

      10. times-frac 89.3%

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

      11. fma-def 89.3%

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

      12. sub-neg 89.3%

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

      13. +-commutative 89.3%

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

      14. neg-sub0 89.3%

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

      15. associate-+l- 89.3%

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

      16. sub0-neg 89.3%

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

      17. neg-mul-1 89.3%

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

      18. *-commutative 89.3%

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

      19. associate-/l* 89.3%

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

      20. metadata-eval 89.3%

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

      21. /-rgt-identity 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around inf 84.7%

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

   if -2.14999999999999994e24 < t < -8.9999999999999999e-10

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. *-commutative 99.3%

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

      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 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. neg-sub0 99.7%

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

      15. associate-+l- 99.7%

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

      16. sub0-neg 99.7%

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

      17. neg-mul-1 99.7%

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

      18. *-commutative 99.7%

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

      19. associate-/l* 99.7%

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

      20. metadata-eval 99.7%

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

      21. /-rgt-identity 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around -inf 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   if -8.9999999999999999e-10 < t < 9.99999999999999961e-81 or 6.00000000000000055e-39 < t < 3.1000000000000002e103

   1. Initial program 96.9%

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

   2. Taylor expanded in a around inf 84.1%

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

   if 9.99999999999999961e-81 < t < 6.00000000000000055e-39

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*l/ 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 100.0%

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

      11. fma-def 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. neg-sub0 100.0%

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

      15. associate-+l- 100.0%

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

      16. sub0-neg 100.0%

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

      17. neg-mul-1 100.0%

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

      18. *-commutative 100.0%

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

      19. associate-/l* 100.0%

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

      20. metadata-eval 100.0%

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

      21. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-/l* 61.9%

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

   6. Simplified 61.9%

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

   7. Taylor expanded in t around 0 90.0%

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

      1. associate-*r/ 90.0%

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

      2. mul-1-neg 90.0%

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

   9. Simplified 90.0%

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

       1. div-inv 90.0%

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

       2. distribute-lft-neg-in 90.0%

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

       3. associate-*l* 71.2%

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

       4. div-inv 71.3%

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

       5. neg-mul-1 71.3%

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

       6. associate-*l* 71.3%

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

       7. metadata-eval 71.3%

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

       8. add-sqr-sqrt 50.2%

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

       9. sqrt-unprod 50.9%

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

       10. sqr-neg 50.9%

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

       11. sqrt-unprod 10.1%

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

       12. add-sqr-sqrt 40.7%

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

       13. div-inv 40.7%

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

       14. associate-*l* 40.7%

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

       15. distribute-lft-neg-in 40.7%

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

       16. div-inv 40.7%

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

       17. cancel-sign-sub-inv 40.7%

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

       18. *-un-lft-identity 40.7%

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

       19. div-inv 40.7%

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

   11. Applied egg-rr 90.1%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-10}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 10^{-80}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-39}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+103}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+245}:\\ \;\;\;\;x + t_1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 2e+245) (+ x (* t_1 y)) (/ (* z (- y)) (- t a)))))

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 <= 2e+245) {
		tmp = x + (t_1 * y);
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= 2d+245) then
        tmp = x + (t_1 * y)
    else
        tmp = (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 t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= 2e+245) {
		tmp = x + (t_1 * y);
	} else {
		tmp = (z * -y) / (t - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= 2e+245:
		tmp = x + (t_1 * y)
	else:
		tmp = (z * -y) / (t - a)
	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 <= 2e+245)
		tmp = Float64(x + Float64(t_1 * y));
	else
		tmp = Float64(Float64(z * Float64(-y)) / Float64(t - a));
	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 <= 2e+245)
		tmp = x + (t_1 * y);
	else
		tmp = (z * -y) / (t - a);
	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, 2e+245], N[(x + N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision], N[(N[(z * (-y)), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000009e245

   1. Initial program 99.4%

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

   if 2.00000000000000009e245 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 41.7%

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

      1. +-commutative 41.7%

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

      2. *-commutative 41.7%

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

      3. associate-*l/ 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate-+l- 100.0%

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

      8. sub0-neg 100.0%

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

      9. neg-mul-1 100.0%

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

      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 z around inf 98.7%

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

      1. associate-*r/ 98.7%

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

      2. associate-*r* 98.7%

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

      3. neg-mul-1 98.7%

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

   6. Simplified 98.7%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{+245}:\\ \;\;\;\;x + \frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t - a}\\ \end{array} \]

