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

Percentage Accurate: 85.2% → 98.1%

Time: 12.5s

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: 85.2% 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: 98.1% 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 86.9%

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

   1. associate-*l/ 97.5%

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

3. Simplified 97.5%

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

4. Final simplification 97.5%

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

Alternative 2: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+218}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+179}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+224}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ (- a z) y)))))
   (if (<= z -6.6e+218)
     (+ x t)
     (if (<= z -5.2e-109)
       t_1
       (if (<= z 4.3e-128)
         (+ x (/ (* (- y z) t) a))
         (if (<= z 3e+104)
           t_1
           (if (<= z 1.06e+179)
             (+ x t)
             (if (<= z 3.4e+224) (+ x (* t (/ y (- a z)))) (+ x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / ((a - z) / y));
	double tmp;
	if (z <= -6.6e+218) {
		tmp = x + t;
	} else if (z <= -5.2e-109) {
		tmp = t_1;
	} else if (z <= 4.3e-128) {
		tmp = x + (((y - z) * t) / a);
	} else if (z <= 3e+104) {
		tmp = t_1;
	} else if (z <= 1.06e+179) {
		tmp = x + t;
	} else if (z <= 3.4e+224) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / ((a - z) / y))
    if (z <= (-6.6d+218)) then
        tmp = x + t
    else if (z <= (-5.2d-109)) then
        tmp = t_1
    else if (z <= 4.3d-128) then
        tmp = x + (((y - z) * t) / a)
    else if (z <= 3d+104) then
        tmp = t_1
    else if (z <= 1.06d+179) then
        tmp = x + t
    else if (z <= 3.4d+224) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / ((a - z) / y));
	double tmp;
	if (z <= -6.6e+218) {
		tmp = x + t;
	} else if (z <= -5.2e-109) {
		tmp = t_1;
	} else if (z <= 4.3e-128) {
		tmp = x + (((y - z) * t) / a);
	} else if (z <= 3e+104) {
		tmp = t_1;
	} else if (z <= 1.06e+179) {
		tmp = x + t;
	} else if (z <= 3.4e+224) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / ((a - z) / y))
	tmp = 0
	if z <= -6.6e+218:
		tmp = x + t
	elif z <= -5.2e-109:
		tmp = t_1
	elif z <= 4.3e-128:
		tmp = x + (((y - z) * t) / a)
	elif z <= 3e+104:
		tmp = t_1
	elif z <= 1.06e+179:
		tmp = x + t
	elif z <= 3.4e+224:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(Float64(a - z) / y)))
	tmp = 0.0
	if (z <= -6.6e+218)
		tmp = Float64(x + t);
	elseif (z <= -5.2e-109)
		tmp = t_1;
	elseif (z <= 4.3e-128)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / a));
	elseif (z <= 3e+104)
		tmp = t_1;
	elseif (z <= 1.06e+179)
		tmp = Float64(x + t);
	elseif (z <= 3.4e+224)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / ((a - z) / y));
	tmp = 0.0;
	if (z <= -6.6e+218)
		tmp = x + t;
	elseif (z <= -5.2e-109)
		tmp = t_1;
	elseif (z <= 4.3e-128)
		tmp = x + (((y - z) * t) / a);
	elseif (z <= 3e+104)
		tmp = t_1;
	elseif (z <= 1.06e+179)
		tmp = x + t;
	elseif (z <= 3.4e+224)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+218], N[(x + t), $MachinePrecision], If[LessEqual[z, -5.2e-109], t$95$1, If[LessEqual[z, 4.3e-128], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+104], t$95$1, If[LessEqual[z, 1.06e+179], N[(x + t), $MachinePrecision], If[LessEqual[z, 3.4e+224], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.59999999999999996e218 or 2.99999999999999969e104 < z < 1.05999999999999998e179 or 3.4000000000000002e224 < z

