Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Percentage Accurate: 85.1% → 97.4%

Time: 10.8s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt[3]{a - z}\\ x + \frac{y - z}{{t\_1}^{2}} \cdot \frac{t}{t\_1} \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (cbrt (- a z)))) (+ x (* (/ (- y z) (pow t_1 2.0)) (/ t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = cbrt((a - z));
	return x + (((y - z) / pow(t_1, 2.0)) * (t / t_1));
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = Math.cbrt((a - z));
	return x + (((y - z) / Math.pow(t_1, 2.0)) * (t / t_1));
}

Julia

function code(x, y, z, t, a)
	t_1 = cbrt(Float64(a - z))
	return Float64(x + Float64(Float64(Float64(y - z) / (t_1 ^ 2.0)) * Float64(t / t_1)))
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Power[N[(a - z), $MachinePrecision], 1/3], $MachinePrecision]}, N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision] * N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 86.3%

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

   1. add-cube-cbrt 86.0%

      \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}} \]

   2. times-frac 98.6%

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t}{\sqrt[3]{a - z}}} \]

   3. pow2 98.6%

      \[\leadsto x + \frac{y - z}{\color{blue}{{\left(\sqrt[3]{a - z}\right)}^{2}}} \cdot \frac{t}{\sqrt[3]{a - z}} \]

4. Applied egg-rr 98.6%

   \[\leadsto x + \color{blue}{\frac{y - z}{{\left(\sqrt[3]{a - z}\right)}^{2}} \cdot \frac{t}{\sqrt[3]{a - z}}} \]
5. Add Preprocessing

Alternative 2: 86.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-71}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t \cdot \frac{-1}{z - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.1e+56)
   (- x (* y (/ t (- z a))))
   (if (<= y 6.6e-71)
     (+ x (* t (/ z (- z a))))
     (+ x (* y (* t (/ -1.0 (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+56) {
		tmp = x - (y * (t / (z - a)));
	} else if (y <= 6.6e-71) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y * (t * (-1.0 / (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 (y <= (-1.1d+56)) then
        tmp = x - (y * (t / (z - a)))
    else if (y <= 6.6d-71) then
        tmp = x + (t * (z / (z - a)))
    else
        tmp = x + (y * (t * ((-1.0d0) / (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 (y <= -1.1e+56) {
		tmp = x - (y * (t / (z - a)));
	} else if (y <= 6.6e-71) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y * (t * (-1.0 / (z - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.1e+56:
		tmp = x - (y * (t / (z - a)))
	elif y <= 6.6e-71:
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = x + (y * (t * (-1.0 / (z - a))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.1e+56)
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	elseif (y <= 6.6e-71)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y * Float64(t * Float64(-1.0 / Float64(z - a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.1e+56)
		tmp = x - (y * (t / (z - a)));
	elseif (y <= 6.6e-71)
		tmp = x + (t * (z / (z - a)));
	else
		tmp = x + (y * (t * (-1.0 / (z - a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.1e+56], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-71], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t * N[(-1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.10000000000000008e56

   1. Initial program 77.6%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around inf 96.0%

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

   if -1.10000000000000008e56 < y < 6.6000000000000003e-71

   1. Initial program 88.0%

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

      1. add-cube-cbrt 87.7%

         \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}} \]

      2. times-frac 99.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t}{\sqrt[3]{a - z}}} \]

      3. pow2 99.3%

         \[\leadsto x + \frac{y - z}{\color{blue}{{\left(\sqrt[3]{a - z}\right)}^{2}}} \cdot \frac{t}{\sqrt[3]{a - z}} \]

   4. Applied egg-rr 99.3%

      \[\leadsto x + \color{blue}{\frac{y - z}{{\left(\sqrt[3]{a - z}\right)}^{2}} \cdot \frac{t}{\sqrt[3]{a - z}}} \]
   5. Step-by-step derivation

