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

Percentage Accurate: 85.8% → 99.4%

Time: 10.7s

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: 85.8% 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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := \frac{t\_1}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+253} \lor \neg \left(t\_2 \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t\_1}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (/ t_1 (- a z))))
   (if (or (<= t_2 -2e+253) (not (<= t_2 2e+306)))
     (+ x (* (- y z) (/ t (- a z))))
     (- x (/ t_1 (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * t;
	double t_2 = t_1 / (a - z);
	double tmp;
	if ((t_2 <= -2e+253) || !(t_2 <= 2e+306)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x - (t_1 / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * t
    t_2 = t_1 / (a - z)
    if ((t_2 <= (-2d+253)) .or. (.not. (t_2 <= 2d+306))) then
        tmp = x + ((y - z) * (t / (a - z)))
    else
        tmp = x - (t_1 / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * t;
	double t_2 = t_1 / (a - z);
	double tmp;
	if ((t_2 <= -2e+253) || !(t_2 <= 2e+306)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x - (t_1 / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * t
	t_2 = t_1 / (a - z)
	tmp = 0
	if (t_2 <= -2e+253) or not (t_2 <= 2e+306):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = x - (t_1 / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(t_1 / Float64(a - z))
	tmp = 0.0
	if ((t_2 <= -2e+253) || !(t_2 <= 2e+306))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t_1 / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * t;
	t_2 = t_1 / (a - z);
	tmp = 0.0;
	if ((t_2 <= -2e+253) || ~((t_2 <= 2e+306)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = x - (t_1 / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+253], N[Not[LessEqual[t$95$2, 2e+306]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t$95$1 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -1.9999999999999999e253 or 2.00000000000000003e306 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 44.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -1.9999999999999999e253 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2.00000000000000003e306

   1. Initial program 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -2 \cdot 10^{+253} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+127}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-42}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+79}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+127)
   (+ t x)
   (if (<= z -4.4e-42)
     (- x (* y (/ t z)))
     (if (<= z 6.6e-124)
       (+ x (/ (* y t) a))
       (if (<= z 2.05e+79) (- x (/ y (/ z t))) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+127) {
		tmp = t + x;
	} else if (z <= -4.4e-42) {
		tmp = x - (y * (t / z));
	} else if (z <= 6.6e-124) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.05e+79) {
		tmp = x - (y / (z / t));
	} else {
		tmp = t + 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 <= (-3.4d+127)) then
        tmp = t + x
    else if (z <= (-4.4d-42)) then
        tmp = x - (y * (t / z))
    else if (z <= 6.6d-124) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.05d+79) then
        tmp = x - (y / (z / t))
    else
        tmp = t + 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 <= -3.4e+127) {
		tmp = t + x;
	} else if (z <= -4.4e-42) {
		tmp = x - (y * (t / z));
	} else if (z <= 6.6e-124) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.05e+79) {
		tmp = x - (y / (z / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e+127:
		tmp = t + x
	elif z <= -4.4e-42:
		tmp = x - (y * (t / z))
	elif z <= 6.6e-124:
		tmp = x + ((y * t) / a)
	elif z <= 2.05e+79:
		tmp = x - (y / (z / t))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+127)
		tmp = Float64(t + x);
	elseif (z <= -4.4e-42)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 6.6e-124)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.05e+79)
		tmp = Float64(x - Float64(y / Float64(z / t)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.4e+127)
		tmp = t + x;
	elseif (z <= -4.4e-42)
		tmp = x - (y * (t / z));
	elseif (z <= 6.6e-124)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.05e+79)
		tmp = x - (y / (z / t));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+127], N[(t + x), $MachinePrecision], If[LessEqual[z, -4.4e-42], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-124], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+79], N[(x - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.39999999999999977e127 or 2.05e79 < z

