Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.1% → 89.6%

Time: 13.7s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+154}:\\ \;\;\;\;\left(t - \frac{a}{\frac{z}{t - x}} \cdot \frac{y - a}{z}\right) + t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+131}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x t) (/ z (- y a)))))
   (if (<= z -4.5e+154)
     (+ (- t (* (/ a (/ z (- t x))) (/ (- y a) z))) t_1)
     (if (<= z 1.55e+131) (+ x (* (- t x) (/ (- y z) (- a z)))) (+ t t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - t) / (z / (y - a));
	double tmp;
	if (z <= -4.5e+154) {
		tmp = (t - ((a / (z / (t - x))) * ((y - a) / z))) + t_1;
	} else if (z <= 1.55e+131) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + 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 - a))
    if (z <= (-4.5d+154)) then
        tmp = (t - ((a / (z / (t - x))) * ((y - a) / z))) + t_1
    else if (z <= 1.55d+131) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + 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 - a));
	double tmp;
	if (z <= -4.5e+154) {
		tmp = (t - ((a / (z / (t - x))) * ((y - a) / z))) + t_1;
	} else if (z <= 1.55e+131) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - t) / (z / (y - a))
	tmp = 0
	if z <= -4.5e+154:
		tmp = (t - ((a / (z / (t - x))) * ((y - a) / z))) + t_1
	elif z <= 1.55e+131:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - t) / Float64(z / Float64(y - a)))
	tmp = 0.0
	if (z <= -4.5e+154)
		tmp = Float64(Float64(t - Float64(Float64(a / Float64(z / Float64(t - x))) * Float64(Float64(y - a) / z))) + t_1);
	elseif (z <= 1.55e+131)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - t) / (z / (y - a));
	tmp = 0.0;
	if (z <= -4.5e+154)
		tmp = (t - ((a / (z / (t - x))) * ((y - a) / z))) + t_1;
	elseif (z <= 1.55e+131)
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+154], N[(N[(t - N[(N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 1.55e+131], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.50000000000000009e154

   1. Initial program 30.0%

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

      1. associate-*l/ 59.3%

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

   3. Simplified 59.3%

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

   4. Taylor expanded in z around -inf 47.3%

      \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{a \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}{{z}^{2}} + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 47.3%

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

      2. mul-1-neg 47.3%

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

      3. distribute-rgt-out-- 47.2%

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

      4. unsub-neg 47.2%

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

   6. Simplified 89.8%

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

   if -4.50000000000000009e154 < z < 1.55000000000000008e131

   1. Initial program 83.7%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   if 1.55000000000000008e131 < z

   1. Initial program 34.4%

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

      1. associate-*l/ 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in z around inf 61.9%

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

      1. associate--l+ 61.9%

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

      2. associate-*r/ 61.9%

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

      3. associate-*r/ 61.9%

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

      4. div-sub 61.9%

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

      5. distribute-lft-out-- 61.9%

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

      6. mul-1-neg 61.9%

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

      7. distribute-neg-frac 61.9%

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

      8. distribute-rgt-out-- 62.4%

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

      9. unsub-neg 62.4%

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

      10. associate-/l* 86.9%

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

   6. Simplified 86.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+154}:\\ \;\;\;\;\left(t - \frac{a}{\frac{z}{t - x}} \cdot \frac{y - a}{z}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+131}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 2: 36.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.56 \cdot 10^{+122}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-83}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= y -1.7e+229)
     t_1
     (if (<= y -1.56e+122)
       (/ (* x (- y)) a)
       (if (<= y -1.05e+118)
         t_1
         (if (<= y 2.8e-83)
           (+ t x)
           (if (<= y 1.4e+175) (* x (+ (/ z a) 1.0)) (/ (- x) (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / z);
	double tmp;
	if (y <= -1.7e+229) {
		tmp = t_1;
	} else if (y <= -1.56e+122) {
		tmp = (x * -y) / a;
	} else if (y <= -1.05e+118) {
		tmp = t_1;
	} else if (y <= 2.8e-83) {
		tmp = t + x;
	} else if (y <= 1.4e+175) {
		tmp = x * ((z / a) + 1.0);
	} else {
		tmp = -x / (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) :: t_1
    real(8) :: tmp
    t_1 = y * (x / z)
    if (y <= (-1.7d+229)) then
        tmp = t_1
    else if (y <= (-1.56d+122)) then
        tmp = (x * -y) / a
    else if (y <= (-1.05d+118)) then
        tmp = t_1
    else if (y <= 2.8d-83) then
        tmp = t + x
    else if (y <= 1.4d+175) then
        tmp = x * ((z / a) + 1.0d0)
    else
        tmp = -x / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / z);
	double tmp;
	if (y <= -1.7e+229) {
		tmp = t_1;
	} else if (y <= -1.56e+122) {
		tmp = (x * -y) / a;
	} else if (y <= -1.05e+118) {
		tmp = t_1;
	} else if (y <= 2.8e-83) {
		tmp = t + x;
	} else if (y <= 1.4e+175) {
		tmp = x * ((z / a) + 1.0);
	} else {
		tmp = -x / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (x / z)
	tmp = 0
	if y <= -1.7e+229:
		tmp = t_1
	elif y <= -1.56e+122:
		tmp = (x * -y) / a
	elif y <= -1.05e+118:
		tmp = t_1
	elif y <= 2.8e-83:
		tmp = t + x
	elif y <= 1.4e+175:
		tmp = x * ((z / a) + 1.0)
	else:
		tmp = -x / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -1.7e+229)
		tmp = t_1;
	elseif (y <= -1.56e+122)
		tmp = Float64(Float64(x * Float64(-y)) / a);
	elseif (y <= -1.05e+118)
		tmp = t_1;
	elseif (y <= 2.8e-83)
		tmp = Float64(t + x);
	elseif (y <= 1.4e+175)
		tmp = Float64(x * Float64(Float64(z / a) + 1.0));
	else
		tmp = Float64(Float64(-x) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (x / z);
	tmp = 0.0;
	if (y <= -1.7e+229)
		tmp = t_1;
	elseif (y <= -1.56e+122)
		tmp = (x * -y) / a;
	elseif (y <= -1.05e+118)
		tmp = t_1;
	elseif (y <= 2.8e-83)
		tmp = t + x;
	elseif (y <= 1.4e+175)
		tmp = x * ((z / a) + 1.0);
	else
		tmp = -x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+229], t$95$1, If[LessEqual[y, -1.56e+122], N[(N[(x * (-y)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -1.05e+118], t$95$1, If[LessEqual[y, 2.8e-83], N[(t + x), $MachinePrecision], If[LessEqual[y, 1.4e+175], N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.7e229 or -1.55999999999999993e122 < y < -1.05e118

