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

Percentage Accurate: 85.3% → 98.1%

Time: 11.9s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

   1. associate-/l* 99.1%

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

3. Simplified 99.1%

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

   1. clear-num 99.1%

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

   2. un-div-inv 99.4%

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

6. Applied egg-rr 99.4%

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

7. Final simplification 99.4%

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

Alternative 2: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y t) (- t z)))))
   (if (<= t -1.45e-40)
     t_1
     (if (<= t 4.6e-262)
       (+ x (/ y (/ a (- z t))))
       (if (<= t 2.6e+14) (+ x (/ (* y z) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / t) * (t - z));
	double tmp;
	if (t <= -1.45e-40) {
		tmp = t_1;
	} else if (t <= 4.6e-262) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 2.6e+14) {
		tmp = x + ((y * z) / (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 / t) * (t - z))
    if (t <= (-1.45d-40)) then
        tmp = t_1
    else if (t <= 4.6d-262) then
        tmp = x + (y / (a / (z - t)))
    else if (t <= 2.6d+14) then
        tmp = x + ((y * z) / (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 / t) * (t - z));
	double tmp;
	if (t <= -1.45e-40) {
		tmp = t_1;
	} else if (t <= 4.6e-262) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 2.6e+14) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y / t) * (t - z))
	tmp = 0
	if t <= -1.45e-40:
		tmp = t_1
	elif t <= 4.6e-262:
		tmp = x + (y / (a / (z - t)))
	elif t <= 2.6e+14:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y / t) * Float64(t - z)))
	tmp = 0.0
	if (t <= -1.45e-40)
		tmp = t_1;
	elseif (t <= 4.6e-262)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t <= 2.6e+14)
		tmp = Float64(x + Float64(Float64(y * z) / 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 / t) * (t - z));
	tmp = 0.0;
	if (t <= -1.45e-40)
		tmp = t_1;
	elseif (t <= 4.6e-262)
		tmp = x + (y / (a / (z - t)));
	elseif (t <= 2.6e+14)
		tmp = x + ((y * z) / (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[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-40], t$95$1, If[LessEqual[t, 4.6e-262], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+14], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4499999999999999e-40 or 2.6e14 < t

   1. Initial program 76.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. frac-2neg 99.9%

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

      2. associate-/r/ 93.1%

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

      3. sub-neg 93.1%

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

      4. distribute-neg-in 93.1%

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

      5. add-sqr-sqrt 47.3%

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

      6. sqrt-unprod 68.8%

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

      7. sqr-neg 68.8%

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

      8. sqrt-unprod 29.2%

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

      9. add-sqr-sqrt 56.4%

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

      10. add-sqr-sqrt 27.2%

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

      11. sqrt-unprod 63.9%

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

      12. sqr-neg 63.9%

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

      13. sqrt-unprod 45.6%

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

      14. add-sqr-sqrt 93.1%

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

      15. sub-neg 93.1%

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

      16. distribute-neg-in 93.1%

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

      17. add-sqr-sqrt 47.3%

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

      18. sqrt-unprod 47.8%

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

      19. sqr-neg 47.8%

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

      20. sqrt-unprod 31.3%

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

      21. add-sqr-sqrt 61.8%

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

   8. Applied egg-rr 93.1%

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

      1. +-commutative 93.1%

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

      2. unsub-neg 93.1%

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

      3. +-commutative 93.1%

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

      4. unsub-neg 93.1%

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

   10. Simplified 93.1%

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

   11. Taylor expanded in t around inf 80.7%

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

   if -1.4499999999999999e-40 < t < 4.6000000000000002e-262

   1. Initial program 91.2%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.4%

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

      2. un-div-inv 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in a around inf 88.9%