   1. Initial program 64.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 84.7%

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

   if -3.39999999999999977e127 < z < -4.4000000000000001e-42

   1. Initial program 91.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 88.8%

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

   8. Taylor expanded in a around 0 83.4%

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

      1. neg-mul-1 83.4%

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

      2. distribute-neg-frac2 83.4%

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

   10. Simplified 83.4%

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

   11. Taylor expanded in y around 0 78.2%

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

       1. associate-*r/ 78.2%

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

       2. *-commutative 78.2%

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

       3. neg-mul-1 78.2%

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

       4. distribute-lft-neg-in 78.2%

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

       5. associate-*r/ 83.6%

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

       6. *-commutative 83.6%

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

   13. Simplified 83.6%

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

   if -4.4000000000000001e-42 < z < 6.59999999999999969e-124

   1. Initial program 96.5%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0 81.3%

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

      1. +-commutative 81.3%

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

   7. Simplified 81.3%

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

   if 6.59999999999999969e-124 < z < 2.05e79

   1. Initial program 95.0%

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

      1. clear-num 97.5%

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

      2. un-div-inv 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in y around inf 89.1%

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

   8. Taylor expanded in a around 0 75.3%

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

      1. neg-mul-1 75.3%

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

      2. distribute-neg-frac2 75.3%

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

   10. Simplified 75.3%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+127}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-42}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-124}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+79}:\\ \;\;\;\;x - \frac{y}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+128}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ t z)))))
   (if (<= z -2.05e+128)
     (+ t x)
     (if (<= z -8.5e-43)
       t_1
       (if (<= z 3.1e-123)
         (+ x (/ (* y t) a))
         (if (<= z 1.05e+78) t_1 (+ t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -2.05e+128) {
		tmp = t + x;
	} else if (z <= -8.5e-43) {
		tmp = t_1;
	} else if (z <= 3.1e-123) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.05e+78) {
		tmp = t_1;
	} else {
		tmp = t + 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (t / z))
    if (z <= (-2.05d+128)) then
        tmp = t + x
    else if (z <= (-8.5d-43)) then
        tmp = t_1
    else if (z <= 3.1d-123) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.05d+78) then
        tmp = t_1
    else
        tmp = t + x
    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 / z));
	double tmp;
	if (z <= -2.05e+128) {
		tmp = t + x;
	} else if (z <= -8.5e-43) {
		tmp = t_1;
	} else if (z <= 3.1e-123) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.05e+78) {
		tmp = t_1;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (t / z))
	tmp = 0
	if z <= -2.05e+128:
		tmp = t + x
	elif z <= -8.5e-43:
		tmp = t_1
	elif z <= 3.1e-123:
		tmp = x + ((y * t) / a)
	elif z <= 1.05e+78:
		tmp = t_1
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (z <= -2.05e+128)
		tmp = Float64(t + x);
	elseif (z <= -8.5e-43)
		tmp = t_1;
	elseif (z <= 3.1e-123)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.05e+78)
		tmp = t_1;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (t / z));
	tmp = 0.0;
	if (z <= -2.05e+128)
		tmp = t + x;
	elseif (z <= -8.5e-43)
		tmp = t_1;
	elseif (z <= 3.1e-123)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.05e+78)
		tmp = t_1;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+128], N[(t + x), $MachinePrecision], If[LessEqual[z, -8.5e-43], t$95$1, If[LessEqual[z, 3.1e-123], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+78], t$95$1, N[(t + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05000000000000006e128 or 1.05e78 < z

   1. Initial program 64.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 84.7%

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

   if -2.05000000000000006e128 < z < -8.50000000000000056e-43 or 3.09999999999999998e-123 < z < 1.05e78

   1. Initial program 93.6%

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

      1. clear-num 98.5%

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

      2. un-div-inv 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in y around inf 88.9%

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

   8. Taylor expanded in a around 0 79.1%

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

      1. neg-mul-1 79.1%

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

      2. distribute-neg-frac2 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in y around 0 76.6%