   1. Initial program 70.1%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in y around -inf 65.5%

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

   5. Taylor expanded in a around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-/l* 64.3%

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

      3. distribute-neg-frac 64.3%

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

   7. Simplified 64.3%

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

   8. Taylor expanded in t around 0 43.4%

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

      1. associate-/l* 54.9%

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

   10. Simplified 54.9%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 56.1%

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

   12. Applied egg-rr 56.1%

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

   if -1.7e229 < y < -1.55999999999999993e122

   1. Initial program 56.4%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around -inf 56.6%

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

   5. Taylor expanded in t around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. associate-/l* 41.2%

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

      3. distribute-neg-frac 41.2%

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

   7. Simplified 41.2%

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

   8. Taylor expanded in a around inf 33.7%

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

   if -1.05e118 < y < 2.8000000000000001e-83

   1. Initial program 73.8%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. associate-*r/ 62.9%

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

      3. unsub-neg 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in t around inf 62.0%

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

   8. Taylor expanded in z around inf 46.8%

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

      1. mul-1-neg 46.8%

         \[\leadsto x - \color{blue}{\left(-t\right)} \]

   10. Simplified 46.8%

       \[\leadsto x - \color{blue}{\left(-t\right)} \]

   if 2.8000000000000001e-83 < y < 1.4000000000000001e175

   1. Initial program 74.8%

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

      1. associate-*l/ 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in y around 0 42.4%

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

      1. mul-1-neg 42.4%

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

      2. associate-*r/ 52.4%

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

      3. unsub-neg 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in t around 0 38.7%

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

      1. sub-neg 38.7%

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

      2. mul-1-neg 38.7%

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

      3. remove-double-neg 38.7%

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

      4. associate-/l* 38.6%

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

   9. Simplified 38.6%

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

   10. Taylor expanded in a around inf 38.9%

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

   11. Taylor expanded in x around 0 38.9%

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

   if 1.4000000000000001e175 < y

   1. Initial program 77.2%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around -inf 73.0%

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

   5. Taylor expanded in t around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. associate-/l* 67.4%

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

      3. distribute-neg-frac 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in a around inf 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/l* 49.3%

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

      3. distribute-neg-frac 49.3%

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

   10. Simplified 49.3%

       \[\leadsto \color{blue}{\frac{-x}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.56 \cdot 10^{+122}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-83}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \end{array} \]

Alternative 3: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.7e-15)
     t_2
     (if (<= t -5.7e-92)
       t_1
       (if (<= t -5.6e-157)
         (* y (/ (- t x) (- a z)))
         (if (<= t 5e-59) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.7e-15) {
		tmp = t_2;
	} else if (t <= -5.7e-92) {
		tmp = t_1;
	} else if (t <= -5.6e-157) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 5e-59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-1.7d-15)) then
        tmp = t_2
    else if (t <= (-5.7d-92)) then
        tmp = t_1
    else if (t <= (-5.6d-157)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 5d-59) then
        tmp = t_1
    else
        tmp = t_2
    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 - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.7e-15) {
		tmp = t_2;
	} else if (t <= -5.7e-92) {
		tmp = t_1;
	} else if (t <= -5.6e-157) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 5e-59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.7e-15:
		tmp = t_2
	elif t <= -5.7e-92:
		tmp = t_1
	elif t <= -5.6e-157:
		tmp = y * ((t - x) / (a - z))
	elif t <= 5e-59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.7e-15)
		tmp = t_2;
	elseif (t <= -5.7e-92)
		tmp = t_1;
	elseif (t <= -5.6e-157)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 5e-59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.7e-15)
		tmp = t_2;
	elseif (t <= -5.7e-92)
		tmp = t_1;
	elseif (t <= -5.6e-157)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 5e-59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-15], t$95$2, If[LessEqual[t, -5.7e-92], t$95$1, If[LessEqual[t, -5.6e-157], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e-15 or 5.0000000000000001e-59 < t