   1. Initial program 60.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 97.8%

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

   if -6.59999999999999996e218 < z < -5.1999999999999997e-109 or 4.29999999999999994e-128 < z < 2.99999999999999969e104

   1. Initial program 92.1%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

      1. *-commutative 99.1%

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

      2. clear-num 99.0%

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

      3. un-div-inv 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in y around inf 79.4%

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

   if -5.1999999999999997e-109 < z < 4.29999999999999994e-128

   1. Initial program 96.2%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 93.6%

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

   if 1.05999999999999998e179 < z < 3.4000000000000002e224

   1. Initial program 72.6%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 92.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+218}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-109}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+104}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+179}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+224}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-128}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-20}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+178} \lor \neg \left(z \leq 1.35 \cdot 10^{+224}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ z y)))))
   (if (<= z -2.1e+96)
     (+ x t)
     (if (<= z -1.4e-57)
       t_1
       (if (<= z 3.95e-128)
         (+ x (* t (/ y a)))
         (if (<= z 6e-20)
           (- x (* y (/ t z)))
           (if (or (<= z 4.6e+178) (not (<= z 1.35e+224))) (+ x t) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -2.1e+96) {
		tmp = x + t;
	} else if (z <= -1.4e-57) {
		tmp = t_1;
	} else if (z <= 3.95e-128) {
		tmp = x + (t * (y / a));
	} else if (z <= 6e-20) {
		tmp = x - (y * (t / z));
	} else if ((z <= 4.6e+178) || !(z <= 1.35e+224)) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t / (z / y))
    if (z <= (-2.1d+96)) then
        tmp = x + t
    else if (z <= (-1.4d-57)) then
        tmp = t_1
    else if (z <= 3.95d-128) then
        tmp = x + (t * (y / a))
    else if (z <= 6d-20) then
        tmp = x - (y * (t / z))
    else if ((z <= 4.6d+178) .or. (.not. (z <= 1.35d+224))) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -2.1e+96) {
		tmp = x + t;
	} else if (z <= -1.4e-57) {
		tmp = t_1;
	} else if (z <= 3.95e-128) {
		tmp = x + (t * (y / a));
	} else if (z <= 6e-20) {
		tmp = x - (y * (t / z));
	} else if ((z <= 4.6e+178) || !(z <= 1.35e+224)) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / (z / y))
	tmp = 0
	if z <= -2.1e+96:
		tmp = x + t
	elif z <= -1.4e-57:
		tmp = t_1
	elif z <= 3.95e-128:
		tmp = x + (t * (y / a))
	elif z <= 6e-20:
		tmp = x - (y * (t / z))
	elif (z <= 4.6e+178) or not (z <= 1.35e+224):
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -2.1e+96)
		tmp = Float64(x + t);
	elseif (z <= -1.4e-57)
		tmp = t_1;
	elseif (z <= 3.95e-128)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 6e-20)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif ((z <= 4.6e+178) || !(z <= 1.35e+224))
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / (z / y));
	tmp = 0.0;
	if (z <= -2.1e+96)
		tmp = x + t;
	elseif (z <= -1.4e-57)
		tmp = t_1;
	elseif (z <= 3.95e-128)
		tmp = x + (t * (y / a));
	elseif (z <= 6e-20)
		tmp = x - (y * (t / z));
	elseif ((z <= 4.6e+178) || ~((z <= 1.35e+224)))
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+96], N[(x + t), $MachinePrecision], If[LessEqual[z, -1.4e-57], t$95$1, If[LessEqual[z, 3.95e-128], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-20], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.6e+178], N[Not[LessEqual[z, 1.35e+224]], $MachinePrecision]], N[(x + t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1000000000000001e96 or 6.00000000000000057e-20 < z < 4.6000000000000002e178 or 1.3499999999999999e224 < z

   1. Initial program 74.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 79.0%

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

   if -2.1000000000000001e96 < z < -1.4e-57 or 4.6000000000000002e178 < z < 1.3499999999999999e224