      1. clear-num 99.4%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z}}} \cdot \frac{t}{\sqrt[3]{a - z}} \]

      2. frac-times 98.6%

         \[\leadsto x + \color{blue}{\frac{1 \cdot t}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z} \cdot \sqrt[3]{a - z}}} \]

      3. *-un-lft-identity 98.6%

         \[\leadsto x + \frac{\color{blue}{t}}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z} \cdot \sqrt[3]{a - z}} \]

   6. Applied egg-rr 98.6%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z} \cdot \sqrt[3]{a - z}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 98.6%

         \[\leadsto x + \frac{t}{\color{blue}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2} \cdot \sqrt[3]{a - z}}{y - z}}} \]

      2. unpow2 98.6%

         \[\leadsto x + \frac{t}{\frac{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right)} \cdot \sqrt[3]{a - z}}{y - z}} \]

      3. rem-3cbrt-lft 99.2%

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

   8. Simplified 99.2%

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

   9. Taylor expanded in y around 0 81.8%

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

       1. mul-1-neg 81.8%

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

       2. unsub-neg 81.8%

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

       3. associate-/l* 93.0%

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

   11. Simplified 93.0%

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

   if 6.6000000000000003e-71 < y

   1. Initial program 89.3%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

      1. clear-num 98.7%

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

      2. associate-/r/ 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in y around inf 91.3%

      \[\leadsto x + \color{blue}{y} \cdot \left(\frac{1}{a - z} \cdot t\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-71}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t \cdot \frac{-1}{z - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z - a}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{-110} \lor \neg \left(y \leq 1.05 \cdot 10^{-70}\right):\\ \;\;\;\;x - y \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- z a))))
   (if (or (<= y -3.9e-110) (not (<= y 1.05e-70)))
     (- x (* y t_1))
     (+ x (* z t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (z - a);
	double tmp;
	if ((y <= -3.9e-110) || !(y <= 1.05e-70)) {
		tmp = x - (y * t_1);
	} else {
		tmp = x + (z * 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 = t / (z - a)
    if ((y <= (-3.9d-110)) .or. (.not. (y <= 1.05d-70))) then
        tmp = x - (y * t_1)
    else
        tmp = x + (z * 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 = t / (z - a);
	double tmp;
	if ((y <= -3.9e-110) || !(y <= 1.05e-70)) {
		tmp = x - (y * t_1);
	} else {
		tmp = x + (z * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (z - a)
	tmp = 0
	if (y <= -3.9e-110) or not (y <= 1.05e-70):
		tmp = x - (y * t_1)
	else:
		tmp = x + (z * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(z - a))
	tmp = 0.0
	if ((y <= -3.9e-110) || !(y <= 1.05e-70))
		tmp = Float64(x - Float64(y * t_1));
	else
		tmp = Float64(x + Float64(z * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (z - a);
	tmp = 0.0;
	if ((y <= -3.9e-110) || ~((y <= 1.05e-70)))
		tmp = x - (y * t_1);
	else
		tmp = x + (z * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -3.9e-110], N[Not[LessEqual[y, 1.05e-70]], $MachinePrecision]], N[(x - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9e-110 or 1.0500000000000001e-70 < y