   1. Initial program 70.1%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around 0 47.1%

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

      1. associate-*r/ 68.7%

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

   6. Simplified 68.7%

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

   if -1.7e-15 < t < -5.70000000000000009e-92 or -5.6000000000000002e-157 < t < 5.0000000000000001e-59

   1. Initial program 74.2%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in z around 0 68.0%

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

   5. Taylor expanded in x around inf 66.1%

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

      1. distribute-lft-in 66.1%

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

      2. *-rgt-identity 66.1%

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

      3. mul-1-neg 66.1%

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

      4. distribute-rgt-neg-in 66.1%

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

      5. unsub-neg 66.1%

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

   7. Simplified 66.1%

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

   if -5.70000000000000009e-92 < t < -5.6000000000000002e-157

   1. Initial program 80.6%

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

      1. associate-*l/ 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in y around inf 80.4%

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

      1. div-sub 80.4%

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

   6. Simplified 80.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-92}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-59}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 4: 89.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+156} \lor \neg \left(z \leq 3.5 \cdot 10^{+130}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+156) (not (<= z 3.5e+130)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (* (- t x) (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+156) || !(z <= 3.5e+130)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * ((y - z) / (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 <= (-1.1d+156)) .or. (.not. (z <= 3.5d+130))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((t - x) * ((y - z) / (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 <= -1.1e+156) || !(z <= 3.5e+130)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+156) or not (z <= 3.5e+130):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+156) || !(z <= 3.5e+130))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+156) || ~((z <= 3.5e+130)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+156], N[Not[LessEqual[z, 3.5e+130]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000002e156 or 3.5000000000000001e130 < z

   1. Initial program 32.9%

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

      1. associate-*l/ 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in z around inf 59.3%

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

      1. associate--l+ 59.3%

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

      2. associate-*r/ 59.3%

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

      3. associate-*r/ 59.3%

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

      4. div-sub 59.3%

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

      5. distribute-lft-out-- 59.3%

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

      6. mul-1-neg 59.3%

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

      7. distribute-neg-frac 59.3%

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

      8. distribute-rgt-out-- 59.6%

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

      9. unsub-neg 59.6%

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

      10. associate-/l* 87.8%

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

   6. Simplified 87.8%

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

   if -1.10000000000000002e156 < z < 3.5000000000000001e130

   1. Initial program 83.7%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+156} \lor \neg \left(z \leq 3.5 \cdot 10^{+130}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 5: 36.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{\frac{a}{y}}\\ t_2 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-44}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x) (/ a y))) (t_2 (* y (/ x z))))
   (if (<= y -2.1e+229)
     t_2
     (if (<= y -2.5e+122)
       t_1
       (if (<= y -3.8e+118)
         t_2
         (if (<= y 4.1e-44) (+ t x) (if (<= y 2.5e+174) x t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (a / y);
	double t_2 = y * (x / z);
	double tmp;
	if (y <= -2.1e+229) {
		tmp = t_2;
	} else if (y <= -2.5e+122) {
		tmp = t_1;
	} else if (y <= -3.8e+118) {
		tmp = t_2;
	} else if (y <= 4.1e-44) {
		tmp = t + x;
	} else if (y <= 2.5e+174) {
		tmp = x;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = -x / (a / y)
    t_2 = y * (x / z)
    if (y <= (-2.1d+229)) then
        tmp = t_2
    else if (y <= (-2.5d+122)) then
        tmp = t_1
    else if (y <= (-3.8d+118)) then
        tmp = t_2
    else if (y <= 4.1d-44) then
        tmp = t + x
    else if (y <= 2.5d+174) then
        tmp = x
    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 / (a / y);
	double t_2 = y * (x / z);
	double tmp;
	if (y <= -2.1e+229) {
		tmp = t_2;
	} else if (y <= -2.5e+122) {
		tmp = t_1;
	} else if (y <= -3.8e+118) {
		tmp = t_2;
	} else if (y <= 4.1e-44) {
		tmp = t + x;
	} else if (y <= 2.5e+174) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x / (a / y)
	t_2 = y * (x / z)
	tmp = 0
	if y <= -2.1e+229:
		tmp = t_2
	elif y <= -2.5e+122:
		tmp = t_1
	elif y <= -3.8e+118:
		tmp = t_2
	elif y <= 4.1e-44:
		tmp = t + x
	elif y <= 2.5e+174:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) / Float64(a / y))
	t_2 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -2.1e+229)
		tmp = t_2;
	elseif (y <= -2.5e+122)
		tmp = t_1;
	elseif (y <= -3.8e+118)
		tmp = t_2;
	elseif (y <= 4.1e-44)
		tmp = Float64(t + x);
	elseif (y <= 2.5e+174)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x / (a / y);
	t_2 = y * (x / z);
	tmp = 0.0;
	if (y <= -2.1e+229)
		tmp = t_2;
	elseif (y <= -2.5e+122)
		tmp = t_1;
	elseif (y <= -3.8e+118)
		tmp = t_2;
	elseif (y <= 4.1e-44)
		tmp = t + x;
	elseif (y <= 2.5e+174)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+229], t$95$2, If[LessEqual[y, -2.5e+122], t$95$1, If[LessEqual[y, -3.8e+118], t$95$2, If[LessEqual[y, 4.1e-44], N[(t + x), $MachinePrecision], If[LessEqual[y, 2.5e+174], x, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.09999999999999988e229 or -2.49999999999999994e122 < y < -3.80000000000000016e118