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

       1. associate-*r/ 76.6%

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

       2. *-commutative 76.6%

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

       3. neg-mul-1 76.6%

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

       4. distribute-lft-neg-in 76.6%

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

       5. associate-*r/ 79.1%

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

       6. *-commutative 79.1%

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

   13. Simplified 79.1%

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

   if -8.50000000000000056e-43 < z < 3.09999999999999998e-123

   1. Initial program 96.5%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0 81.3%

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

      1. +-commutative 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+128}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-43}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+78}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-44}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+129)
   (+ t x)
   (if (<= z -1.8e-44)
     (- x (* t (/ y z)))
     (if (<= z 1.15e+67) (+ x (/ (* y t) a)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+129) {
		tmp = t + x;
	} else if (z <= -1.8e-44) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.15e+67) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t + 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 <= (-9.5d+129)) then
        tmp = t + x
    else if (z <= (-1.8d-44)) then
        tmp = x - (t * (y / z))
    else if (z <= 1.15d+67) then
        tmp = x + ((y * t) / a)
    else
        tmp = t + 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 <= -9.5e+129) {
		tmp = t + x;
	} else if (z <= -1.8e-44) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.15e+67) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+129:
		tmp = t + x
	elif z <= -1.8e-44:
		tmp = x - (t * (y / z))
	elif z <= 1.15e+67:
		tmp = x + ((y * t) / a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+129)
		tmp = Float64(t + x);
	elseif (z <= -1.8e-44)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.15e+67)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+129)
		tmp = t + x;
	elseif (z <= -1.8e-44)
		tmp = x - (t * (y / z));
	elseif (z <= 1.15e+67)
		tmp = x + ((y * t) / a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+129], N[(t + x), $MachinePrecision], If[LessEqual[z, -1.8e-44], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+67], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000004e129 or 1.1499999999999999e67 < z

   1. Initial program 65.6%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around inf 84.0%

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

   if -9.5000000000000004e129 < z < -1.7999999999999999e-44

   1. Initial program 91.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 88.8%

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

   8. Taylor expanded in a around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. unsub-neg 78.2%

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

      3. associate-/l* 83.4%

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

   10. Simplified 83.4%

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

   if -1.7999999999999999e-44 < z < 1.1499999999999999e67

   1. Initial program 96.0%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around 0 76.8%

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

      1. +-commutative 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-44}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+76} \lor \neg \left(z \leq 1.2 \cdot 10^{+67}\right):\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+76) (not (<= z 1.2e+67)))
   (+ x (* t (/ (- z y) z)))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+76) || !(z <= 1.2e+67)) {
		tmp = x + (t * ((z - y) / z));
	} 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 ((z <= (-1.45d+76)) .or. (.not. (z <= 1.2d+67))) then
        tmp = x + (t * ((z - y) / z))
    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 ((z <= -1.45e+76) || !(z <= 1.2e+67)) {
		tmp = x + (t * ((z - y) / z));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+76) or not (z <= 1.2e+67):
		tmp = x + (t * ((z - y) / z))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+76) || !(z <= 1.2e+67))
		tmp = Float64(x + Float64(t * Float64(Float64(z - y) / z)));
	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 ((z <= -1.45e+76) || ~((z <= 1.2e+67)))
		tmp = x + (t * ((z - y) / z));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+76], N[Not[LessEqual[z, 1.2e+67]], $MachinePrecision]], N[(x + N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4500000000000001e76 or 1.20000000000000001e67 < z

   1. Initial program 65.8%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in a around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. unsub-neg 64.0%