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

   if 4.6000000000000002e-262 < t < 2.6e14

   1. Initial program 95.2%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around inf 87.1%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (+ (/ z t) -1.0)))))
   (if (<= t -1e-41)
     t_1
     (if (<= t 4.8e-262)
       (+ x (/ y (/ a (- z t))))
       (if (<= t 1.6e+27) (+ x (/ (* y z) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((z / t) + -1.0));
	double tmp;
	if (t <= -1e-41) {
		tmp = t_1;
	} else if (t <= 4.8e-262) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 1.6e+27) {
		tmp = x + ((y * z) / (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) + (-1.0d0)))
    if (t <= (-1d-41)) then
        tmp = t_1
    else if (t <= 4.8d-262) then
        tmp = x + (y / (a / (z - t)))
    else if (t <= 1.6d+27) then
        tmp = x + ((y * z) / (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) + -1.0));
	double tmp;
	if (t <= -1e-41) {
		tmp = t_1;
	} else if (t <= 4.8e-262) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 1.6e+27) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((z / t) + -1.0))
	tmp = 0
	if t <= -1e-41:
		tmp = t_1
	elif t <= 4.8e-262:
		tmp = x + (y / (a / (z - t)))
	elif t <= 1.6e+27:
		tmp = x + ((y * z) / (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) + -1.0)))
	tmp = 0.0
	if (t <= -1e-41)
		tmp = t_1;
	elseif (t <= 4.8e-262)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t <= 1.6e+27)
		tmp = Float64(x + Float64(Float64(y * z) / 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) + -1.0));
	tmp = 0.0;
	if (t <= -1e-41)
		tmp = t_1;
	elseif (t <= 4.8e-262)
		tmp = x + (y / (a / (z - t)));
	elseif (t <= 1.6e+27)
		tmp = x + ((y * z) / (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] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e-41], t$95$1, If[LessEqual[t, 4.8e-262], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+27], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.00000000000000001e-41 or 1.60000000000000008e27 < t

   1. Initial program 76.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. unsub-neg 68.6%

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

      3. associate-/l* 87.6%

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

      4. div-sub 87.6%

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

      5. sub-neg 87.6%

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

      6. *-inverses 87.6%

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

      7. metadata-eval 87.6%

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

   7. Simplified 87.6%

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

   if -1.00000000000000001e-41 < t < 4.8000000000000001e-262

   1. Initial program 91.2%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.4%

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

      2. un-div-inv 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in a around inf 88.9%

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

   if 4.8000000000000001e-262 < t < 1.60000000000000008e27

   1. Initial program 95.2%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around inf 87.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-41}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-41}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e-41)
   (- x (* y (+ (/ z t) -1.0)))
   (if (<= t 4.6e-262)
     (+ x (/ y (/ a (- z t))))
     (if (<= t 1.2e-60) (+ x (/ (* y z) (- a t))) (+ x (* y (/ t (- t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e-41) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 4.6e-262) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 1.2e-60) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.8d-41)) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else if (t <= 4.6d-262) then
        tmp = x + (y / (a / (z - t)))
    else if (t <= 1.2d-60) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (y * (t / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e-41) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= 4.6e-262) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 1.2e-60) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e-41:
		tmp = x - (y * ((z / t) + -1.0))
	elif t <= 4.6e-262:
		tmp = x + (y / (a / (z - t)))
	elif t <= 1.2e-60:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e-41)
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	elseif (t <= 4.6e-262)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t <= 1.2e-60)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.8e-41)
		tmp = x - (y * ((z / t) + -1.0));
	elseif (t <= 4.6e-262)
		tmp = x + (y / (a / (z - t)));
	elseif (t <= 1.2e-60)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e-41], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-262], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-60], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.7999999999999997e-41

   1. Initial program 77.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

      3. associate-/l* 86.8%

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

      4. div-sub 86.8%

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

      5. sub-neg 86.8%

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

      6. *-inverses 86.8%

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

      7. metadata-eval 86.8%

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

   7. Simplified 86.8%

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

   if -6.7999999999999997e-41 < t < 4.6000000000000002e-262

   1. Initial program 91.2%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.4%

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

      2. un-div-inv 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in a around inf 88.9%