   1. Initial program 70.1%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in y around -inf 65.5%

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

   5. Taylor expanded in a around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-/l* 64.3%

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

      3. distribute-neg-frac 64.3%

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

   7. Simplified 64.3%

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

   8. Taylor expanded in t around 0 43.4%

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

      1. associate-/l* 54.9%

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

   10. Simplified 54.9%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 56.1%

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

   12. Applied egg-rr 56.1%

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

   if -2.09999999999999988e229 < y < -2.49999999999999994e122 or 2.4999999999999998e174 < y

   1. Initial program 66.5%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around -inf 64.6%

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

   5. Taylor expanded in t around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. associate-/l* 54.0%

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

      3. distribute-neg-frac 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in a around inf 34.8%

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

      1. mul-1-neg 34.8%

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

      2. associate-/l* 41.3%

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

      3. distribute-neg-frac 41.3%

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

   10. Simplified 41.3%

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

   if -3.80000000000000016e118 < y < 4.09999999999999992e-44

   1. Initial program 73.6%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. associate-*r/ 63.0%

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

      3. unsub-neg 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in t around inf 62.0%

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

   8. Taylor expanded in z around inf 46.8%

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

      1. mul-1-neg 46.8%

         \[\leadsto x - \color{blue}{\left(-t\right)} \]

   10. Simplified 46.8%

       \[\leadsto x - \color{blue}{\left(-t\right)} \]

   if 4.09999999999999992e-44 < y < 2.4999999999999998e174

   1. Initial program 75.9%

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

      1. associate-*l/ 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in a around inf 37.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-44}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 36.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+122}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-44}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= y -1.9e+229)
     t_1
     (if (<= y -1.7e+122)
       (/ (* x (- y)) a)
       (if (<= y -3.6e+118)
         t_1
         (if (<= y 1.15e-44)
           (+ t x)
           (if (<= y 2.4e+174) x (/ (- x) (/ a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / z);
	double tmp;
	if (y <= -1.9e+229) {
		tmp = t_1;
	} else if (y <= -1.7e+122) {
		tmp = (x * -y) / a;
	} else if (y <= -3.6e+118) {
		tmp = t_1;
	} else if (y <= 1.15e-44) {
		tmp = t + x;
	} else if (y <= 2.4e+174) {
		tmp = x;
	} else {
		tmp = -x / (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) :: t_1
    real(8) :: tmp
    t_1 = y * (x / z)
    if (y <= (-1.9d+229)) then
        tmp = t_1
    else if (y <= (-1.7d+122)) then
        tmp = (x * -y) / a
    else if (y <= (-3.6d+118)) then
        tmp = t_1
    else if (y <= 1.15d-44) then
        tmp = t + x
    else if (y <= 2.4d+174) then
        tmp = x
    else
        tmp = -x / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (x / z);
	double tmp;
	if (y <= -1.9e+229) {
		tmp = t_1;
	} else if (y <= -1.7e+122) {
		tmp = (x * -y) / a;
	} else if (y <= -3.6e+118) {
		tmp = t_1;
	} else if (y <= 1.15e-44) {
		tmp = t + x;
	} else if (y <= 2.4e+174) {
		tmp = x;
	} else {
		tmp = -x / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (x / z)
	tmp = 0
	if y <= -1.9e+229:
		tmp = t_1
	elif y <= -1.7e+122:
		tmp = (x * -y) / a
	elif y <= -3.6e+118:
		tmp = t_1
	elif y <= 1.15e-44:
		tmp = t + x
	elif y <= 2.4e+174:
		tmp = x
	else:
		tmp = -x / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -1.9e+229)
		tmp = t_1;
	elseif (y <= -1.7e+122)
		tmp = Float64(Float64(x * Float64(-y)) / a);
	elseif (y <= -3.6e+118)
		tmp = t_1;
	elseif (y <= 1.15e-44)
		tmp = Float64(t + x);
	elseif (y <= 2.4e+174)
		tmp = x;
	else
		tmp = Float64(Float64(-x) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (x / z);
	tmp = 0.0;
	if (y <= -1.9e+229)
		tmp = t_1;
	elseif (y <= -1.7e+122)
		tmp = (x * -y) / a;
	elseif (y <= -3.6e+118)
		tmp = t_1;
	elseif (y <= 1.15e-44)
		tmp = t + x;
	elseif (y <= 2.4e+174)
		tmp = x;
	else
		tmp = -x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+229], t$95$1, If[LessEqual[y, -1.7e+122], N[(N[(x * (-y)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -3.6e+118], t$95$1, If[LessEqual[y, 1.15e-44], N[(t + x), $MachinePrecision], If[LessEqual[y, 2.4e+174], x, N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.90000000000000009e229 or -1.7e122 < y < -3.6e118