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

      3. associate-/l* 93.0%

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

   7. Simplified 93.0%

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

   if -1.4500000000000001e76 < z < 1.20000000000000001e67

   1. Initial program 96.1%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

      1. clear-num 95.3%

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

      2. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in y around inf 90.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+76} \lor \neg \left(z \leq 1.2 \cdot 10^{+67}\right):\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-7} \lor \neg \left(y \leq 8.2 \cdot 10^{+71}\right):\\ \;\;\;\;x + y \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- a z))))
   (if (or (<= y -4.8e-7) (not (<= y 8.2e+71)))
     (+ 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 / (a - z);
	double tmp;
	if ((y <= -4.8e-7) || !(y <= 8.2e+71)) {
		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 / (a - z)
    if ((y <= (-4.8d-7)) .or. (.not. (y <= 8.2d+71))) 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 / (a - z);
	double tmp;
	if ((y <= -4.8e-7) || !(y <= 8.2e+71)) {
		tmp = x + (y * t_1);
	} else {
		tmp = x - (z * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a - z)
	tmp = 0
	if (y <= -4.8e-7) or not (y <= 8.2e+71):
		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(a - z))
	tmp = 0.0
	if ((y <= -4.8e-7) || !(y <= 8.2e+71))
		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 / (a - z);
	tmp = 0.0;
	if ((y <= -4.8e-7) || ~((y <= 8.2e+71)))
		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[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -4.8e-7], N[Not[LessEqual[y, 8.2e+71]], $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 < -4.79999999999999957e-7 or 8.2000000000000004e71 < y

   1. Initial program 87.0%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around inf 91.8%

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

   if -4.79999999999999957e-7 < y < 8.2000000000000004e71

   1. Initial program 82.7%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. mul-1-neg 75.0%

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

      3. distribute-rgt-neg-out 75.0%

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

      4. associate-*l/ 88.2%

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

      5. *-commutative 88.2%

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

      6. distribute-lft-neg-out 88.2%

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

      7. distribute-rgt-neg-in 88.2%

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

      8. distribute-frac-neg2 88.2%

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

      9. neg-sub0 88.2%

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

      10. sub-neg 88.2%

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

      11. +-commutative 88.2%

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

      12. associate--r+ 88.2%

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

      13. neg-sub0 88.2%

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

      14. remove-double-neg 88.2%

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

   7. Simplified 88.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-7} \lor \neg \left(y \leq 8.2 \cdot 10^{+71}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+129} \lor \neg \left(z \leq 2.55 \cdot 10^{+79}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.8e+129) (not (<= z 2.55e+79)))
   (+ t x)
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.8e+129) || !(z <= 2.55e+79)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / (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 ((z <= (-7.8d+129)) .or. (.not. (z <= 2.55d+79))) then
        tmp = t + x
    else
        tmp = x + (y * (t / (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 ((z <= -7.8e+129) || !(z <= 2.55e+79)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.8e+129) or not (z <= 2.55e+79):
		tmp = t + x
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.8e+129) || !(z <= 2.55e+79))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.8e+129) || ~((z <= 2.55e+79)))
		tmp = t + x;
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.8e+129], N[Not[LessEqual[z, 2.55e+79]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.7999999999999994e129 or 2.5500000000000001e79 < z

   1. Initial program 64.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around inf 84.7%

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

   if -7.7999999999999994e129 < z < 2.5500000000000001e79

   1. Initial program 95.2%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 89.3%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+129} \lor \neg \left(z \leq 2.55 \cdot 10^{+79}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+73}:\\ \;\;\;\;x - z \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- a z))))
   (if (<= y -5.4e-7)
     (+ x (/ (* y t) (- a z)))
     (if (<= y 2.9e+73) (- x (* z t_1)) (+ x (* y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a - z);
	double tmp;
	if (y <= -5.4e-7) {
		tmp = x + ((y * t) / (a - z));
	} else if (y <= 2.9e+73) {
		tmp = x - (z * t_1);
	} else {
		tmp = x + (y * 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 / (a - z)
    if (y <= (-5.4d-7)) then
        tmp = x + ((y * t) / (a - z))
    else if (y <= 2.9d+73) then
        tmp = x - (z * t_1)
    else
        tmp = x + (y * 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 / (a - z);
	double tmp;
	if (y <= -5.4e-7) {
		tmp = x + ((y * t) / (a - z));
	} else if (y <= 2.9e+73) {
		tmp = x - (z * t_1);
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a - z)
	tmp = 0
	if y <= -5.4e-7:
		tmp = x + ((y * t) / (a - z))
	elif y <= 2.9e+73:
		tmp = x - (z * t_1)
	else:
		tmp = x + (y * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a - z))
	tmp = 0.0
	if (y <= -5.4e-7)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	elseif (y <= 2.9e+73)
		tmp = Float64(x - Float64(z * t_1));
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a - z);
	tmp = 0.0;
	if (y <= -5.4e-7)
		tmp = x + ((y * t) / (a - z));
	elseif (y <= 2.9e+73)
		tmp = x - (z * t_1);
	else
		tmp = x + (y * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e-7], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+73], N[(x - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.40000000000000018e-7