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

   if 4.6000000000000002e-262 < t < 1.20000000000000005e-60

   1. Initial program 96.1%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around inf 92.2%

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

   if 1.20000000000000005e-60 < t

   1. Initial program 78.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 69.5%

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

      1. mul-1-neg 69.5%

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

      2. unsub-neg 69.5%

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

      3. *-commutative 69.5%

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

      4. sub-neg 69.5%

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

      5. remove-double-neg 69.5%

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

      6. distribute-neg-in 69.5%

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

      7. associate-/l* 85.1%

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

      8. distribute-neg-in 85.1%

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

      9. remove-double-neg 85.1%

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

      10. sub-neg 85.1%

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

   9. Simplified 85.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-41}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-42}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.5e-42)
   (+ x (- y (* y (/ z t))))
   (if (<= t 4.8e-262)
     (+ x (/ y (/ a (- z t))))
     (if (<= t 4.3e-62) (+ x (/ (* y z) (- a t))) (+ x (* y (/ t (- t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e-42) {
		tmp = x + (y - (y * (z / t)));
	} else if (t <= 4.8e-262) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 4.3e-62) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.5d-42)) then
        tmp = x + (y - (y * (z / t)))
    else if (t <= 4.8d-262) then
        tmp = x + (y / (a / (z - t)))
    else if (t <= 4.3d-62) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (y * (t / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.5e-42) {
		tmp = x + (y - (y * (z / t)));
	} else if (t <= 4.8e-262) {
		tmp = x + (y / (a / (z - t)));
	} else if (t <= 4.3e-62) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (y * (t / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.5e-42:
		tmp = x + (y - (y * (z / t)))
	elif t <= 4.8e-262:
		tmp = x + (y / (a / (z - t)))
	elif t <= 4.3e-62:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (y * (t / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.5e-42)
		tmp = Float64(x + Float64(y - Float64(y * Float64(z / t))));
	elseif (t <= 4.8e-262)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t <= 4.3e-62)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.5e-42)
		tmp = x + (y - (y * (z / t)));
	elseif (t <= 4.8e-262)
		tmp = x + (y / (a / (z - t)));
	elseif (t <= 4.3e-62)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (y * (t / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.5e-42], N[(x + N[(y - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-262], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-62], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.49999999999999972e-42

   1. Initial program 77.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in a around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

      3. associate-/l* 86.8%

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

      4. div-sub 86.8%

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

      5. *-inverses 86.8%

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

   9. Simplified 86.8%

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

       1. sub-neg 86.8%

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

       2. distribute-rgt-in 86.9%

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

       3. metadata-eval 86.9%

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

       4. neg-mul-1 86.9%

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

   11. Applied egg-rr 86.9%

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

   if -7.49999999999999972e-42 < t < 4.8000000000000001e-262

   1. Initial program 91.2%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.4%

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

      2. un-div-inv 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in a around inf 88.9%

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

   if 4.8000000000000001e-262 < t < 4.2999999999999997e-62

   1. Initial program 96.1%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around inf 92.2%

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

   if 4.2999999999999997e-62 < t

   1. Initial program 78.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 69.5%

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

      1. mul-1-neg 69.5%

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

      2. unsub-neg 69.5%

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

      3. *-commutative 69.5%

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

      4. sub-neg 69.5%

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

      5. remove-double-neg 69.5%

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

      6. distribute-neg-in 69.5%

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

      7. associate-/l* 85.1%

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

      8. distribute-neg-in 85.1%

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

      9. remove-double-neg 85.1%

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

      10. sub-neg 85.1%

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

   9. Simplified 85.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-42}:\\ \;\;\;\;x + \left(y - y \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-51} \lor \neg \left(a \leq 2.6 \cdot 10^{-46}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.4e-51) (not (<= a 2.6e-46)))
   (+ x (/ y (/ a (- z t))))
   (+ x (* (/ y t) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.4e-51) || !(a <= 2.6e-46)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + ((y / t) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.4d-51)) .or. (.not. (a <= 2.6d-46))) then
        tmp = x + (y / (a / (z - t)))
    else
        tmp = x + ((y / t) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.4e-51) || !(a <= 2.6e-46)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + ((y / t) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.4e-51) or not (a <= 2.6e-46):
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + ((y / t) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.4e-51) || !(a <= 2.6e-46))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(y / t) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.4e-51) || ~((a <= 2.6e-46)))
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + ((y / t) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.4e-51], N[Not[LessEqual[a, 2.6e-46]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.4e-51 or 2.6000000000000002e-46 < a