   1. Initial program 70.1%

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

      1. associate-*l/ 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in y around -inf 65.5%

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

   5. Taylor expanded in a around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-/l* 64.3%

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

      3. distribute-neg-frac 64.3%

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

   7. Simplified 64.3%

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

   8. Taylor expanded in t around 0 43.4%

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

      1. associate-/l* 54.9%

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

   10. Simplified 54.9%

       \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 56.1%

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

   12. Applied egg-rr 56.1%

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

   if -1.90000000000000009e229 < y < -1.7e122

   1. Initial program 56.4%

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

      1. associate-*l/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around -inf 56.6%

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

   5. Taylor expanded in t around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. associate-/l* 41.2%

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

      3. distribute-neg-frac 41.2%

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

   7. Simplified 41.2%

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

   8. Taylor expanded in a around inf 33.7%

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

   if -3.6e118 < y < 1.14999999999999999e-44

   1. Initial program 73.6%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. associate-*r/ 63.0%

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

      3. unsub-neg 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in t around inf 62.0%

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

   8. Taylor expanded in z around inf 46.8%

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

      1. mul-1-neg 46.8%

         \[\leadsto x - \color{blue}{\left(-t\right)} \]

   10. Simplified 46.8%

       \[\leadsto x - \color{blue}{\left(-t\right)} \]

   if 1.14999999999999999e-44 < y < 2.3999999999999998e174

   1. Initial program 75.9%

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

      1. associate-*l/ 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in a around inf 37.5%

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

   if 2.3999999999999998e174 < y

   1. Initial program 77.2%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around -inf 73.0%

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

   5. Taylor expanded in t around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. associate-/l* 67.4%

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

      3. distribute-neg-frac 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in a around inf 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/l* 49.3%

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

      3. distribute-neg-frac 49.3%

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

   10. Simplified 49.3%

       \[\leadsto \color{blue}{\frac{-x}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+122}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-44}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+174}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+138}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-79}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -2.05e+138)
     t
     (if (<= z -4e-301)
       t_1
       (if (<= z 7e-79) (- x (* x (/ y a))) (if (<= z 1.6e+126) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -2.05e+138) {
		tmp = t;
	} else if (z <= -4e-301) {
		tmp = t_1;
	} else if (z <= 7e-79) {
		tmp = x - (x * (y / a));
	} else if (z <= 1.6e+126) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (z <= (-2.05d+138)) then
        tmp = t
    else if (z <= (-4d-301)) then
        tmp = t_1
    else if (z <= 7d-79) then
        tmp = x - (x * (y / a))
    else if (z <= 1.6d+126) then
        tmp = t_1
    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 t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -2.05e+138) {
		tmp = t;
	} else if (z <= -4e-301) {
		tmp = t_1;
	} else if (z <= 7e-79) {
		tmp = x - (x * (y / a));
	} else if (z <= 1.6e+126) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -2.05e+138:
		tmp = t
	elif z <= -4e-301:
		tmp = t_1
	elif z <= 7e-79:
		tmp = x - (x * (y / a))
	elif z <= 1.6e+126:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -2.05e+138)
		tmp = t;
	elseif (z <= -4e-301)
		tmp = t_1;
	elseif (z <= 7e-79)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (z <= 1.6e+126)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -2.05e+138)
		tmp = t;
	elseif (z <= -4e-301)
		tmp = t_1;
	elseif (z <= 7e-79)
		tmp = x - (x * (y / a));
	elseif (z <= 1.6e+126)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+138], t, If[LessEqual[z, -4e-301], t$95$1, If[LessEqual[z, 7e-79], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+126], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0499999999999999e138 or 1.5999999999999999e126 < z

   1. Initial program 34.5%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in z around inf 50.9%

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

   if -2.0499999999999999e138 < z < -4.00000000000000027e-301 or 7.00000000000000059e-79 < z < 1.5999999999999999e126