Alternative 4: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+78}:\\ \;\;\;\;x + t_1 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 2e+78) (+ x (* t_1 y)) (+ x (/ (* (- z t) 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 <= 2e+78) {
		tmp = x + (t_1 * y);
	} else {
		tmp = x + (((z - t) * 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 <= 2d+78) then
        tmp = x + (t_1 * y)
    else
        tmp = x + (((z - t) * 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 <= 2e+78) {
		tmp = x + (t_1 * y);
	} else {
		tmp = x + (((z - t) * y) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= 2e+78:
		tmp = x + (t_1 * y)
	else:
		tmp = x + (((z - t) * 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 <= 2e+78)
		tmp = Float64(x + Float64(t_1 * y));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - t) * 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 <= 2e+78)
		tmp = x + (t_1 * y);
	else
		tmp = x + (((z - t) * 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, 2e+78], N[(x + N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000002e78

   1. Initial program 99.3%

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

   if 2.00000000000000002e78 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 81.3%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 2 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{z - t}{a - t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]

Alternative 5: 81.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a}\\ t_2 := x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-41}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) a)))) (t_2 (+ x (/ y (/ t (- t z))))))
   (if (<= t -3.6e-44)
     t_2
     (if (<= t 8.5e-81)
       t_1
       (if (<= t 2.05e-41)
         (- x (* z (/ y t)))
         (if (<= t 1.95e+100) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / a));
	double t_2 = x + (y / (t / (t - z)));
	double tmp;
	if (t <= -3.6e-44) {
		tmp = t_2;
	} else if (t <= 8.5e-81) {
		tmp = t_1;
	} else if (t <= 2.05e-41) {
		tmp = x - (z * (y / t));
	} else if (t <= 1.95e+100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / a))
    t_2 = x + (y / (t / (t - z)))
    if (t <= (-3.6d-44)) then
        tmp = t_2
    else if (t <= 8.5d-81) then
        tmp = t_1
    else if (t <= 2.05d-41) then
        tmp = x - (z * (y / t))
    else if (t <= 1.95d+100) then
        tmp = t_1
    else
        tmp = t_2
    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));
	double t_2 = x + (y / (t / (t - z)));
	double tmp;
	if (t <= -3.6e-44) {
		tmp = t_2;
	} else if (t <= 8.5e-81) {
		tmp = t_1;
	} else if (t <= 2.05e-41) {
		tmp = x - (z * (y / t));
	} else if (t <= 1.95e+100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / a))
	t_2 = x + (y / (t / (t - z)))
	tmp = 0
	if t <= -3.6e-44:
		tmp = t_2
	elif t <= 8.5e-81:
		tmp = t_1
	elif t <= 2.05e-41:
		tmp = x - (z * (y / t))
	elif t <= 1.95e+100:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / a)))
	t_2 = Float64(x + Float64(y / Float64(t / Float64(t - z))))
	tmp = 0.0
	if (t <= -3.6e-44)
		tmp = t_2;
	elseif (t <= 8.5e-81)
		tmp = t_1;
	elseif (t <= 2.05e-41)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= 1.95e+100)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / a));
	t_2 = x + (y / (t / (t - z)));
	tmp = 0.0;
	if (t <= -3.6e-44)
		tmp = t_2;
	elseif (t <= 8.5e-81)
		tmp = t_1;
	elseif (t <= 2.05e-41)
		tmp = x - (z * (y / t));
	elseif (t <= 1.95e+100)
		tmp = t_1;
	else
		tmp = t_2;
	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] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e-44], t$95$2, If[LessEqual[t, 8.5e-81], t$95$1, If[LessEqual[t, 2.05e-41], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+100], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5999999999999999e-44 or 1.95e100 < 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/ 79.5%

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

      4. sub-neg 79.5%

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

      5. +-commutative 79.5%

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

      6. neg-sub0 79.5%

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

      7. associate-+l- 79.5%

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

      8. sub0-neg 79.5%

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

      9. neg-mul-1 79.5%

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

      10. times-frac 90.1%

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

      11. fma-def 90.1%

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

      12. sub-neg 90.1%

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

      13. +-commutative 90.1%

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

      14. neg-sub0 90.1%

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

      15. associate-+l- 90.1%

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

      16. sub0-neg 90.1%

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

      17. neg-mul-1 90.1%

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

      18. *-commutative 90.1%

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

      19. associate-/l* 90.1%

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

      20. metadata-eval 90.1%

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

      21. /-rgt-identity 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in a around 0 72.1%