   1. Initial program 82.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around inf 81.7%

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

   if -4.4e-51 < a < 2.6000000000000002e-46

   1. Initial program 87.9%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.8%

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

   6. Applied egg-rr 98.8%

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

      1. frac-2neg 98.8%

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

      2. associate-/r/ 94.2%

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

      3. sub-neg 94.2%

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

      4. distribute-neg-in 94.2%

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

      5. add-sqr-sqrt 50.1%

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

      6. sqrt-unprod 69.7%

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

      7. sqr-neg 69.7%

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

      8. sqrt-unprod 21.9%

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

      9. add-sqr-sqrt 50.6%

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

      10. add-sqr-sqrt 28.7%

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

      11. sqrt-unprod 66.8%

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

      12. sqr-neg 66.8%

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

      13. sqrt-unprod 43.8%

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

      14. add-sqr-sqrt 94.2%

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

      15. sub-neg 94.2%

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

      16. distribute-neg-in 94.2%

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

      17. add-sqr-sqrt 50.2%

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

      18. sqrt-unprod 70.4%

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

      19. sqr-neg 70.4%

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

      20. sqrt-unprod 32.9%

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

      21. add-sqr-sqrt 71.3%

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

   8. Applied egg-rr 94.2%

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

      1. +-commutative 94.2%

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

      2. unsub-neg 94.2%

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

      3. +-commutative 94.2%

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

      4. unsub-neg 94.2%

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

   10. Simplified 94.2%

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

   11. Taylor expanded in t around inf 82.1%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-51} \lor \neg \left(a \leq 2.6 \cdot 10^{-46}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+41} \lor \neg \left(z \leq 1350000\right):\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+41) (not (<= z 1350000.0)))
   (+ x (/ (* y z) (- a t)))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+41) || !(z <= 1350000.0)) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.5d+41)) .or. (.not. (z <= 1350000.0d0))) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + (t * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+41) || !(z <= 1350000.0)) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+41) or not (z <= 1350000.0):
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+41) || !(z <= 1350000.0))
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+41) || ~((z <= 1350000.0)))
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+41], N[Not[LessEqual[z, 1350000.0]], $MachinePrecision]], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4999999999999999e41 or 1.35e6 < z

   1. Initial program 83.5%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in z around inf 80.3%

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

   if -1.4999999999999999e41 < z < 1.35e6

   1. Initial program 86.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

      3. associate-/l* 86.2%

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

   7. Simplified 86.2%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+41} \lor \neg \left(z \leq 1350000\right):\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000165:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.000165)
   (+ x (/ y (/ a z)))
   (if (<= a 2.6e-49) (+ x (* (/ y t) (- t z))) (+ x (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.000165) {
		tmp = x + (y / (a / z));
	} else if (a <= 2.6e-49) {
		tmp = x + ((y / t) * (t - z));
	} 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 (a <= (-0.000165d0)) then
        tmp = x + (y / (a / z))
    else if (a <= 2.6d-49) then
        tmp = x + ((y / t) * (t - z))
    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 (a <= -0.000165) {
		tmp = x + (y / (a / z));
	} else if (a <= 2.6e-49) {
		tmp = x + ((y / t) * (t - z));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.000165:
		tmp = x + (y / (a / z))
	elif a <= 2.6e-49:
		tmp = x + ((y / t) * (t - z))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.000165)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (a <= 2.6e-49)
		tmp = Float64(x + Float64(Float64(y / t) * Float64(t - z)));
	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 (a <= -0.000165)
		tmp = x + (y / (a / z));
	elseif (a <= 2.6e-49)
		tmp = x + ((y / t) * (t - z));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.000165], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-49], N[(x + N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65e-4