   1. Initial program 82.6%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 68.3%

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

   5. Taylor expanded in t around inf 56.3%

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

      1. associate-*r/ 61.2%

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

   7. Simplified 61.2%

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

   if -4.00000000000000027e-301 < z < 7.00000000000000059e-79

   1. Initial program 90.4%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 76.4%

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

   5. Taylor expanded in x around inf 62.9%

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

      1. distribute-lft-in 62.9%

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

      2. *-rgt-identity 62.9%

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

      3. mul-1-neg 62.9%

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

      4. distribute-rgt-neg-in 62.9%

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

      5. unsub-neg 62.9%

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

   7. Simplified 62.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+138}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-301}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-79}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+126}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-131} \lor \neg \left(a \leq 4.5 \cdot 10^{-33}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.1e-131) (not (<= a 4.5e-33)))
   (+ x (/ (- t x) (/ a (- y z))))
   (+ t (/ (- x t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e-131) || !(a <= 4.5e-33)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / 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 ((a <= (-3.1d-131)) .or. (.not. (a <= 4.5d-33))) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t + ((x - t) / (z / 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 ((a <= -3.1e-131) || !(a <= 4.5e-33)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.1e-131) or not (a <= 4.5e-33):
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.1e-131) || !(a <= 4.5e-33))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.1e-131) || ~((a <= 4.5e-33)))
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.1e-131], N[Not[LessEqual[a, 4.5e-33]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.10000000000000021e-131 or 4.49999999999999991e-33 < a

   1. Initial program 73.9%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in a around inf 69.2%

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

      1. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   if -3.10000000000000021e-131 < a < 4.49999999999999991e-33

   1. Initial program 69.6%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in z around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. associate-*r/ 73.3%

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

      3. associate-*r/ 73.3%

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

      4. div-sub 73.4%

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

      5. distribute-lft-out-- 73.4%

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

      6. mul-1-neg 73.4%

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

      7. distribute-neg-frac 73.4%

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

      8. distribute-rgt-out-- 73.4%

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

      9. unsub-neg 73.4%

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

      10. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in y around inf 78.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-131} \lor \neg \left(a \leq 4.5 \cdot 10^{-33}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 9: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-131} \lor \neg \left(a \leq 7.4 \cdot 10^{-34}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.1e-131) (not (<= a 7.4e-34)))
   (+ x (/ (- t x) (/ a (- y z))))
   (+ t (/ (- x t) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e-131) || !(a <= 7.4e-34)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (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 ((a <= (-3.1d-131)) .or. (.not. (a <= 7.4d-34))) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t + ((x - t) / (z / (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 ((a <= -3.1e-131) || !(a <= 7.4e-34)) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.1e-131) or not (a <= 7.4e-34):
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.1e-131) || !(a <= 7.4e-34))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.1e-131) || ~((a <= 7.4e-34)))
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.1e-131], N[Not[LessEqual[a, 7.4e-34]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.10000000000000021e-131 or 7.39999999999999976e-34 < a

   1. Initial program 73.9%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in a around inf 69.2%

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

      1. associate-/l* 80.2%

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

   6. Simplified 80.2%

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

   if -3.10000000000000021e-131 < a < 7.39999999999999976e-34

   1. Initial program 69.6%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in z around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. associate-*r/ 73.3%

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

      3. associate-*r/ 73.3%

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

      4. div-sub 73.4%

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

      5. distribute-lft-out-- 73.4%

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

      6. mul-1-neg 73.4%

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

      7. distribute-neg-frac 73.4%

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

      8. distribute-rgt-out-- 73.4%

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

      9. unsub-neg 73.4%

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

      10. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-131} \lor \neg \left(a \leq 7.4 \cdot 10^{-34}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 10: 37.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+118}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-82}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3e+118)
   (* (- y a) (/ x z))
   (if (<= y 5.5e-82)
     (+ t x)
     (if (<= y 2.5e+174) (* x (+ (/ z a) 1.0)) (/ (- x) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3e+118) {
		tmp = (y - a) * (x / z);
	} else if (y <= 5.5e-82) {
		tmp = t + x;
	} else if (y <= 2.5e+174) {
		tmp = x * ((z / a) + 1.0);
	} else {
		tmp = -x / (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 (y <= (-3d+118)) then
        tmp = (y - a) * (x / z)
    else if (y <= 5.5d-82) then
        tmp = t + x
    else if (y <= 2.5d+174) then
        tmp = x * ((z / a) + 1.0d0)
    else
        tmp = -x / (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 (y <= -3e+118) {
		tmp = (y - a) * (x / z);
	} else if (y <= 5.5e-82) {
		tmp = t + x;
	} else if (y <= 2.5e+174) {
		tmp = x * ((z / a) + 1.0);
	} else {
		tmp = -x / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3e+118:
		tmp = (y - a) * (x / z)
	elif y <= 5.5e-82:
		tmp = t + x
	elif y <= 2.5e+174:
		tmp = x * ((z / a) + 1.0)
	else:
		tmp = -x / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3e+118)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (y <= 5.5e-82)
		tmp = Float64(t + x);
	elseif (y <= 2.5e+174)
		tmp = Float64(x * Float64(Float64(z / a) + 1.0));
	else
		tmp = Float64(Float64(-x) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3e+118)
		tmp = (y - a) * (x / z);
	elseif (y <= 5.5e-82)
		tmp = t + x;
	elseif (y <= 2.5e+174)
		tmp = x * ((z / a) + 1.0);
	else
		tmp = -x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3e+118], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-82], N[(t + x), $MachinePrecision], If[LessEqual[y, 2.5e+174], N[(x * N[(N[(z / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3e118