   1. Initial program 85.6%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around inf 90.5%

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

   if -3.9e-110 < y < 1.0500000000000001e-70

   1. Initial program 87.6%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 84.4%

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

      1. associate-*r/ 84.4%

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

      2. mul-1-neg 84.4%

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

      3. distribute-rgt-neg-out 84.4%

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

      4. associate-*l/ 94.6%

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

      5. *-commutative 94.6%

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

      6. distribute-lft-neg-out 94.6%

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

      7. distribute-rgt-neg-in 94.6%

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

      8. distribute-frac-neg2 94.6%

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

      9. neg-sub0 94.6%

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

      10. sub-neg 94.6%

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

      11. +-commutative 94.6%

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

      12. associate--r+ 94.6%

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

      13. neg-sub0 94.6%

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

      14. remove-double-neg 94.6%

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

   7. Simplified 94.6%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-110} \lor \neg \left(y \leq 1.05 \cdot 10^{-70}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.5e+56)
   (- x (* y (/ t (- z a))))
   (if (<= y 5.2e-68) (+ x (* t (/ z (- z a)))) (+ x (/ y (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.5e+56) {
		tmp = x - (y * (t / (z - a)));
	} else if (y <= 5.2e-68) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.5d+56)) then
        tmp = x - (y * (t / (z - a)))
    else if (y <= 5.2d-68) then
        tmp = x + (t * (z / (z - a)))
    else
        tmp = x + (y / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.5e+56) {
		tmp = x - (y * (t / (z - a)));
	} else if (y <= 5.2e-68) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.5e+56:
		tmp = x - (y * (t / (z - a)))
	elif y <= 5.2e-68:
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.5e+56)
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	elseif (y <= 5.2e-68)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.5e+56)
		tmp = x - (y * (t / (z - a)));
	elseif (y <= 5.2e-68)
		tmp = x + (t * (z / (z - a)));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.5e+56], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-68], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.49999999999999999e56

   1. Initial program 77.6%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around inf 96.0%

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

   if -3.49999999999999999e56 < y < 5.1999999999999996e-68

   1. Initial program 88.0%

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

      1. add-cube-cbrt 87.7%

         \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}} \]

      2. times-frac 99.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t}{\sqrt[3]{a - z}}} \]

      3. pow2 99.3%

         \[\leadsto x + \frac{y - z}{\color{blue}{{\left(\sqrt[3]{a - z}\right)}^{2}}} \cdot \frac{t}{\sqrt[3]{a - z}} \]

   4. Applied egg-rr 99.3%

      \[\leadsto x + \color{blue}{\frac{y - z}{{\left(\sqrt[3]{a - z}\right)}^{2}} \cdot \frac{t}{\sqrt[3]{a - z}}} \]
   5. Step-by-step derivation

      1. clear-num 99.4%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z}}} \cdot \frac{t}{\sqrt[3]{a - z}} \]

      2. frac-times 98.6%

         \[\leadsto x + \color{blue}{\frac{1 \cdot t}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z} \cdot \sqrt[3]{a - z}}} \]

      3. *-un-lft-identity 98.6%

         \[\leadsto x + \frac{\color{blue}{t}}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z} \cdot \sqrt[3]{a - z}} \]

   6. Applied egg-rr 98.6%

      \[\leadsto x + \color{blue}{\frac{t}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z} \cdot \sqrt[3]{a - z}}} \]
   7. Step-by-step derivation

      1. associate-*l/ 98.6%

         \[\leadsto x + \frac{t}{\color{blue}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2} \cdot \sqrt[3]{a - z}}{y - z}}} \]

      2. unpow2 98.6%

         \[\leadsto x + \frac{t}{\frac{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right)} \cdot \sqrt[3]{a - z}}{y - z}} \]