   1. Initial program 83.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 68.1%

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

      1. +-commutative 68.1%

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

      2. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

      1. clear-num 75.7%

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

      2. un-div-inv 75.7%

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

   9. Applied egg-rr 75.7%

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

   if -1.65e-4 < a < 2.59999999999999995e-49

   1. Initial program 88.3%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

      1. clear-num 98.4%

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

      2. un-div-inv 98.9%

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

   6. Applied egg-rr 98.9%

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

      1. frac-2neg 98.9%

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

      2. associate-/r/ 94.3%

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

      3. sub-neg 94.3%

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

      4. distribute-neg-in 94.3%

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

      5. add-sqr-sqrt 50.1%

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

      6. sqrt-unprod 69.9%

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

      7. sqr-neg 69.9%

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

      8. sqrt-unprod 22.0%

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

      9. add-sqr-sqrt 50.6%

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

      10. add-sqr-sqrt 28.6%

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

      11. sqrt-unprod 67.1%

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

      12. sqr-neg 67.1%

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

      13. sqrt-unprod 44.0%

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

      14. add-sqr-sqrt 94.3%

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

      15. sub-neg 94.3%

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

      16. distribute-neg-in 94.3%

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

      17. add-sqr-sqrt 50.2%

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

      18. sqrt-unprod 70.0%

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

      19. sqr-neg 70.0%

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

      20. sqrt-unprod 32.0%

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

      21. add-sqr-sqrt 70.8%

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

   8. Applied egg-rr 94.3%

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

      1. +-commutative 94.3%

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

      2. unsub-neg 94.3%

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

      3. +-commutative 94.3%

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

      4. unsub-neg 94.3%

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

   10. Simplified 94.3%

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

   11. Taylor expanded in t around inf 81.1%

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

   if 2.59999999999999995e-49 < a

   1. Initial program 80.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 74.9%

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

      1. +-commutative 74.9%

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

      2. associate-/l* 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000165:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+58} \lor \neg \left(y \leq 2.25 \cdot 10^{+106}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.2e+58) (not (<= y 2.25e+106)))
   (* y (- 1.0 (/ z t)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.2e+58) || !(y <= 2.25e+106)) {
		tmp = y * (1.0 - (z / 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 ((y <= (-8.2d+58)) .or. (.not. (y <= 2.25d+106))) then
        tmp = y * (1.0d0 - (z / 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 ((y <= -8.2e+58) || !(y <= 2.25e+106)) {
		tmp = y * (1.0 - (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.2e+58) or not (y <= 2.25e+106):
		tmp = y * (1.0 - (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.2e+58) || !(y <= 2.25e+106))
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8.2e+58) || ~((y <= 2.25e+106)))
		tmp = y * (1.0 - (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.2e+58], N[Not[LessEqual[y, 2.25e+106]], $MachinePrecision]], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2e58 or 2.2499999999999998e106 < y

   1. Initial program 70.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 38.3%

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

      1. mul-1-neg 38.3%

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

      2. unsub-neg 38.3%

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

      3. associate-/l* 56.7%

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

      4. div-sub 56.7%

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

      5. *-inverses 56.7%

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

   9. Simplified 56.7%

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

   10. Taylor expanded in x around 0 50.7%

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

       1. sub-neg 50.7%

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

       2. metadata-eval 50.7%

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

       3. *-rgt-identity 50.7%

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

       4. neg-mul-1 50.7%

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

       5. *-rgt-identity 50.7%

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

       6. distribute-rgt-neg-in 50.7%

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

       7. neg-sub0 50.7%

          \[\leadsto y \cdot \color{blue}{\left(0 - \left(\frac{z}{t} + -1\right)\right)} \]

       8. +-commutative 50.7%

          \[\leadsto y \cdot \left(0 - \color{blue}{\left(-1 + \frac{z}{t}\right)}\right) \]

       9. associate--r+ 50.7%

          \[\leadsto y \cdot \color{blue}{\left(\left(0 - -1\right) - \frac{z}{t}\right)} \]

