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

Percentage Accurate: 86.0% → 97.8%

Time: 9.0s

Alternatives: 12

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: 86.0% 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: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.8%

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

   1. +-commutative 86.8%

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

   2. associate-*l/ 99.2%

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

   3. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+35}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-95}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-44}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+35)
   (+ t x)
   (if (<= z 2.1e-95)
     (+ x (* t (/ y a)))
     (if (<= z 1.4e-44)
       (- x (* z (/ t a)))
       (if (<= z 1.1e+54) (+ x (/ (* y t) a)) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+35) {
		tmp = t + x;
	} else if (z <= 2.1e-95) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.4e-44) {
		tmp = x - (z * (t / a));
	} else if (z <= 1.1e+54) {
		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 <= (-1.3d+35)) then
        tmp = t + x
    else if (z <= 2.1d-95) then
        tmp = x + (t * (y / a))
    else if (z <= 1.4d-44) then
        tmp = x - (z * (t / a))
    else if (z <= 1.1d+54) 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 <= -1.3e+35) {
		tmp = t + x;
	} else if (z <= 2.1e-95) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.4e-44) {
		tmp = x - (z * (t / a));
	} else if (z <= 1.1e+54) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+35:
		tmp = t + x
	elif z <= 2.1e-95:
		tmp = x + (t * (y / a))
	elif z <= 1.4e-44:
		tmp = x - (z * (t / a))
	elif z <= 1.1e+54:
		tmp = x + ((y * t) / a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+35)
		tmp = Float64(t + x);
	elseif (z <= 2.1e-95)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.4e-44)
		tmp = Float64(x - Float64(z * Float64(t / a)));
	elseif (z <= 1.1e+54)
		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 <= -1.3e+35)
		tmp = t + x;
	elseif (z <= 2.1e-95)
		tmp = x + (t * (y / a));
	elseif (z <= 1.4e-44)
		tmp = x - (z * (t / a));
	elseif (z <= 1.1e+54)
		tmp = x + ((y * t) / a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+35], N[(t + x), $MachinePrecision], If[LessEqual[z, 2.1e-95], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-44], N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+54], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.30000000000000003e35 or 1.09999999999999995e54 < z

   1. Initial program 76.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -1.30000000000000003e35 < z < 2.1e-95

   1. Initial program 93.6%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 80.4%

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

   if 2.1e-95 < z < 1.4e-44

   1. Initial program 99.7%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

      3. associate-/l* 62.0%

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

      4. div-sub 62.0%

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

      5. *-inverses 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in a around inf 81.2%

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

      1. associate-/l* 81.4%

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

      2. associate-/r/ 81.1%

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

   9. Simplified 81.1%

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

   if 1.4e-44 < z < 1.09999999999999995e54

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 73.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+35}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-95}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-44}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 3: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-95}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+35)
   (+ t x)
   (if (<= z 2.8e-95)
     (+ x (* t (/ y a)))
     (if (<= z 2.5e-45)
       (- x (* t (/ z a)))
       (if (<= z 1.16e+57) (+ x (/ (* y t) a)) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+35) {
		tmp = t + x;
	} else if (z <= 2.8e-95) {
		tmp = x + (t * (y / a));
	} else if (z <= 2.5e-45) {
		tmp = x - (t * (z / a));
	} else if (z <= 1.16e+57) {
		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 <= (-2.3d+35)) then
        tmp = t + x
    else if (z <= 2.8d-95) then
        tmp = x + (t * (y / a))
    else if (z <= 2.5d-45) then
        tmp = x - (t * (z / a))
    else if (z <= 1.16d+57) 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 <= -2.3e+35) {
		tmp = t + x;
	} else if (z <= 2.8e-95) {
		tmp = x + (t * (y / a));
	} else if (z <= 2.5e-45) {
		tmp = x - (t * (z / a));
	} else if (z <= 1.16e+57) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+35:
		tmp = t + x
	elif z <= 2.8e-95:
		tmp = x + (t * (y / a))
	elif z <= 2.5e-45:
		tmp = x - (t * (z / a))
	elif z <= 1.16e+57:
		tmp = x + ((y * t) / a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+35)
		tmp = Float64(t + x);
	elseif (z <= 2.8e-95)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 2.5e-45)
		tmp = Float64(x - Float64(t * Float64(z / a)));
	elseif (z <= 1.16e+57)
		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 <= -2.3e+35)
		tmp = t + x;
	elseif (z <= 2.8e-95)
		tmp = x + (t * (y / a));
	elseif (z <= 2.5e-45)
		tmp = x - (t * (z / a));
	elseif (z <= 1.16e+57)
		tmp = x + ((y * t) / a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+35], N[(t + x), $MachinePrecision], If[LessEqual[z, 2.8e-95], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-45], N[(x - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e+57], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2999999999999998e35 or 1.16000000000000003e57 < z

   1. Initial program 76.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -2.2999999999999998e35 < z < 2.7999999999999999e-95