   1. Initial program 63.2%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 37.6%

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

      1. associate--l+ 37.6%

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

      2. associate-*r/ 37.6%

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

      3. associate-*r/ 37.6%

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

      4. div-sub 37.7%

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

      5. distribute-lft-out-- 37.7%

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

      6. mul-1-neg 37.7%

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

      7. distribute-neg-frac 37.7%

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

      8. distribute-rgt-out-- 38.3%

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

      9. unsub-neg 38.3%

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

      10. associate-/l* 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in t around 0 29.0%

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

      1. associate-*l/ 37.5%

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

   9. Simplified 37.5%

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

   if -3e118 < y < 5.4999999999999998e-82

   1. Initial program 73.8%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. associate-*r/ 62.9%

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

      3. unsub-neg 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in t around inf 62.0%

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

   8. Taylor expanded in z around inf 46.8%

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

      1. mul-1-neg 46.8%

         \[\leadsto x - \color{blue}{\left(-t\right)} \]

   10. Simplified 46.8%

       \[\leadsto x - \color{blue}{\left(-t\right)} \]

   if 5.4999999999999998e-82 < y < 2.4999999999999998e174

   1. Initial program 74.8%

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

      1. associate-*l/ 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in y around 0 42.4%

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

      1. mul-1-neg 42.4%

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

      2. associate-*r/ 52.4%

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

      3. unsub-neg 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in t around 0 38.7%

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

      1. sub-neg 38.7%

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

      2. mul-1-neg 38.7%

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

      3. remove-double-neg 38.7%

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

      4. associate-/l* 38.6%

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

   9. Simplified 38.6%

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

   10. Taylor expanded in a around inf 38.9%

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

   11. Taylor expanded in x around 0 38.9%

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

   if 2.4999999999999998e174 < y

   1. Initial program 77.2%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around -inf 73.0%

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

   5. Taylor expanded in t around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. associate-/l* 67.4%

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

      3. distribute-neg-frac 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in a around inf 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/l* 49.3%

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

      3. distribute-neg-frac 49.3%

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

   10. Simplified 49.3%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+118}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-82}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \left(\frac{z}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-11} \lor \neg \left(t \leq 8.3 \cdot 10^{-63}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3e-11) (not (<= t 8.3e-63)))
   (* t (/ (- y z) (- a z)))
   (- x (* x (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3e-11) || !(t <= 8.3e-63)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - (x * (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 ((t <= (-3d-11)) .or. (.not. (t <= 8.3d-63))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x - (x * (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 ((t <= -3e-11) || !(t <= 8.3e-63)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3e-11) or not (t <= 8.3e-63):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x - (x * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3e-11) || !(t <= 8.3e-63))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3e-11) || ~((t <= 8.3e-63)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x - (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3e-11], N[Not[LessEqual[t, 8.3e-63]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e-11 or 8.29999999999999959e-63 < t

   1. Initial program 70.1%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around 0 47.1%

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

      1. associate-*r/ 68.7%

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

   6. Simplified 68.7%

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

   if -3e-11 < t < 8.29999999999999959e-63

   1. Initial program 75.4%

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

      1. associate-*l/ 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in z around 0 65.1%

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

   5. Taylor expanded in x around inf 62.6%

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

      1. distribute-lft-in 62.6%

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

      2. *-rgt-identity 62.6%

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

      3. mul-1-neg 62.6%

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

      4. distribute-rgt-neg-in 62.6%

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

      5. unsub-neg 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-11} \lor \neg \left(t \leq 8.3 \cdot 10^{-63}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 12: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+47} \lor \neg \left(z \leq 2.5 \cdot 10^{+68}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+47) (not (<= z 2.5e+68)))
   (* t (/ (- y z) (- a z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+47) || !(z <= 2.5e+68)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (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 <= (-1.3d+47)) .or. (.not. (z <= 2.5d+68))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) * (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 <= -1.3e+47) || !(z <= 2.5e+68)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+47) or not (z <= 2.5e+68):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+47) || !(z <= 2.5e+68))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e+47) || ~((z <= 2.5e+68)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+47], N[Not[LessEqual[z, 2.5e+68]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000002e47 or 2.5000000000000002e68 < z

   1. Initial program 41.3%

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

      1. associate-*l/ 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in x around 0 34.7%