   1. Initial program 89.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 a around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. associate-/l* 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in z around 0 78.7%

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

   if -1.4e-57 < z < 3.9500000000000001e-128

   1. Initial program 94.6%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around 0 85.5%

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

   if 3.9500000000000001e-128 < z < 6.00000000000000057e-20

   1. Initial program 99.7%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around inf 89.1%

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

   5. Taylor expanded in a around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. mul-1-neg 78.8%

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

      3. unsub-neg 78.8%

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

      4. associate-*r/ 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-57}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-128}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-20}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+178} \lor \neg \left(z \leq 1.35 \cdot 10^{+224}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \end{array} \]

Alternative 4: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-128}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-21}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+177} \lor \neg \left(z \leq 1.35 \cdot 10^{+224}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ z y)))))
   (if (<= z -9.2e+96)
     (+ x t)
     (if (<= z -2e-54)
       t_1
       (if (<= z 3.95e-128)
         (+ x (* t (/ y a)))
         (if (<= z 4.5e-21)
           (- x (/ (* y t) z))
           (if (or (<= z 3.2e+177) (not (<= z 1.35e+224))) (+ x t) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -9.2e+96) {
		tmp = x + t;
	} else if (z <= -2e-54) {
		tmp = t_1;
	} else if (z <= 3.95e-128) {
		tmp = x + (t * (y / a));
	} else if (z <= 4.5e-21) {
		tmp = x - ((y * t) / z);
	} else if ((z <= 3.2e+177) || !(z <= 1.35e+224)) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t / (z / y))
    if (z <= (-9.2d+96)) then
        tmp = x + t
    else if (z <= (-2d-54)) then
        tmp = t_1
    else if (z <= 3.95d-128) then
        tmp = x + (t * (y / a))
    else if (z <= 4.5d-21) then
        tmp = x - ((y * t) / z)
    else if ((z <= 3.2d+177) .or. (.not. (z <= 1.35d+224))) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -9.2e+96) {
		tmp = x + t;
	} else if (z <= -2e-54) {
		tmp = t_1;
	} else if (z <= 3.95e-128) {
		tmp = x + (t * (y / a));
	} else if (z <= 4.5e-21) {
		tmp = x - ((y * t) / z);
	} else if ((z <= 3.2e+177) || !(z <= 1.35e+224)) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / (z / y))
	tmp = 0
	if z <= -9.2e+96:
		tmp = x + t
	elif z <= -2e-54:
		tmp = t_1
	elif z <= 3.95e-128:
		tmp = x + (t * (y / a))
	elif z <= 4.5e-21:
		tmp = x - ((y * t) / z)
	elif (z <= 3.2e+177) or not (z <= 1.35e+224):
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -9.2e+96)
		tmp = Float64(x + t);
	elseif (z <= -2e-54)
		tmp = t_1;
	elseif (z <= 3.95e-128)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 4.5e-21)
		tmp = Float64(x - Float64(Float64(y * t) / z));
	elseif ((z <= 3.2e+177) || !(z <= 1.35e+224))
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / (z / y));
	tmp = 0.0;
	if (z <= -9.2e+96)
		tmp = x + t;
	elseif (z <= -2e-54)
		tmp = t_1;
	elseif (z <= 3.95e-128)
		tmp = x + (t * (y / a));
	elseif (z <= 4.5e-21)
		tmp = x - ((y * t) / z);
	elseif ((z <= 3.2e+177) || ~((z <= 1.35e+224)))
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+96], N[(x + t), $MachinePrecision], If[LessEqual[z, -2e-54], t$95$1, If[LessEqual[z, 3.95e-128], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-21], N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.2e+177], N[Not[LessEqual[z, 1.35e+224]], $MachinePrecision]], N[(x + t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.2000000000000006e96 or 4.49999999999999968e-21 < z < 3.2e177 or 1.3499999999999999e224 < z