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

      1. +-commutative 72.1%

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

      2. associate-/l* 91.8%

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

   6. Simplified 91.8%

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

   if -3.5999999999999999e-44 < t < 8.5000000000000001e-81 or 2.05000000000000007e-41 < t < 1.95e100

   1. Initial program 96.7%

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

   2. Taylor expanded in a around inf 86.1%

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

   if 8.5000000000000001e-81 < t < 2.05000000000000007e-41

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*l/ 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 100.0%

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

      11. fma-def 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. neg-sub0 100.0%

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

      15. associate-+l- 100.0%

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

      16. sub0-neg 100.0%

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

      17. neg-mul-1 100.0%

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

      18. *-commutative 100.0%

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

      19. associate-/l* 100.0%

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

      20. metadata-eval 100.0%

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

      21. /-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-/l* 61.9%

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

   6. Simplified 61.9%

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

   7. Taylor expanded in t around 0 90.0%

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

      1. associate-*r/ 90.0%

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

      2. mul-1-neg 90.0%

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

   9. Simplified 90.0%

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

       1. div-inv 90.0%

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

       2. distribute-lft-neg-in 90.0%

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

       3. associate-*l* 71.2%

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

       4. div-inv 71.3%

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

       5. neg-mul-1 71.3%

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

       6. associate-*l* 71.3%

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

       7. metadata-eval 71.3%

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

       8. add-sqr-sqrt 50.2%

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

       9. sqrt-unprod 50.9%

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

       10. sqr-neg 50.9%

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

       11. sqrt-unprod 10.1%

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

       12. add-sqr-sqrt 40.7%

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

       13. div-inv 40.7%

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

       14. associate-*l* 40.7%

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

       15. distribute-lft-neg-in 40.7%

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

       16. div-inv 40.7%

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

       17. cancel-sign-sub-inv 40.7%

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

       18. *-un-lft-identity 40.7%

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

       19. div-inv 40.7%

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

   11. Applied egg-rr 90.1%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-44}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-41}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+100}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \end{array} \]

Alternative 6: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-11}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+41}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e+24)
   (+ x y)
   (if (<= t -5.4e-11)
     (* (- t z) (/ y (- t a)))
     (if (<= t 5e-81)
       (+ x (/ y (/ a z)))
       (if (<= t 5e+41) (- x (* z (/ y t))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+24) {
		tmp = x + y;
	} else if (t <= -5.4e-11) {
		tmp = (t - z) * (y / (t - a));
	} else if (t <= 5e-81) {
		tmp = x + (y / (a / z));
	} else if (t <= 5e+41) {
		tmp = x - (z * (y / 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 (t <= (-1.2d+24)) then
        tmp = x + y
    else if (t <= (-5.4d-11)) then
        tmp = (t - z) * (y / (t - a))
    else if (t <= 5d-81) then
        tmp = x + (y / (a / z))
    else if (t <= 5d+41) then
        tmp = x - (z * (y / 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 (t <= -1.2e+24) {
		tmp = x + y;
	} else if (t <= -5.4e-11) {
		tmp = (t - z) * (y / (t - a));
	} else if (t <= 5e-81) {
		tmp = x + (y / (a / z));
	} else if (t <= 5e+41) {
		tmp = x - (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e+24:
		tmp = x + y
	elif t <= -5.4e-11:
		tmp = (t - z) * (y / (t - a))
	elif t <= 5e-81:
		tmp = x + (y / (a / z))
	elif t <= 5e+41:
		tmp = x - (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e+24)
		tmp = Float64(x + y);
	elseif (t <= -5.4e-11)
		tmp = Float64(Float64(t - z) * Float64(y / Float64(t - a)));
	elseif (t <= 5e-81)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 5e+41)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e+24)
		tmp = x + y;
	elseif (t <= -5.4e-11)
		tmp = (t - z) * (y / (t - a));
	elseif (t <= 5e-81)
		tmp = x + (y / (a / z));
	elseif (t <= 5e+41)
		tmp = x - (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e+24], N[(x + y), $MachinePrecision], If[LessEqual[t, -5.4e-11], N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-81], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+41], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2e24 or 5.00000000000000022e41 < t