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf 88.5%

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

   if -5.40000000000000018e-7 < y < 2.9000000000000002e73

   1. Initial program 82.7%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. mul-1-neg 75.0%

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

      3. distribute-rgt-neg-out 75.0%

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

      4. associate-*l/ 88.2%

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

      5. *-commutative 88.2%

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

      6. distribute-lft-neg-out 88.2%

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

      7. distribute-rgt-neg-in 88.2%

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

      8. distribute-frac-neg2 88.2%

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

      9. neg-sub0 88.2%

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

      10. sub-neg 88.2%

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

      11. +-commutative 88.2%

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

      12. associate--r+ 88.2%

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

      13. neg-sub0 88.2%

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

      14. remove-double-neg 88.2%

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

   7. Simplified 88.2%

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

   if 2.9000000000000002e73 < y

   1. Initial program 78.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 97.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+73}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z}\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+72}:\\ \;\;\;\;x - z \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (- a z))))
   (if (<= y -2.05e-7)
     (+ x (/ y (/ (- a z) t)))
     (if (<= y 4.5e+72) (- x (* z t_1)) (+ x (* y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a - z);
	double tmp;
	if (y <= -2.05e-7) {
		tmp = x + (y / ((a - z) / t));
	} else if (y <= 4.5e+72) {
		tmp = x - (z * t_1);
	} else {
		tmp = x + (y * 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 / (a - z)
    if (y <= (-2.05d-7)) then
        tmp = x + (y / ((a - z) / t))
    else if (y <= 4.5d+72) then
        tmp = x - (z * t_1)
    else
        tmp = x + (y * 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 / (a - z);
	double tmp;
	if (y <= -2.05e-7) {
		tmp = x + (y / ((a - z) / t));
	} else if (y <= 4.5e+72) {
		tmp = x - (z * t_1);
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a - z)
	tmp = 0
	if y <= -2.05e-7:
		tmp = x + (y / ((a - z) / t))
	elif y <= 4.5e+72:
		tmp = x - (z * t_1)
	else:
		tmp = x + (y * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a - z))
	tmp = 0.0
	if (y <= -2.05e-7)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	elseif (y <= 4.5e+72)
		tmp = Float64(x - Float64(z * t_1));
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a - z);
	tmp = 0.0;
	if (y <= -2.05e-7)
		tmp = x + (y / ((a - z) / t));
	elseif (y <= 4.5e+72)
		tmp = x - (z * t_1);
	else
		tmp = x + (y * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.05e-7], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+72], N[(x - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e-7