   1. Initial program 74.1%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 79.0%

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

   if -9.2000000000000006e96 < z < -2.0000000000000001e-54 or 3.2e177 < z < 1.3499999999999999e224

   1. Initial program 89.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 a around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. associate-/l* 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in z around 0 78.7%

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

   if -2.0000000000000001e-54 < z < 3.9500000000000001e-128

   1. Initial program 94.6%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around 0 85.5%

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

   if 3.9500000000000001e-128 < z < 4.49999999999999968e-21

   1. Initial program 99.7%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in a around 0 84.0%

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

      1. +-commutative 84.0%

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

      2. mul-1-neg 84.0%

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

      3. unsub-neg 84.0%

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

      4. associate-/l* 80.9%

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

   6. Simplified 80.9%

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

   7. Taylor expanded in z around 0 78.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-54}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-128}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-21}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+177} \lor \neg \left(z \leq 1.35 \cdot 10^{+224}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \end{array} \]

Alternative 5: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-128}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ t z)))))
   (if (<= z -4.9e+96)
     (+ x t)
     (if (<= z -7e-64)
       t_1
       (if (<= z -4.8e-65)
         (* t (- 1.0 (/ y z)))
         (if (<= z 3.95e-128)
           (+ x (* t (/ y a)))
           (if (<= z 5.8e-20) t_1 (+ x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -4.9e+96) {
		tmp = x + t;
	} else if (z <= -7e-64) {
		tmp = t_1;
	} else if (z <= -4.8e-65) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 3.95e-128) {
		tmp = x + (t * (y / a));
	} else if (z <= 5.8e-20) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (t / z))
    if (z <= (-4.9d+96)) then
        tmp = x + t
    else if (z <= (-7d-64)) then
        tmp = t_1
    else if (z <= (-4.8d-65)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 3.95d-128) then
        tmp = x + (t * (y / a))
    else if (z <= 5.8d-20) then
        tmp = t_1
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / z));
	double tmp;
	if (z <= -4.9e+96) {
		tmp = x + t;
	} else if (z <= -7e-64) {
		tmp = t_1;
	} else if (z <= -4.8e-65) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 3.95e-128) {
		tmp = x + (t * (y / a));
	} else if (z <= 5.8e-20) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (t / z))
	tmp = 0
	if z <= -4.9e+96:
		tmp = x + t
	elif z <= -7e-64:
		tmp = t_1
	elif z <= -4.8e-65:
		tmp = t * (1.0 - (y / z))
	elif z <= 3.95e-128:
		tmp = x + (t * (y / a))
	elif z <= 5.8e-20:
		tmp = t_1
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(t / z)))
	tmp = 0.0
	if (z <= -4.9e+96)
		tmp = Float64(x + t);
	elseif (z <= -7e-64)
		tmp = t_1;
	elseif (z <= -4.8e-65)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 3.95e-128)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 5.8e-20)
		tmp = t_1;
	else
		tmp = Float64(x + t);
	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 <= -4.9e+96)
		tmp = x + t;
	elseif (z <= -7e-64)
		tmp = t_1;
	elseif (z <= -4.8e-65)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 3.95e-128)
		tmp = x + (t * (y / a));
	elseif (z <= 5.8e-20)
		tmp = t_1;
	else
		tmp = x + t;
	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, -4.9e+96], N[(x + t), $MachinePrecision], If[LessEqual[z, -7e-64], t$95$1, If[LessEqual[z, -4.8e-65], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.95e-128], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-20], t$95$1, N[(x + t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8999999999999996e96 or 5.8e-20 < z

   1. Initial program 73.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 76.2%

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

   if -4.8999999999999996e96 < z < -7.0000000000000006e-64 or 3.9500000000000001e-128 < z < 5.8e-20

   1. Initial program 98.3%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 82.5%

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

   5. Taylor expanded in a around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. mul-1-neg 74.8%

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

      3. unsub-neg 74.8%

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

      4. associate-*r/ 73.7%

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

   7. Simplified 73.7%

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

   if -7.0000000000000006e-64 < z < -4.8000000000000003e-65

   1. Initial program 100.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 a around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in t around inf 100.0%

