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

Percentage Accurate: 68.0% → 90.6%

Time: 12.6s

Alternatives: 16

Speedup: 0.9×

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: 68.0% 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: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-286} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -4e-286) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (* (- y a) (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -4e-286) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-4d-286)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + (((y - a) * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -4e-286) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -4e-286) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -4e-286) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -4e-286) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-286], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.0000000000000002e-286 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.5%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   if -4.0000000000000002e-286 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.4%

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

      1. associate-*l/ 4.4%

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

   3. Simplified 4.4%

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

   4. Taylor expanded in z around -inf 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. mul-1-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. mul-1-neg 99.7%

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

      6. unsub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. mul-1-neg 99.7%

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

      9. sub-neg 99.7%

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

      10. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -4 \cdot 10^{-286} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 2: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+139}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+190}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -3.1e+114)
     t_1
     (if (<= z 1.6e+19)
       (* x (- 1.0 (/ y a)))
       (if (<= z 2.1e+102)
         t_1
         (if (<= z 2.8e+139)
           (+ x t)
           (if (<= z 3.5e+190) (* y (/ x z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -3.1e+114) {
		tmp = t_1;
	} else if (z <= 1.6e+19) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.1e+102) {
		tmp = t_1;
	} else if (z <= 2.8e+139) {
		tmp = x + t;
	} else if (z <= 3.5e+190) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-3.1d+114)) then
        tmp = t_1
    else if (z <= 1.6d+19) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.1d+102) then
        tmp = t_1
    else if (z <= 2.8d+139) then
        tmp = x + t
    else if (z <= 3.5d+190) then
        tmp = y * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -3.1e+114) {
		tmp = t_1;
	} else if (z <= 1.6e+19) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.1e+102) {
		tmp = t_1;
	} else if (z <= 2.8e+139) {
		tmp = x + t;
	} else if (z <= 3.5e+190) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -3.1e+114:
		tmp = t_1
	elif z <= 1.6e+19:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.1e+102:
		tmp = t_1
	elif z <= 2.8e+139:
		tmp = x + t
	elif z <= 3.5e+190:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3.1e+114)
		tmp = t_1;
	elseif (z <= 1.6e+19)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.1e+102)
		tmp = t_1;
	elseif (z <= 2.8e+139)
		tmp = Float64(x + t);
	elseif (z <= 3.5e+190)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3.1e+114)
		tmp = t_1;
	elseif (z <= 1.6e+19)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.1e+102)
		tmp = t_1;
	elseif (z <= 2.8e+139)
		tmp = x + t;
	elseif (z <= 3.5e+190)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+114], t$95$1, If[LessEqual[z, 1.6e+19], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+102], t$95$1, If[LessEqual[z, 2.8e+139], N[(x + t), $MachinePrecision], If[LessEqual[z, 3.5e+190], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1e114 or 1.6e19 < z < 2.10000000000000001e102 or 3.4999999999999999e190 < z

   1. Initial program 36.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 a around 0 25.1%

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

      1. associate-*r/ 25.1%

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

      2. neg-mul-1 25.1%

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

      3. *-commutative 25.1%

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

      4. distribute-rgt-neg-in 25.1%

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

   6. Simplified 25.1%

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

   7. Taylor expanded in t around inf 70.5%

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

   if -3.1e114 < z < 1.6e19

   1. Initial program 88.6%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 73.9%

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

   5. Taylor expanded in t around 0 57.5%

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

      1. mul-1-neg 57.5%

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

      2. associate-/l* 58.6%

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

      3. distribute-neg-frac 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in x around 0 59.7%