   1. Initial program 93.6%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 80.4%

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

   if 2.7999999999999999e-95 < z < 2.49999999999999988e-45

   1. Initial program 99.7%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

      3. associate-/l* 62.0%

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

      4. div-sub 62.0%

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

      5. *-inverses 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in a around inf 81.2%

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

      1. associate-/l* 81.4%

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

   9. Simplified 81.4%

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

       1. clear-num 81.2%

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

       2. associate-/r/ 81.4%

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

       3. clear-num 81.2%

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

   11. Applied egg-rr 81.2%

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

   if 2.49999999999999988e-45 < z < 1.16000000000000003e57

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 73.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-95}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 4: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+35}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-95}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-45}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+35)
   (+ t x)
   (if (<= z 2.8e-95)
     (+ x (* t (/ y a)))
     (if (<= z 3e-45)
       (- x (/ t (/ a z)))
       (if (<= z 1.12e+55) (+ x (/ (* y t) a)) (+ t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+35) {
		tmp = t + x;
	} else if (z <= 2.8e-95) {
		tmp = x + (t * (y / a));
	} else if (z <= 3e-45) {
		tmp = x - (t / (a / z));
	} else if (z <= 1.12e+55) {
		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 <= (-2.4d+35)) then
        tmp = t + x
    else if (z <= 2.8d-95) then
        tmp = x + (t * (y / a))
    else if (z <= 3d-45) then
        tmp = x - (t / (a / z))
    else if (z <= 1.12d+55) 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 <= -2.4e+35) {
		tmp = t + x;
	} else if (z <= 2.8e-95) {
		tmp = x + (t * (y / a));
	} else if (z <= 3e-45) {
		tmp = x - (t / (a / z));
	} else if (z <= 1.12e+55) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+35:
		tmp = t + x
	elif z <= 2.8e-95:
		tmp = x + (t * (y / a))
	elif z <= 3e-45:
		tmp = x - (t / (a / z))
	elif z <= 1.12e+55:
		tmp = x + ((y * t) / a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+35)
		tmp = Float64(t + x);
	elseif (z <= 2.8e-95)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 3e-45)
		tmp = Float64(x - Float64(t / Float64(a / z)));
	elseif (z <= 1.12e+55)
		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 <= -2.4e+35)
		tmp = t + x;
	elseif (z <= 2.8e-95)
		tmp = x + (t * (y / a));
	elseif (z <= 3e-45)
		tmp = x - (t / (a / z));
	elseif (z <= 1.12e+55)
		tmp = x + ((y * t) / a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+35], N[(t + x), $MachinePrecision], If[LessEqual[z, 2.8e-95], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-45], N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+55], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.40000000000000015e35 or 1.12000000000000006e55 < z

   1. Initial program 76.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -2.40000000000000015e35 < z < 2.7999999999999999e-95

   1. Initial program 93.6%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 80.4%

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

   if 2.7999999999999999e-95 < z < 3.00000000000000011e-45

   1. Initial program 99.7%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

      3. associate-/l* 62.0%

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

      4. div-sub 62.0%

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

      5. *-inverses 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in a around inf 81.2%

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

      1. associate-/l* 81.4%

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

   9. Simplified 81.4%

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

   if 3.00000000000000011e-45 < z < 1.12000000000000006e55

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 73.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+35}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-95}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-45}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 5: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+35} \lor \neg \left(z \leq 1.65 \cdot 10^{+59}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+35) (not (<= z 1.65e+59)))
   (+ t x)
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+35) || !(z <= 1.65e+59)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.8d+35)) .or. (.not. (z <= 1.65d+59))) then
        tmp = t + x
    else
        tmp = x + (t * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+35) || !(z <= 1.65e+59)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+35) or not (z <= 1.65e+59):
		tmp = t + x
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+35) || !(z <= 1.65e+59))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e+35) || ~((z <= 1.65e+59)))
		tmp = t + x;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+35], N[Not[LessEqual[z, 1.65e+59]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999999e35 or 1.65e59 < z

   1. Initial program 76.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -2.79999999999999999e35 < z < 1.65e59

   1. Initial program 94.8%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in y around inf 86.8%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+35} \lor \neg \left(z \leq 1.65 \cdot 10^{+59}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 6: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1550 \lor \neg \left(y \leq 5.8 \cdot 10^{+81}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1550.0) (not (<= y 5.8e+81)))
   (+ x (* t (/ y (- a z))))
   (- x (/ t (+ (/ a z) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1550.0) || !(y <= 5.8e+81)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t / ((a / z) + -1.0));
	}
	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 <= (-1550.0d0)) .or. (.not. (y <= 5.8d+81))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x - (t / ((a / z) + (-1.0d0)))
    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 <= -1550.0) || !(y <= 5.8e+81)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t / ((a / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1550.0) or not (y <= 5.8e+81):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x - (t / ((a / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1550.0) || !(y <= 5.8e+81))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1550.0) || ~((y <= 5.8e+81)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x - (t / ((a / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1550.0], N[Not[LessEqual[y, 5.8e+81]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1550 or 5.7999999999999999e81 < y