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l/ 78.2%

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

      4. sub-neg 78.2%

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

      5. +-commutative 78.2%

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

      6. neg-sub0 78.2%

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

      7. associate-+l- 78.2%

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

      8. sub0-neg 78.2%

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

      9. neg-mul-1 78.2%

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

      10. times-frac 90.3%

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

      11. fma-def 90.3%

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

      12. sub-neg 90.3%

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

      13. +-commutative 90.3%

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

      14. neg-sub0 90.3%

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

      15. associate-+l- 90.3%

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

      16. sub0-neg 90.3%

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

      17. neg-mul-1 90.3%

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

      18. *-commutative 90.3%

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

      19. associate-/l* 90.3%

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

      20. metadata-eval 90.3%

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

      21. /-rgt-identity 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in t around inf 82.7%

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

   if -1.2e24 < t < -5.40000000000000009e-11

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. *-commutative 99.3%

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

      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 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. neg-sub0 99.7%

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

      15. associate-+l- 99.7%

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

      16. sub0-neg 99.7%

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

      17. neg-mul-1 99.7%

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

      18. *-commutative 99.7%

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

      19. associate-/l* 99.7%

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

      20. metadata-eval 99.7%

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

      21. /-rgt-identity 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around -inf 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   if -5.40000000000000009e-11 < t < 4.99999999999999981e-81

   1. Initial program 96.3%

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

      1. +-commutative 96.3%

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

      2. *-commutative 96.3%

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

      3. associate-*l/ 97.4%

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

      4. sub-neg 97.4%

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

      5. +-commutative 97.4%

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

      6. neg-sub0 97.4%

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

      7. associate-+l- 97.4%

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

      8. sub0-neg 97.4%

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

      9. neg-mul-1 97.4%

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

      10. times-frac 96.6%

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

      11. fma-def 96.6%

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

      12. sub-neg 96.6%

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

      13. +-commutative 96.6%

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

      14. neg-sub0 96.6%

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

      15. associate-+l- 96.6%

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

      16. sub0-neg 96.6%

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

      17. neg-mul-1 96.6%

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

      18. *-commutative 96.6%

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

      19. associate-/l* 96.6%

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

      20. metadata-eval 96.6%

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

      21. /-rgt-identity 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around 0 81.2%

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

      1. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   if 4.99999999999999981e-81 < t < 5.00000000000000022e41

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l/ 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      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 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-/l* 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in t around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. mul-1-neg 75.6%

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

   9. Simplified 75.6%

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

       1. div-inv 75.6%

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

       2. distribute-lft-neg-in 75.6%

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

       3. associate-*l* 66.2%

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

       4. div-inv 66.3%

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

       5. neg-mul-1 66.3%

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

       6. associate-*l* 66.3%

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

       7. metadata-eval 66.3%

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

       8. add-sqr-sqrt 45.2%

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

       9. sqrt-unprod 50.5%

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

       10. sqr-neg 50.5%

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

       11. sqrt-unprod 10.1%

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

       12. add-sqr-sqrt 45.7%

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

       13. div-inv 45.7%

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

       14. associate-*l* 45.7%

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

       15. distribute-lft-neg-in 45.7%

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

       16. div-inv 45.7%

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

       17. cancel-sign-sub-inv 45.7%

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

       18. *-un-lft-identity 45.7%

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

       19. div-inv 45.7%

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

   11. Applied egg-rr 75.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-11}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+41}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-40}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+39}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e-40)
   (+ x y)
   (if (<= t 6.5e-81)
     (+ x (/ y (/ a z)))
     (if (<= t 2.15e+39) (- x (* z (/ y t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e-40) {
		tmp = x + y;
	} else if (t <= 6.5e-81) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.15e+39) {
		tmp = x - (z * (y / 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 (t <= (-8.5d-40)) then
        tmp = x + y
    else if (t <= 6.5d-81) then
        tmp = x + (y / (a / z))
    else if (t <= 2.15d+39) then
        tmp = x - (z * (y / 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 (t <= -8.5e-40) {
		tmp = x + y;
	} else if (t <= 6.5e-81) {
		tmp = x + (y / (a / z));
	} else if (t <= 2.15e+39) {
		tmp = x - (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e-40:
		tmp = x + y
	elif t <= 6.5e-81:
		tmp = x + (y / (a / z))
	elif t <= 2.15e+39:
		tmp = x - (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e-40)
		tmp = Float64(x + y);
	elseif (t <= 6.5e-81)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 2.15e+39)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.5e-40)
		tmp = x + y;
	elseif (t <= 6.5e-81)
		tmp = x + (y / (a / z));
	elseif (t <= 2.15e+39)
		tmp = x - (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e-40], N[(x + y), $MachinePrecision], If[LessEqual[t, 6.5e-81], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e+39], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.4999999999999998e-40 or 2.15e39 < 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/ 80.3%