      3. rem-3cbrt-lft 99.2%

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

   8. Simplified 99.2%

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

   9. Taylor expanded in y around 0 81.8%

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

       1. mul-1-neg 81.8%

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

       2. unsub-neg 81.8%

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

       3. associate-/l* 93.0%

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

   11. Simplified 93.0%

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

   if 5.1999999999999996e-68 < y

   1. Initial program 89.3%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around inf 91.3%

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

      1. clear-num 91.3%

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

      2. un-div-inv 91.3%

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

   7. Applied egg-rr 91.3%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-68}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z - a}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{-110}:\\ \;\;\;\;x - y \cdot t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;x + z \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- z a))))
   (if (<= y -3.7e-110)
     (- x (* y t_1))
     (if (<= y 3.6e-68) (+ x (* z t_1)) (+ x (/ y (/ (- a z) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (z - a);
	double tmp;
	if (y <= -3.7e-110) {
		tmp = x - (y * t_1);
	} else if (y <= 3.6e-68) {
		tmp = x + (z * t_1);
	} else {
		tmp = x + (y / ((a - z) / 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 = t / (z - a)
    if (y <= (-3.7d-110)) then
        tmp = x - (y * t_1)
    else if (y <= 3.6d-68) then
        tmp = x + (z * t_1)
    else
        tmp = x + (y / ((a - z) / 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 = t / (z - a);
	double tmp;
	if (y <= -3.7e-110) {
		tmp = x - (y * t_1);
	} else if (y <= 3.6e-68) {
		tmp = x + (z * t_1);
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (z - a)
	tmp = 0
	if y <= -3.7e-110:
		tmp = x - (y * t_1)
	elif y <= 3.6e-68:
		tmp = x + (z * t_1)
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(z - a))
	tmp = 0.0
	if (y <= -3.7e-110)
		tmp = Float64(x - Float64(y * t_1));
	elseif (y <= 3.6e-68)
		tmp = Float64(x + Float64(z * t_1));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (z - a);
	tmp = 0.0;
	if (y <= -3.7e-110)
		tmp = x - (y * t_1);
	elseif (y <= 3.6e-68)
		tmp = x + (z * t_1);
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e-110], N[(x - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-68], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.70000000000000016e-110

   1. Initial program 82.3%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in y around inf 89.8%

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

   if -3.70000000000000016e-110 < y < 3.60000000000000007e-68

   1. Initial program 87.6%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 84.4%

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

      1. associate-*r/ 84.4%

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

      2. mul-1-neg 84.4%

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

      3. distribute-rgt-neg-out 84.4%

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

      4. associate-*l/ 94.6%

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

      5. *-commutative 94.6%

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

      6. distribute-lft-neg-out 94.6%

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

      7. distribute-rgt-neg-in 94.6%

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

      8. distribute-frac-neg2 94.6%

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

      9. neg-sub0 94.6%

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

      10. sub-neg 94.6%

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

      11. +-commutative 94.6%

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

      12. associate--r+ 94.6%

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

      13. neg-sub0 94.6%

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

      14. remove-double-neg 94.6%

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

   7. Simplified 94.6%

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

   if 3.60000000000000007e-68 < y

   1. Initial program 89.3%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around inf 91.3%

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

      1. clear-num 91.3%

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

      2. un-div-inv 91.3%

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

   7. Applied egg-rr 91.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-110}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-68}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-20} \lor \neg \left(z \leq 1.3 \cdot 10^{-16}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e-20) (not (<= z 1.3e-16))) (+ x t) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e-20) || !(z <= 1.3e-16)) {
		tmp = x + t;
	} else {
		tmp = x + (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 <= (-3.8d-20)) .or. (.not. (z <= 1.3d-16))) then
        tmp = x + t
    else
        tmp = x + (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 <= -3.8e-20) || !(z <= 1.3e-16)) {
		tmp = x + t;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e-20) or not (z <= 1.3e-16):
		tmp = x + t
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.8e-20) || !(z <= 1.3e-16))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.8e-20) || ~((z <= 1.3e-16)))
		tmp = x + t;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.8e-20], N[Not[LessEqual[z, 1.3e-16]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999998e-20 or 1.2999999999999999e-16 < z