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

   if -4.8000000000000003e-65 < z < 3.9500000000000001e-128

   1. Initial program 94.3%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 87.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+96}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-64}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-128}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-20}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 6: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+218}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+106} \lor \neg \left(z \leq 1.06 \cdot 10^{+179}\right) \land z \leq 1.35 \cdot 10^{+224}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+218)
   (+ x t)
   (if (or (<= z 1.35e+106) (and (not (<= z 1.06e+179)) (<= z 1.35e+224)))
     (+ x (* t (/ y (- a z))))
     (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+218) {
		tmp = x + t;
	} else if ((z <= 1.35e+106) || (!(z <= 1.06e+179) && (z <= 1.35e+224))) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + 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 <= (-6.6d+218)) then
        tmp = x + t
    else if ((z <= 1.35d+106) .or. (.not. (z <= 1.06d+179)) .and. (z <= 1.35d+224)) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + 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 <= -6.6e+218) {
		tmp = x + t;
	} else if ((z <= 1.35e+106) || (!(z <= 1.06e+179) && (z <= 1.35e+224))) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+218:
		tmp = x + t
	elif (z <= 1.35e+106) or (not (z <= 1.06e+179) and (z <= 1.35e+224)):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+218)
		tmp = Float64(x + t);
	elseif ((z <= 1.35e+106) || (!(z <= 1.06e+179) && (z <= 1.35e+224)))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.6e+218)
		tmp = x + t;
	elseif ((z <= 1.35e+106) || (~((z <= 1.06e+179)) && (z <= 1.35e+224)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+218], N[(x + t), $MachinePrecision], If[Or[LessEqual[z, 1.35e+106], And[N[Not[LessEqual[z, 1.06e+179]], $MachinePrecision], LessEqual[z, 1.35e+224]]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.59999999999999996e218 or 1.35000000000000003e106 < z < 1.05999999999999998e179 or 1.3499999999999999e224 < z

   1. Initial program 60.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 97.8%

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

   if -6.59999999999999996e218 < z < 1.35000000000000003e106 or 1.05999999999999998e179 < z < 1.3499999999999999e224

   1. Initial program 92.3%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around inf 82.9%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+218}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+106} \lor \neg \left(z \leq 1.06 \cdot 10^{+179}\right) \land z \leq 1.35 \cdot 10^{+224}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 7: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+218}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+105}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+174} \lor \neg \left(z \leq 1.35 \cdot 10^{+224}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+218)
   (+ x t)
   (if (<= z 7.2e+105)
     (+ x (/ t (/ (- a z) y)))
     (if (or (<= z 7.5e+174) (not (<= z 1.35e+224)))
       (+ x t)
       (+ x (* t (/ y (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+218) {
		tmp = x + t;
	} else if (z <= 7.2e+105) {
		tmp = x + (t / ((a - z) / y));
	} else if ((z <= 7.5e+174) || !(z <= 1.35e+224)) {
		tmp = x + t;
	} 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 <= (-6.6d+218)) then
        tmp = x + t
    else if (z <= 7.2d+105) then
        tmp = x + (t / ((a - z) / y))
    else if ((z <= 7.5d+174) .or. (.not. (z <= 1.35d+224))) then
        tmp = x + t
    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 <= -6.6e+218) {
		tmp = x + t;
	} else if (z <= 7.2e+105) {
		tmp = x + (t / ((a - z) / y));
	} else if ((z <= 7.5e+174) || !(z <= 1.35e+224)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+218:
		tmp = x + t
	elif z <= 7.2e+105:
		tmp = x + (t / ((a - z) / y))
	elif (z <= 7.5e+174) or not (z <= 1.35e+224):
		tmp = x + t
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+218)
		tmp = Float64(x + t);
	elseif (z <= 7.2e+105)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	elseif ((z <= 7.5e+174) || !(z <= 1.35e+224))
		tmp = Float64(x + t);
	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 <= -6.6e+218)
		tmp = x + t;
	elseif (z <= 7.2e+105)
		tmp = x + (t / ((a - z) / y));
	elseif ((z <= 7.5e+174) || ~((z <= 1.35e+224)))
		tmp = x + t;
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+218], N[(x + t), $MachinePrecision], If[LessEqual[z, 7.2e+105], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7.5e+174], N[Not[LessEqual[z, 1.35e+224]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.59999999999999996e218 or 7.1999999999999998e105 < z < 7.5000000000000004e174 or 1.3499999999999999e224 < z