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

      4. sub-neg 80.3%

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

      5. +-commutative 80.3%

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

      6. neg-sub0 80.3%

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

      7. associate-+l- 80.3%

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

      8. sub0-neg 80.3%

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

      9. neg-mul-1 80.3%

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

      10. times-frac 90.8%

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

      11. fma-def 90.8%

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

      12. sub-neg 90.8%

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

      13. +-commutative 90.8%

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

      14. neg-sub0 90.8%

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

      15. associate-+l- 90.8%

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

      16. sub0-neg 90.8%

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

      17. neg-mul-1 90.8%

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

      18. *-commutative 90.8%

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

      19. associate-/l* 90.8%

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

      20. metadata-eval 90.8%

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

      21. /-rgt-identity 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 78.5%

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

   if -8.4999999999999998e-40 < t < 6.5000000000000002e-81

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. *-commutative 96.1%

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

      3. associate-*l/ 97.3%

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

      4. sub-neg 97.3%

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

      5. +-commutative 97.3%

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

      6. neg-sub0 97.3%

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

      7. associate-+l- 97.3%

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

      8. sub0-neg 97.3%

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

      9. neg-mul-1 97.3%

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

      10. times-frac 97.2%

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

      11. fma-def 97.2%

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

      12. sub-neg 97.2%

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

      13. +-commutative 97.2%

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

      14. neg-sub0 97.2%

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

      15. associate-+l- 97.2%

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

      16. sub0-neg 97.2%

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

      17. neg-mul-1 97.2%

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

      18. *-commutative 97.2%

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

      19. associate-/l* 97.2%

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

      20. metadata-eval 97.2%

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

      21. /-rgt-identity 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around 0 83.4%

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

      1. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

   if 6.5000000000000002e-81 < t < 2.15e39

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. *-commutative 90.6%

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

      3. associate-*l/ 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      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 75.4%

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

      1. +-commutative 75.4%

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

      2. associate-/l* 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in t around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. mul-1-neg 75.6%

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

   9. Simplified 75.6%

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

       1. div-inv 75.6%

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

       2. distribute-lft-neg-in 75.6%

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

       3. associate-*l* 66.2%

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

       4. div-inv 66.3%

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

       5. neg-mul-1 66.3%

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

       6. associate-*l* 66.3%

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

       7. metadata-eval 66.3%

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

       8. add-sqr-sqrt 45.2%

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

       9. sqrt-unprod 50.5%

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

       10. sqr-neg 50.5%

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

       11. sqrt-unprod 10.1%

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

       12. add-sqr-sqrt 45.7%

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

       13. div-inv 45.7%

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

       14. associate-*l* 45.7%

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

       15. distribute-lft-neg-in 45.7%

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

       16. div-inv 45.7%

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

       17. cancel-sign-sub-inv 45.7%

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

       18. *-un-lft-identity 45.7%

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

       19. div-inv 45.7%

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

   11. Applied egg-rr 75.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-40}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+39}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-40} \lor \neg \left(t \leq 150\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e-40) (not (<= t 150.0))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e-40) || !(t <= 150.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.5d-40)) .or. (.not. (t <= 150.0d0))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e-40) || !(t <= 150.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.5e-40) or not (t <= 150.0):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.5e-40) || !(t <= 150.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.5e-40) || ~((t <= 150.0)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.5e-40], N[Not[LessEqual[t, 150.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5000000000000001e-40 or 150 < 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/ 81.2%

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

      4. sub-neg 81.2%

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

      5. +-commutative 81.2%

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

      6. neg-sub0 81.2%

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

      7. associate-+l- 81.2%

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

      8. sub0-neg 81.2%

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

      9. neg-mul-1 81.2%

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

      10. times-frac 91.2%

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

      11. fma-def 91.2%

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

      12. sub-neg 91.2%

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

      13. +-commutative 91.2%

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

      14. neg-sub0 91.2%

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

      15. associate-+l- 91.2%

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

      16. sub0-neg 91.2%

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

      17. neg-mul-1 91.2%

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

      18. *-commutative 91.2%

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

      19. associate-/l* 91.2%

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

      20. metadata-eval 91.2%

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

      21. /-rgt-identity 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in t around inf 77.3%