   1. Initial program 77.6%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 75.9%

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

   if -3.7999999999999998e-20 < z < 1.2999999999999999e-16

   1. Initial program 95.4%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around inf 95.9%

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

   6. Taylor expanded in a around inf 83.4%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-20} \lor \neg \left(z \leq 1.3 \cdot 10^{-16}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-20} \lor \neg \left(z \leq 2.6 \cdot 10^{-11}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e-20) (not (<= z 2.6e-11))) (+ x t) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e-20) || !(z <= 2.6e-11)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / 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 <= (-4.8d-20)) .or. (.not. (z <= 2.6d-11))) then
        tmp = x + t
    else
        tmp = x + (t * (y / 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 <= -4.8e-20) || !(z <= 2.6e-11)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e-20) or not (z <= 2.6e-11):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e-20) || !(z <= 2.6e-11))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e-20) || ~((z <= 2.6e-11)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e-20], N[Not[LessEqual[z, 2.6e-11]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999986e-20 or 2.6000000000000001e-11 < z

   1. Initial program 77.6%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 75.9%

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

   if -4.79999999999999986e-20 < z < 2.6000000000000001e-11

   1. Initial program 95.4%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 81.0%

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

      1. associate-/l* 83.2%

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

   7. Simplified 83.2%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-20} \lor \neg \left(z \leq 2.6 \cdot 10^{-11}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-20}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.86 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.9e-20)
   (+ x t)
   (if (<= z 1.86e-59) (+ x (* y (/ t a))) (- x (* y (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.9e-20) {
		tmp = x + t;
	} else if (z <= 1.86e-59) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y * (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 (z <= (-4.9d-20)) then
        tmp = x + t
    else if (z <= 1.86d-59) then
        tmp = x + (y * (t / a))
    else
        tmp = x - (y * (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 (z <= -4.9e-20) {
		tmp = x + t;
	} else if (z <= 1.86e-59) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.9e-20:
		tmp = x + t
	elif z <= 1.86e-59:
		tmp = x + (y * (t / a))
	else:
		tmp = x - (y * (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.9e-20)
		tmp = Float64(x + t);
	elseif (z <= 1.86e-59)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(y * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.9e-20)
		tmp = x + t;
	elseif (z <= 1.86e-59)
		tmp = x + (y * (t / a));
	else
		tmp = x - (y * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.9e-20], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.86e-59], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9000000000000002e-20

   1. Initial program 73.0%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 77.1%

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

   if -4.9000000000000002e-20 < z < 1.86000000000000004e-59

   1. Initial program 95.7%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 96.3%

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

   6. Taylor expanded in a around inf 84.1%

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

   if 1.86000000000000004e-59 < z

   1. Initial program 84.4%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 79.1%

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

   6. Taylor expanded in a around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. neg-mul-1 75.0%

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

   8. Simplified 75.0%

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

      1. *-commutative 75.0%

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

      2. add-sqr-sqrt 34.4%

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

      3. sqrt-unprod 60.5%

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

      4. sqr-neg 60.5%

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

      5. sqrt-unprod 31.1%

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

      6. add-sqr-sqrt 58.5%

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

      7. cancel-sign-sub 58.5%

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

      8. distribute-frac-neg 58.5%

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

      9. *-commutative 58.5%

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

      10. add-sqr-sqrt 27.4%

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

      11. sqrt-unprod 65.5%

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

      12. sqr-neg 65.5%

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

      13. sqrt-unprod 40.7%

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

      14. add-sqr-sqrt 75.0%

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

   10. Applied egg-rr 75.0%

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

Alternative 9: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+58}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+58) (+ x t) (- x (* y (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+58) {
		tmp = x + t;
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+58)) then
        tmp = x + t
    else
        tmp = x - (y * (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+58) {
		tmp = x + t;
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+58:
		tmp = x + t
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+58)
		tmp = Float64(x + t);
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+58)
		tmp = x + t;
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+58], N[(x + t), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000001e58

   1. Initial program 61.1%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in z around inf 85.8%

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

   if -1.45000000000000001e58 < z

   1. Initial program 91.9%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around inf 88.2%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+58}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-20} \lor \neg \left(z \leq 36\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e-20) (not (<= z 36.0))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-20) || !(z <= 36.0)) {
		tmp = x + t;
	} 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 ((z <= (-2.5d-20)) .or. (.not. (z <= 36.0d0))) then
        tmp = x + t
    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 ((z <= -2.5e-20) || !(z <= 36.0)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e-20) or not (z <= 36.0):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e-20) || !(z <= 36.0))
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e-20) || ~((z <= 36.0)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e-20], N[Not[LessEqual[z, 36.0]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999999e-20 or 36 < z