   1. Initial program 60.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 97.8%

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

   if -6.59999999999999996e218 < z < 7.1999999999999998e105

   1. Initial program 93.7%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

      1. *-commutative 96.8%

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

      2. clear-num 96.5%

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

      3. un-div-inv 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in y around inf 82.4%

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

   if 7.5000000000000004e174 < z < 1.3499999999999999e224

   1. Initial program 72.6%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 92.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+218}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+105}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+174} \lor \neg \left(z \leq 1.35 \cdot 10^{+224}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 8: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+23} \lor \neg \left(y \leq 1.6 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.9e+23) (not (<= y 1.6e+66)))
   (+ x (/ t (/ (- a z) y)))
   (- x (/ t (+ (/ a z) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.9e+23) || !(y <= 1.6e+66)) {
		tmp = x + (t / ((a - z) / y));
	} 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 <= (-4.9d+23)) .or. (.not. (y <= 1.6d+66))) then
        tmp = x + (t / ((a - z) / y))
    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 <= -4.9e+23) || !(y <= 1.6e+66)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (t / ((a / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.9e+23) or not (y <= 1.6e+66):
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x - (t / ((a / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.9e+23) || !(y <= 1.6e+66))
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	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 <= -4.9e+23) || ~((y <= 1.6e+66)))
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x - (t / ((a / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.9e+23], N[Not[LessEqual[y, 1.6e+66]], $MachinePrecision]], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $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 < -4.9000000000000003e23 or 1.6e66 < y

   1. Initial program 83.7%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

      1. *-commutative 95.4%

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

      2. clear-num 95.3%

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

      3. un-div-inv 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in y around inf 89.1%

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

   if -4.9000000000000003e23 < y < 1.6e66

   1. Initial program 89.1%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 79.7%

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

      1. +-commutative 79.7%

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

      2. mul-1-neg 79.7%

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

      3. unsub-neg 79.7%

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

      4. associate-/l* 89.8%

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

      5. div-sub 89.8%

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

      6. *-inverses 89.8%

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

   6. Simplified 89.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+23} \lor \neg \left(y \leq 1.6 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \]

Alternative 9: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+235} \lor \neg \left(t \leq 6.2 \cdot 10^{+129}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e+235) (not (<= t 6.2e+129)))
   (* t (- 1.0 (/ y z)))
   (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e+235) || !(t <= 6.2e+129)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + 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 <= (-4.8d+235)) .or. (.not. (t <= 6.2d+129))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + 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 <= -4.8e+235) || !(t <= 6.2e+129)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e+235) or not (t <= 6.2e+129):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e+235) || !(t <= 6.2e+129))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.8e+235) || ~((t <= 6.2e+129)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e+235], N[Not[LessEqual[t, 6.2e+129]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.7999999999999998e235 or 6.1999999999999999e129 < t

   1. Initial program 76.3%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in a around 0 38.5%

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

      1. +-commutative 38.5%

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

      2. mul-1-neg 38.5%

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

      3. unsub-neg 38.5%

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

      4. associate-/l* 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in t around inf 50.9%