   1. Initial program 85.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 91.7%

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

   if -1550 < y < 5.7999999999999999e81

   1. Initial program 87.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

      3. associate-/l* 92.8%

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

      4. div-sub 92.8%

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

      5. *-inverses 92.8%

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

   6. Simplified 92.8%

      \[\leadsto \color{blue}{x - \frac{t}{\frac{a}{z} - 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1550 \lor \neg \left(y \leq 5.8 \cdot 10^{+81}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \]

Alternative 7: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+34} \lor \neg \left(z \leq 7.2 \cdot 10^{+53}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+34) (not (<= z 7.2e+53))) (+ t x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+34) || !(z <= 7.2e+53)) {
		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 <= (-9d+34)) .or. (.not. (z <= 7.2d+53))) 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 <= -9e+34) || !(z <= 7.2e+53)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+34) or not (z <= 7.2e+53):
		tmp = t + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+34) || !(z <= 7.2e+53))
		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 <= -9e+34) || ~((z <= 7.2e+53)))
		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, -9e+34], N[Not[LessEqual[z, 7.2e+53]], $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 < -9.0000000000000001e34 or 7.2e53 < z

   1. Initial program 76.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -9.0000000000000001e34 < z < 7.2e53

   1. Initial program 94.8%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 76.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+34} \lor \neg \left(z \leq 7.2 \cdot 10^{+53}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+35} \lor \neg \left(z \leq 3.1 \cdot 10^{+53}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.2e+35) (not (<= z 3.1e+53))) (+ t x) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e+35) || !(z <= 3.1e+53)) {
		tmp = t + x;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.2d+35)) .or. (.not. (z <= 3.1d+53))) then
        tmp = t + x
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e+35) || !(z <= 3.1e+53)) {
		tmp = t + x;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.2e+35) or not (z <= 3.1e+53):
		tmp = t + x
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.2e+35) || !(z <= 3.1e+53))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.2e+35) || ~((z <= 3.1e+53)))
		tmp = t + x;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.2e+35], N[Not[LessEqual[z, 3.1e+53]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e35 or 3.10000000000000019e53 < z

   1. Initial program 76.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -2.1999999999999999e35 < z < 3.10000000000000019e53

   1. Initial program 94.8%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 73.5%

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

      1. +-commutative 73.5%

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

      2. associate-/l* 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+35} \lor \neg \left(z \leq 3.1 \cdot 10^{+53}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.8%

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

   1. associate-*l/ 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 10: 62.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-106} \lor \neg \left(z \leq 3.6 \cdot 10^{-10}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e-106) (not (<= z 3.6e-10))) (+ t x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e-106) || !(z <= 3.6e-10)) {
		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 <= (-8d-106)) .or. (.not. (z <= 3.6d-10))) 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 <= -8e-106) || !(z <= 3.6e-10)) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e-106) or not (z <= 3.6e-10):
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e-106) || !(z <= 3.6e-10))
		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 <= -8e-106) || ~((z <= 3.6e-10)))
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e-106], N[Not[LessEqual[z, 3.6e-10]], $MachinePrecision]], N[(t + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999953e-106 or 3.6e-10 < z

   1. Initial program 81.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.2%

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

   if -7.99999999999999953e-106 < z < 3.6e-10

   1. Initial program 94.4%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in x around inf 56.4%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-106} \lor \neg \left(z \leq 3.6 \cdot 10^{-10}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 53.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+147}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+224}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.85e+147) t (if (<= t 4.5e+224) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.85e+147) {
		tmp = t;
	} else if (t <= 4.5e+224) {
		tmp = x;
	} else {
		tmp = 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 (t <= (-2.85d+147)) then
        tmp = t
    else if (t <= 4.5d+224) then
        tmp = x
    else
        tmp = 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 (t <= -2.85e+147) {
		tmp = t;
	} else if (t <= 4.5e+224) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.85e+147:
		tmp = t
	elif t <= 4.5e+224:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.85e+147)
		tmp = t;
	elseif (t <= 4.5e+224)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.85e+147)
		tmp = t;
	elseif (t <= 4.5e+224)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.85e+147], t, If[LessEqual[t, 4.5e+224], x, t]]

Derivation

1. Split input into 2 regimes

2. if t < -2.84999999999999996e147 or 4.4999999999999998e224 < t

   1. Initial program 51.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. unsub-neg 34.5%

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

      3. associate-/l* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in t around inf 63.6%

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

   8. Taylor expanded in y around 0 42.4%

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

   if -2.84999999999999996e147 < t < 4.4999999999999998e224

   1. Initial program 94.5%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 63.7%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+147}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+224}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 18.5% 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 86.8%

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

   1. associate-*l/ 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in a around 0 62.6%

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

   1. mul-1-neg 62.6%

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

   2. unsub-neg 62.6%

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

   3. associate-/l* 69.8%

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

6. Simplified 69.8%

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

7. Taylor expanded in t around inf 29.0%

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

8. Taylor expanded in y around 0 19.3%

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

9. Final simplification 19.3%

   \[\leadsto t \]

Developer target: 99.0% accurate, 0.7× 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 2023320 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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