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

   if -1.5000000000000001e-40 < t < 150

   1. Initial program 95.0%

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

   2. Taylor expanded in t around 0 81.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-40} \lor \neg \left(t \leq 150\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 9: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-41} \lor \neg \left(t \leq 820\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.5e-41) (not (<= t 820.0))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e-41) || !(t <= 820.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.5d-41)) .or. (.not. (t <= 820.0d0))) then
        tmp = x + y
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e-41) || !(t <= 820.0)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.5e-41) or not (t <= 820.0):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.5e-41) || !(t <= 820.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.5e-41) || ~((t <= 820.0)))
		tmp = x + y;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.5e-41], N[Not[LessEqual[t, 820.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.50000000000000049e-41 or 820 < 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/ 81.2%

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

      4. sub-neg 81.2%

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

      5. +-commutative 81.2%

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

      6. neg-sub0 81.2%

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

      7. associate-+l- 81.2%

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

      8. sub0-neg 81.2%

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

      9. neg-mul-1 81.2%

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

      10. times-frac 91.2%

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

      11. fma-def 91.2%

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

      12. sub-neg 91.2%

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

      13. +-commutative 91.2%

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

      14. neg-sub0 91.2%

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

      15. associate-+l- 91.2%

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

      16. sub0-neg 91.2%

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

      17. neg-mul-1 91.2%

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

      18. *-commutative 91.2%

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

      19. associate-/l* 91.2%

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

      20. metadata-eval 91.2%

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

      21. /-rgt-identity 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in t around inf 77.3%

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

   if -7.50000000000000049e-41 < t < 820

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*l/ 97.6%

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

      4. sub-neg 97.6%

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

      5. +-commutative 97.6%

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

      6. neg-sub0 97.6%

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

      7. associate-+l- 97.6%

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

      8. sub0-neg 97.6%

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

      9. neg-mul-1 97.6%

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

      10. times-frac 97.5%

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

      11. fma-def 97.5%

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

      12. sub-neg 97.5%

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

      13. +-commutative 97.5%

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

      14. neg-sub0 97.5%

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

      15. associate-+l- 97.5%

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

      16. sub0-neg 97.5%

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

      17. neg-mul-1 97.5%

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

      18. *-commutative 97.5%

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

      19. associate-/l* 97.5%

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

      20. metadata-eval 97.5%

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

      21. /-rgt-identity 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in t around 0 79.8%

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

      1. associate-/l* 81.3%

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

   6. Simplified 81.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-41} \lor \neg \left(t \leq 820\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 10: 63.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 38:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e-44) (+ x y) (if (<= t 38.0) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e-44) {
		tmp = x + y;
	} else if (t <= 38.0) {
		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 <= (-7d-44)) then
        tmp = x + y
    else if (t <= 38.0d0) 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 <= -7e-44) {
		tmp = x + y;
	} else if (t <= 38.0) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e-44:
		tmp = x + y
	elif t <= 38.0:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e-44)
		tmp = Float64(x + y);
	elseif (t <= 38.0)
		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 <= -7e-44)
		tmp = x + y;
	elseif (t <= 38.0)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e-44], N[(x + y), $MachinePrecision], If[LessEqual[t, 38.0], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.9999999999999995e-44 or 38 < 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/ 81.2%

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

      4. sub-neg 81.2%

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

      5. +-commutative 81.2%

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

      6. neg-sub0 81.2%

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

      7. associate-+l- 81.2%

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

      8. sub0-neg 81.2%

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

      9. neg-mul-1 81.2%

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

      10. times-frac 91.2%

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

      11. fma-def 91.2%

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

      12. sub-neg 91.2%

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

      13. +-commutative 91.2%

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

      14. neg-sub0 91.2%

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

      15. associate-+l- 91.2%

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

      16. sub0-neg 91.2%

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

      17. neg-mul-1 91.2%

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

      18. *-commutative 91.2%

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

      19. associate-/l* 91.2%

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

      20. metadata-eval 91.2%

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

      21. /-rgt-identity 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in t around inf 77.3%