   1. Initial program 93.1%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

      1. clear-num 92.3%

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

      2. un-div-inv 92.4%

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

   6. Applied egg-rr 92.4%

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

   7. Taylor expanded in y around inf 87.5%

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

   if -2.05e-7 < y < 4.4999999999999998e72

   1. Initial program 82.7%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. mul-1-neg 75.0%

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

      3. distribute-rgt-neg-out 75.0%

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

      4. associate-*l/ 88.2%

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

      5. *-commutative 88.2%

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

      6. distribute-lft-neg-out 88.2%

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

      7. distribute-rgt-neg-in 88.2%

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

      8. distribute-frac-neg2 88.2%

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

      9. neg-sub0 88.2%

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

      10. sub-neg 88.2%

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

      11. +-commutative 88.2%

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

      12. associate--r+ 88.2%

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

      13. neg-sub0 88.2%

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

      14. remove-double-neg 88.2%

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

   7. Simplified 88.2%

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

   if 4.4999999999999998e72 < y

   1. Initial program 78.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 97.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+72}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+36} \lor \neg \left(z \leq 2.1 \cdot 10^{+69}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e+36) (not (<= z 2.1e+69))) (+ t x) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+36) || !(z <= 2.1e+69)) {
		tmp = t + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.8d+36)) .or. (.not. (z <= 2.1d+69))) then
        tmp = t + x
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+36) || !(z <= 2.1e+69)) {
		tmp = t + x;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e+36) or not (z <= 2.1e+69):
		tmp = t + x
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e+36) || !(z <= 2.1e+69))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.8e+36) || ~((z <= 2.1e+69)))
		tmp = t + x;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e+36], N[Not[LessEqual[z, 2.1e+69]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e36 or 2.10000000000000015e69 < z

   1. Initial program 69.1%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 79.2%

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

   if -5.8e36 < z < 2.10000000000000015e69

   1. Initial program 95.9%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

      1. clear-num 95.0%

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

      2. un-div-inv 95.7%

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

   6. Applied egg-rr 95.7%

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

   7. Taylor expanded in y around inf 89.3%

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

   8. Taylor expanded in a around inf 74.5%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+36} \lor \neg \left(z \leq 2.1 \cdot 10^{+69}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+37} \lor \neg \left(z \leq 1.15 \cdot 10^{+67}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.2e+37) (not (<= z 1.15e+67))) (+ t x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e+37) || !(z <= 1.15e+67)) {
		tmp = t + x;
	} 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 <= (-2.2d+37)) .or. (.not. (z <= 1.15d+67))) then
        tmp = t + x
    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 <= -2.2e+37) || !(z <= 1.15e+67)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.2e+37) or not (z <= 1.15e+67):
		tmp = t + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.2e+37) || !(z <= 1.15e+67))
		tmp = Float64(t + x);
	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 <= -2.2e+37) || ~((z <= 1.15e+67)))
		tmp = t + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.2e+37], N[Not[LessEqual[z, 1.15e+67]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e37 or 1.1499999999999999e67 < z

   1. Initial program 69.1%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 79.2%

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

   if -2.2000000000000001e37 < z < 1.1499999999999999e67

   1. Initial program 95.9%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in z around 0 73.9%

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

      1. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+37} \lor \neg \left(z \leq 1.15 \cdot 10^{+67}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -48000000000000 \lor \neg \left(z \leq 1.1 \cdot 10^{-99}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -48000000000000.0) (not (<= z 1.1e-99))) (+ t x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -48000000000000.0) || !(z <= 1.1e-99)) {
		tmp = t + x;
	} 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 <= (-48000000000000.0d0)) .or. (.not. (z <= 1.1d-99))) then
        tmp = t + x
    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 <= -48000000000000.0) || !(z <= 1.1e-99)) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -48000000000000.0) or not (z <= 1.1e-99):
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -48000000000000.0) || !(z <= 1.1e-99))
		tmp = Float64(t + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -48000000000000.0) || ~((z <= 1.1e-99)))
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -48000000000000.0], N[Not[LessEqual[z, 1.1e-99]], $MachinePrecision]], N[(t + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e13 or 1.10000000000000002e-99 < z

   1. Initial program 76.7%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around inf 73.8%

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

   if -4.8e13 < z < 1.10000000000000002e-99

   1. Initial program 95.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 x around inf 47.4%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48000000000000 \lor \neg \left(z \leq 1.1 \cdot 10^{-99}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 95.8% 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 84.8%

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

   1. associate-/l* 94.9%

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

3. Simplified 94.9%

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

Alternative 14: 50.8% 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%

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

   1. associate-/l* 94.9%

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

3. Simplified 94.9%

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

5. Taylor expanded in x around inf 49.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.3% 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 2024186 
(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))))