   1. Initial program 77.1%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 76.1%

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

   if -2.4999999999999999e-20 < z < 36

   1. Initial program 95.5%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in x around inf 61.6%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-20} \lor \neg \left(z \leq 36\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-262}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.3e-262) x (if (<= x 2.7e-94) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.3e-262) {
		tmp = x;
	} else if (x <= 2.7e-94) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3.3d-262)) then
        tmp = x
    else if (x <= 2.7d-94) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.3e-262) {
		tmp = x;
	} else if (x <= 2.7e-94) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.3e-262:
		tmp = x
	elif x <= 2.7e-94:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.3e-262)
		tmp = x;
	elseif (x <= 2.7e-94)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.3e-262)
		tmp = x;
	elseif (x <= 2.7e-94)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.3e-262], x, If[LessEqual[x, 2.7e-94], t, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3000000000000003e-262 or 2.7000000000000001e-94 < x

   1. Initial program 87.2%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around inf 68.7%

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

   if -3.3000000000000003e-262 < x < 2.7000000000000001e-94

   1. Initial program 82.7%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in a around 0 51.1%

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

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

      3. associate-/l* 62.3%

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

   7. Simplified 62.3%

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

   8. Taylor expanded in t around inf 59.2%

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

   9. Taylor expanded in y around 0 33.9%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (t / ((a - z) / (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. add-cube-cbrt 86.0%

      \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}} \]

   2. times-frac 98.6%

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t}{\sqrt[3]{a - z}}} \]

   3. pow2 98.6%

      \[\leadsto x + \frac{y - z}{\color{blue}{{\left(\sqrt[3]{a - z}\right)}^{2}}} \cdot \frac{t}{\sqrt[3]{a - z}} \]

4. Applied egg-rr 98.6%

   \[\leadsto x + \color{blue}{\frac{y - z}{{\left(\sqrt[3]{a - z}\right)}^{2}} \cdot \frac{t}{\sqrt[3]{a - z}}} \]
5. Step-by-step derivation

   1. clear-num 98.6%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z}}} \cdot \frac{t}{\sqrt[3]{a - z}} \]

   2. frac-times 97.7%

      \[\leadsto x + \color{blue}{\frac{1 \cdot t}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z} \cdot \sqrt[3]{a - z}}} \]

   3. *-un-lft-identity 97.7%

      \[\leadsto x + \frac{\color{blue}{t}}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z} \cdot \sqrt[3]{a - z}} \]

6. Applied egg-rr 97.7%

   \[\leadsto x + \color{blue}{\frac{t}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{y - z} \cdot \sqrt[3]{a - z}}} \]
7. Step-by-step derivation

   1. associate-*l/ 97.7%

      \[\leadsto x + \frac{t}{\color{blue}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2} \cdot \sqrt[3]{a - z}}{y - z}}} \]

   2. unpow2 97.7%

      \[\leadsto x + \frac{t}{\frac{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right)} \cdot \sqrt[3]{a - z}}{y - z}} \]

   3. rem-3cbrt-lft 98.3%

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

8. Simplified 98.3%

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

Alternative 13: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

Alternative 14: 19.0% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in a around 0 60.4%

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

   1. mul-1-neg 60.4%

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

   2. unsub-neg 60.4%

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

   3. associate-/l* 67.4%

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

7. Simplified 67.4%

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

8. Taylor expanded in t around inf 27.1%

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

9. Taylor expanded in y around 0 14.7%

   \[\leadsto \color{blue}{t} \]
10. Add Preprocessing

Developer Target 1: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} 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) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    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) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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