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

      1. associate-*r/ 63.1%

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

   6. Simplified 63.1%

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

   if -1.30000000000000002e47 < z < 2.5000000000000002e68

   1. Initial program 89.0%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 74.9%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+47} \lor \neg \left(z \leq 2.5 \cdot 10^{+68}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 13: 68.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-33}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e-131)
   (+ x (* (- t x) (/ y a)))
   (if (<= a 5.3e-33) (+ t (/ (- x t) (/ z y))) (+ x (/ y (/ a (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e-131) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 5.3e-33) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + (y / (a / (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 (a <= (-3.1d-131)) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 5.3d-33) then
        tmp = t + ((x - t) / (z / y))
    else
        tmp = x + (y / (a / (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 (a <= -3.1e-131) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 5.3e-33) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e-131:
		tmp = x + ((t - x) * (y / a))
	elif a <= 5.3e-33:
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e-131)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 5.3e-33)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.1e-131)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 5.3e-33)
		tmp = t + ((x - t) / (z / y));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e-131], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.3e-33], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.10000000000000021e-131

   1. Initial program 70.0%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in z around 0 67.9%

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

   if -3.10000000000000021e-131 < a < 5.29999999999999968e-33

   1. Initial program 69.6%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in z around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. associate-*r/ 73.3%

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

      3. associate-*r/ 73.3%

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

      4. div-sub 73.4%

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

      5. distribute-lft-out-- 73.4%

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

      6. mul-1-neg 73.4%

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

      7. distribute-neg-frac 73.4%

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

      8. distribute-rgt-out-- 73.4%

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

      9. unsub-neg 73.4%

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

      10. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in y around inf 78.6%

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

   if 5.29999999999999968e-33 < a

   1. Initial program 78.0%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around 0 69.3%

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

      1. associate-/l* 77.3%

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

   6. Simplified 77.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-33}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 14: 54.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+139}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+124}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+139) t (if (<= z 2.6e+124) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+139) {
		tmp = t;
	} else if (z <= 2.6e+124) {
		tmp = x + (t * (y / a));
	} 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 <= (-8d+139)) then
        tmp = t
    else if (z <= 2.6d+124) then
        tmp = x + (t * (y / a))
    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 <= -8e+139) {
		tmp = t;
	} else if (z <= 2.6e+124) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+139:
		tmp = t
	elif z <= 2.6e+124:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+139)
		tmp = t;
	elseif (z <= 2.6e+124)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+139)
		tmp = t;
	elseif (z <= 2.6e+124)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+139], t, If[LessEqual[z, 2.6e+124], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000026e139 or 2.6e124 < z

   1. Initial program 34.5%

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

      1. associate-*l/ 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in z around inf 50.9%

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

   if -8.00000000000000026e139 < z < 2.6e124

   1. Initial program 85.1%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 70.8%

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

   5. Taylor expanded in t around inf 52.8%

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

      1. associate-*r/ 58.5%

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

   7. Simplified 58.5%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+139}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+124}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 39.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.02e+57) t (if (<= z 1.4e+97) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.02e+57) {
		tmp = t;
	} else if (z <= 1.4e+97) {
		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 <= (-1.02d+57)) then
        tmp = t
    else if (z <= 1.4d+97) 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 <= -1.02e+57) {
		tmp = t;
	} else if (z <= 1.4e+97) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.02e+57:
		tmp = t
	elif z <= 1.4e+97:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.02e+57)
		tmp = t;
	elseif (z <= 1.4e+97)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.02e+57)
		tmp = t;
	elseif (z <= 1.4e+97)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.02e+57], t, If[LessEqual[z, 1.4e+97], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e57 or 1.4e97 < z

   1. Initial program 38.9%

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

      1. associate-*l/ 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in z around inf 45.8%

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

   if -1.02e57 < z < 1.4e97

   1. Initial program 87.9%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in a around inf 40.0%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+57}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 72.4%

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

   1. associate-*l/ 86.5%

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

3. Simplified 86.5%

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

4. Taylor expanded in y around 0 40.5%

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

   1. mul-1-neg 40.5%

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

   2. associate-*r/ 49.3%

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

   3. unsub-neg 49.3%

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

6. Simplified 49.3%

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

7. Taylor expanded in t around 0 29.6%

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

   1. sub-neg 29.6%

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

   2. mul-1-neg 29.6%

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

   3. remove-double-neg 29.6%

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

   4. associate-/l* 30.9%

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

9. Simplified 30.9%

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

10. Taylor expanded in a around 0 2.7%

    \[\leadsto \color{blue}{x + -1 \cdot x} \]
11. Step-by-step derivation

    1. distribute-rgt1-in 2.7%

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

    2. metadata-eval 2.7%

       \[\leadsto \color{blue}{0} \cdot x \]

    3. mul0-lft 2.7%

       \[\leadsto \color{blue}{0} \]

12. Simplified 2.7%

    \[\leadsto \color{blue}{0} \]

13. Final simplification 2.7%

    \[\leadsto 0 \]

Alternative 17: 26.0% accurate, 13.0× 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 72.4%

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

   1. associate-*l/ 86.5%

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

3. Simplified 86.5%

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

4. Taylor expanded in z around inf 19.8%

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

5. Final simplification 19.8%

   \[\leadsto t \]

Developer target: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} 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 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    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 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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