       10. metadata-eval 50.7%

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

   12. Simplified 50.7%

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

   if -8.2e58 < y < 2.2499999999999998e106

   1. Initial program 93.8%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 74.0%

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

      1. +-commutative 74.0%

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

   7. Simplified 74.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+58} \lor \neg \left(y \leq 2.25 \cdot 10^{+106}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-21} \lor \neg \left(t \leq 34000000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.35e-21) (not (<= t 34000000000000.0)))
   (+ x y)
   (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e-21) || !(t <= 34000000000000.0)) {
		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 <= (-1.35d-21)) .or. (.not. (t <= 34000000000000.0d0))) 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 <= -1.35e-21) || !(t <= 34000000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.35e-21) or not (t <= 34000000000000.0):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.35e-21) || !(t <= 34000000000000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.35e-21) || ~((t <= 34000000000000.0)))
		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, -1.35e-21], N[Not[LessEqual[t, 34000000000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3500000000000001e-21 or 3.4e13 < t

   1. Initial program 75.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.9%

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

      1. +-commutative 78.9%

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

   7. Simplified 78.9%

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

   if -1.3500000000000001e-21 < t < 3.4e13

   1. Initial program 93.5%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 73.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-21} \lor \neg \left(t \leq 34000000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-11} \lor \neg \left(t \leq 1.6 \cdot 10^{+27}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e-11) (not (<= t 1.6e+27))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e-11) || !(t <= 1.6e+27)) {
		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 <= (-2.6d-11)) .or. (.not. (t <= 1.6d+27))) 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 <= -2.6e-11) || !(t <= 1.6e+27)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e-11) or not (t <= 1.6e+27):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e-11) || !(t <= 1.6e+27))
		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 <= -2.6e-11) || ~((t <= 1.6e+27)))
		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, -2.6e-11], N[Not[LessEqual[t, 1.6e+27]], $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 < -2.6000000000000001e-11 or 1.60000000000000008e27 < t

   1. Initial program 75.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 80.7%

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

      1. +-commutative 80.7%

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

   7. Simplified 80.7%

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

   if -2.6000000000000001e-11 < t < 1.60000000000000008e27

   1. Initial program 92.9%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-11} \lor \neg \left(t \leq 1.6 \cdot 10^{+27}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-11} \lor \neg \left(t \leq 6.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.6e-11) (not (<= t 6.2e+37))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.6e-11) || !(t <= 6.2e+37)) {
		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 <= (-6.6d-11)) .or. (.not. (t <= 6.2d+37))) 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 <= -6.6e-11) || !(t <= 6.2e+37)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.6e-11) or not (t <= 6.2e+37):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.6e-11) || !(t <= 6.2e+37))
		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 <= -6.6e-11) || ~((t <= 6.2e+37)))
		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, -6.6e-11], N[Not[LessEqual[t, 6.2e+37]], $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 < -6.6000000000000005e-11 or 6.2000000000000004e37 < t

   1. Initial program 75.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 80.7%

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

      1. +-commutative 80.7%

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

   7. Simplified 80.7%

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

   if -6.6000000000000005e-11 < t < 6.2000000000000004e37

   1. Initial program 92.9%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

      1. clear-num 76.5%

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

      2. un-div-inv 77.0%

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

   9. Applied egg-rr 77.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-11} \lor \neg \left(t \leq 6.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-162} \lor \neg \left(t \leq 3.6 \cdot 10^{-68}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.2e-162) (not (<= t 3.6e-68))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e-162) || !(t <= 3.6e-68)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.2d-162)) .or. (.not. (t <= 3.6d-68))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e-162) || !(t <= 3.6e-68)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.2e-162) or not (t <= 3.6e-68):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.2e-162) || !(t <= 3.6e-68))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.2e-162) || ~((t <= 3.6e-68)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.2e-162], N[Not[LessEqual[t, 3.6e-68]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -4.2e-162 or 3.60000000000000007e-68 < t

   1. Initial program 80.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 71.1%

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

      1. +-commutative 71.1%

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

   7. Simplified 71.1%

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

   if -4.2e-162 < t < 3.60000000000000007e-68

   1. Initial program 93.5%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in x around inf 49.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-162} \lor \neg \left(t \leq 3.6 \cdot 10^{-68}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

   1. associate-/l* 99.1%

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

3. Simplified 99.1%

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

5. Final simplification 99.1%

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

Alternative 15: 51.4% 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 84.8%

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

   1. associate-/l* 99.1%

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

3. Simplified 99.1%

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

5. Taylor expanded in x around inf 48.6%

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

6. Final simplification 48.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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