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

   if -4.7999999999999998e235 < t < 6.1999999999999999e129

   1. Initial program 89.6%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around inf 68.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+235} \lor \neg \left(t \leq 6.2 \cdot 10^{+129}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 10: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2) (+ x t) (if (<= z 1.6e-25) (+ x (* y (/ t a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2) {
		tmp = x + t;
	} else if (z <= 1.6e-25) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + 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 <= (-1.2d0)) then
        tmp = x + t
    else if (z <= 1.6d-25) then
        tmp = x + (y * (t / a))
    else
        tmp = x + 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 <= -1.2) {
		tmp = x + t;
	} else if (z <= 1.6e-25) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2:
		tmp = x + t
	elif z <= 1.6e-25:
		tmp = x + (y * (t / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2)
		tmp = Float64(x + t);
	elseif (z <= 1.6e-25)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2)
		tmp = x + t;
	elseif (z <= 1.6e-25)
		tmp = x + (y * (t / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.6e-25], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999996 or 1.6000000000000001e-25 < z

   1. Initial program 78.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 74.1%

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

   if -1.19999999999999996 < z < 1.6000000000000001e-25

   1. Initial program 96.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

      1. *-commutative 95.0%

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

      2. clear-num 94.5%

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

      3. un-div-inv 94.8%

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

   5. Applied egg-rr 94.8%

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

   6. Taylor expanded in z around 0 74.9%

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

      1. associate-*r/ 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 11: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.0) (+ x t) (if (<= z 1.6e-25) (+ x (* t (/ y a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.0) {
		tmp = x + t;
	} else if (z <= 1.6e-25) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + 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 <= (-1.0d0)) then
        tmp = x + t
    else if (z <= 1.6d-25) then
        tmp = x + (t * (y / a))
    else
        tmp = x + 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 <= -1.0) {
		tmp = x + t;
	} else if (z <= 1.6e-25) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.0:
		tmp = x + t
	elif z <= 1.6e-25:
		tmp = x + (t * (y / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x + t);
	elseif (z <= 1.6e-25)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x + t;
	elseif (z <= 1.6e-25)
		tmp = x + (t * (y / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.0], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.6e-25], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.6000000000000001e-25 < z

   1. Initial program 78.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 74.1%

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

   if -1 < z < 1.6000000000000001e-25

   1. Initial program 96.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around 0 75.9%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 12: 49.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+178}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+282}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+178) t (if (<= z 3.9e+282) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+178) {
		tmp = t;
	} else if (z <= 3.9e+282) {
		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 (z <= (-1.8d+178)) then
        tmp = t
    else if (z <= 3.9d+282) 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 (z <= -1.8e+178) {
		tmp = t;
	} else if (z <= 3.9e+282) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+178:
		tmp = t
	elif z <= 3.9e+282:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+178)
		tmp = t;
	elseif (z <= 3.9e+282)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+178)
		tmp = t;
	elseif (z <= 3.9e+282)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+178], t, If[LessEqual[z, 3.9e+282], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e178 or 3.8999999999999998e282 < z

   1. Initial program 56.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

      4. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in t around inf 77.0%

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

   8. Taylor expanded in y around 0 59.4%

      \[\leadsto \color{blue}{1} \cdot t \]

   if -1.7999999999999999e178 < z < 3.8999999999999998e282

   1. Initial program 91.4%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 55.2%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+178}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+282}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 61.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+62}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 7.8e+62) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 7.8e+62) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 7.8d+62) then
        tmp = x + t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 7.8e+62) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 7.8e+62:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 7.8e+62)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 7.8e+62)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 7.8e+62], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 7.8e62

   1. Initial program 86.9%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 61.7%

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

   if 7.8e62 < a

   1. Initial program 87.2%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 67.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+62}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 50.6% 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 86.9%

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

   1. associate-*l/ 97.5%

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

3. Simplified 97.5%

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

4. Taylor expanded in x around inf 51.4%

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

5. Final simplification 51.4%

   \[\leadsto x \]

Developer target: 99.3% 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 2023274 
(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))))