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

   if -6.9999999999999995e-44 < t < 38

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*l/ 97.6%

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

      4. sub-neg 97.6%

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

      5. +-commutative 97.6%

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

      6. neg-sub0 97.6%

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

      7. associate-+l- 97.6%

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

      8. sub0-neg 97.6%

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

      9. neg-mul-1 97.6%

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

      10. times-frac 97.5%

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

      11. fma-def 97.5%

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

      12. sub-neg 97.5%

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

      13. +-commutative 97.5%

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

      14. neg-sub0 97.5%

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

      15. associate-+l- 97.5%

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

      16. sub0-neg 97.5%

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

      17. neg-mul-1 97.5%

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

      18. *-commutative 97.5%

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

      19. associate-/l* 97.5%

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

      20. metadata-eval 97.5%

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

      21. /-rgt-identity 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 52.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 38:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 53.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+103}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+208}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.8e+103) y (if (<= y 1.95e+208) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.8e+103) {
		tmp = y;
	} else if (y <= 1.95e+208) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-5.8d+103)) then
        tmp = y
    else if (y <= 1.95d+208) then
        tmp = x
    else
        tmp = 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 (y <= -5.8e+103) {
		tmp = y;
	} else if (y <= 1.95e+208) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.8e+103:
		tmp = y
	elif y <= 1.95e+208:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.8e+103)
		tmp = y;
	elseif (y <= 1.95e+208)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.8e+103)
		tmp = y;
	elseif (y <= 1.95e+208)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.8e+103], y, If[LessEqual[y, 1.95e+208], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999997e103 or 1.95e208 < y

   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/ 67.2%

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

      4. sub-neg 67.2%

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

      5. +-commutative 67.2%

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

      6. neg-sub0 67.2%

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

      7. associate-+l- 67.2%

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

      8. sub0-neg 67.2%

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

      9. neg-mul-1 67.2%

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

      10. times-frac 93.3%

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

      11. fma-def 93.3%

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

      12. sub-neg 93.3%

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

      13. +-commutative 93.3%

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

      14. neg-sub0 93.3%

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

      15. associate-+l- 93.3%

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

      16. sub0-neg 93.3%

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

      17. neg-mul-1 93.3%

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

      18. *-commutative 93.3%

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

      19. associate-/l* 93.3%

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

      20. metadata-eval 93.3%

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

      21. /-rgt-identity 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around -inf 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-*r/ 79.6%

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

   6. Simplified 79.6%

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

   7. Taylor expanded in z around 0 21.9%

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

      1. associate-/l* 45.8%

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

   9. Simplified 45.8%

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

   10. Taylor expanded in t around inf 36.7%

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

   if -5.7999999999999997e103 < y < 1.95e208

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*l/ 95.1%

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

      4. sub-neg 95.1%

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

      5. +-commutative 95.1%

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

      6. neg-sub0 95.1%

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

      7. associate-+l- 95.1%

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

      8. sub0-neg 95.1%

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

      9. neg-mul-1 95.1%

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

      10. times-frac 94.5%

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

      11. fma-def 94.5%

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

      12. sub-neg 94.5%

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

      13. +-commutative 94.5%

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

      14. neg-sub0 94.5%

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

      15. associate-+l- 94.5%

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

      16. sub0-neg 94.5%

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

      17. neg-mul-1 94.5%

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

      18. *-commutative 94.5%

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

      19. associate-/l* 94.5%

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

      20. metadata-eval 94.5%

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

      21. /-rgt-identity 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around 0 60.7%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+103}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+208}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 12: 50.3% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. *-commutative 97.6%

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

   3. associate-*l/ 88.9%

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

   4. sub-neg 88.9%

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

   5. +-commutative 88.9%

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

   6. neg-sub0 88.9%

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

   7. associate-+l- 88.9%

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

   8. sub0-neg 88.9%

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

   9. neg-mul-1 88.9%

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

   10. times-frac 94.2%

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

   11. fma-def 94.2%

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

   12. sub-neg 94.2%

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

   13. +-commutative 94.2%

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

   14. neg-sub0 94.2%

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

   15. associate-+l- 94.2%

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

   16. sub0-neg 94.2%

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

   17. neg-mul-1 94.2%

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

   18. *-commutative 94.2%

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

   19. associate-/l* 94.2%

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

   20. metadata-eval 94.2%

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

   21. /-rgt-identity 94.2%

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

3. Simplified 94.2%

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

4. Taylor expanded in y around 0 50.5%

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

5. Final simplification 50.5%

   \[\leadsto x \]

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 2023181 
(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)))))