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

      1. mul-1-neg 59.7%

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

      2. sub-neg 59.7%

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

      3. *-commutative 59.7%

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

   10. Simplified 59.7%

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

   if 2.10000000000000001e102 < z < 2.7999999999999998e139

   1. Initial program 25.7%

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

      1. clear-num 25.7%

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

      2. associate-/r/ 25.7%

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

   3. Applied egg-rr 25.7%

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

   4. Taylor expanded in t around inf 41.4%

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

   5. Taylor expanded in z around inf 79.4%

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

   if 2.7999999999999998e139 < z < 3.4999999999999999e190

   1. Initial program 22.6%

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

      1. associate-*l/ 42.5%

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

   3. Simplified 42.5%

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

   4. Taylor expanded in a around 0 22.6%

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

      1. associate-*r/ 22.6%

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

      2. neg-mul-1 22.6%

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

      3. *-commutative 22.6%

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

      4. distribute-rgt-neg-in 22.6%

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

   6. Simplified 22.6%

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

   7. Taylor expanded in x around -inf 33.6%

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

      1. associate-/l* 43.0%

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

   9. Simplified 43.0%

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

   10. Taylor expanded in y around 0 33.6%

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

       1. associate-*r/ 43.3%

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

   12. Simplified 43.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+139}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+190}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 3: 54.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+32}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-22}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a - z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 440000000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -3e+114)
     t_1
     (if (<= z -1e+32)
       (+ x (* y (/ t a)))
       (if (<= z -1.65e-22)
         (/ (* x (- y)) (- a z))
         (if (<= z -1.1e-197)
           (* x (- 1.0 (/ y a)))
           (if (<= z 440000000.0) (+ x (* t (/ y a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -3e+114) {
		tmp = t_1;
	} else if (z <= -1e+32) {
		tmp = x + (y * (t / a));
	} else if (z <= -1.65e-22) {
		tmp = (x * -y) / (a - z);
	} else if (z <= -1.1e-197) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 440000000.0) {
		tmp = x + (t * (y / a));
	} 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 * (1.0d0 - (y / z))
    if (z <= (-3d+114)) then
        tmp = t_1
    else if (z <= (-1d+32)) then
        tmp = x + (y * (t / a))
    else if (z <= (-1.65d-22)) then
        tmp = (x * -y) / (a - z)
    else if (z <= (-1.1d-197)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 440000000.0d0) then
        tmp = x + (t * (y / a))
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -3e+114) {
		tmp = t_1;
	} else if (z <= -1e+32) {
		tmp = x + (y * (t / a));
	} else if (z <= -1.65e-22) {
		tmp = (x * -y) / (a - z);
	} else if (z <= -1.1e-197) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 440000000.0) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -3e+114:
		tmp = t_1
	elif z <= -1e+32:
		tmp = x + (y * (t / a))
	elif z <= -1.65e-22:
		tmp = (x * -y) / (a - z)
	elif z <= -1.1e-197:
		tmp = x * (1.0 - (y / a))
	elif z <= 440000000.0:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3e+114)
		tmp = t_1;
	elseif (z <= -1e+32)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= -1.65e-22)
		tmp = Float64(Float64(x * Float64(-y)) / Float64(a - z));
	elseif (z <= -1.1e-197)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 440000000.0)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3e+114)
		tmp = t_1;
	elseif (z <= -1e+32)
		tmp = x + (y * (t / a));
	elseif (z <= -1.65e-22)
		tmp = (x * -y) / (a - z);
	elseif (z <= -1.1e-197)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 440000000.0)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+114], t$95$1, If[LessEqual[z, -1e+32], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-22], N[(N[(x * (-y)), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-197], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 440000000.0], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3e114 or 4.4e8 < z

   1. Initial program 34.9%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in a around 0 25.4%

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

      1. associate-*r/ 25.4%

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

      2. neg-mul-1 25.4%

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

      3. *-commutative 25.4%

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

      4. distribute-rgt-neg-in 25.4%

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

   6. Simplified 25.4%

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

   7. Taylor expanded in t around inf 61.5%

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

   if -3e114 < z < -1.00000000000000005e32

   1. Initial program 55.6%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 61.7%

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

   5. Taylor expanded in t around inf 49.4%

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

      1. expm1-log1p-u 49.2%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot t}{a}\right)\right)} \]

      2. expm1-udef 49.3%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot t}{a}\right)} - 1\right)} \]

      3. associate-/l* 54.9%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{t}}}\right)} - 1\right) \]

   7. Applied egg-rr 54.9%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{t}}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 54.8%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{t}}\right)\right)} \]

      2. expm1-log1p 62.1%

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

      3. associate-/r/ 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-*r/ 49.4%

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

      6. *-commutative 49.4%

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

      7. associate-*r/ 62.1%

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

   9. Simplified 62.1%

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

   if -1.00000000000000005e32 < z < -1.65e-22

   1. Initial program 86.0%

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

      1. associate-*l/ 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around -inf 72.4%

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

   5. Taylor expanded in t around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. mul-1-neg 64.9%

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

      3. distribute-rgt-neg-out 64.9%

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

   7. Simplified 64.9%

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

   if -1.65e-22 < z < -1.1e-197

   1. Initial program 95.5%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   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 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. associate-/l* 65.1%

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

      3. distribute-neg-frac 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in x around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. sub-neg 67.9%

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

      3. *-commutative 67.9%

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

   10. Simplified 67.9%

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

   if -1.1e-197 < z < 4.4e8

   1. Initial program 91.5%

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

      1. clear-num 91.5%

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

      2. associate-/r/ 91.5%

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

   3. Applied egg-rr 91.5%

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

   4. Taylor expanded in t around inf 78.7%

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

   5. Taylor expanded in z around 0 68.6%

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

      1. associate-*l/ 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+32}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-22}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a - z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 440000000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 4: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ t a)))))
   (if (<= a -1.4e+83)
     t_2
     (if (<= a -6.1e-193)
       t_1
       (if (<= a 8.2e-151)
         (* y (/ (- t x) (- a z)))
         (if (<= a 9e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -1.4e+83) {
		tmp = t_2;
	} else if (a <= -6.1e-193) {
		tmp = t_1;
	} else if (a <= 8.2e-151) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 9e+69) {
		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 = t * ((y - z) / (a - z))
    t_2 = x + (y * (t / a))
    if (a <= (-1.4d+83)) then
        tmp = t_2
    else if (a <= (-6.1d-193)) then
        tmp = t_1
    else if (a <= 8.2d-151) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 9d+69) 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 = t * ((y - z) / (a - z));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -1.4e+83) {
		tmp = t_2;
	} else if (a <= -6.1e-193) {
		tmp = t_1;
	} else if (a <= 8.2e-151) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 9e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y * (t / a))
	tmp = 0
	if a <= -1.4e+83:
		tmp = t_2
	elif a <= -6.1e-193:
		tmp = t_1
	elif a <= 8.2e-151:
		tmp = y * ((t - x) / (a - z))
	elif a <= 9e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -1.4e+83)
		tmp = t_2;
	elseif (a <= -6.1e-193)
		tmp = t_1;
	elseif (a <= 8.2e-151)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 9e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y * (t / a));
	tmp = 0.0;
	if (a <= -1.4e+83)
		tmp = t_2;
	elseif (a <= -6.1e-193)
		tmp = t_1;
	elseif (a <= 8.2e-151)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 9e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+83], t$95$2, If[LessEqual[a, -6.1e-193], t$95$1, If[LessEqual[a, 8.2e-151], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.4e83 or 8.9999999999999999e69 < a

   1. Initial program 75.2%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around 0 80.7%

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

   5. Taylor expanded in t around inf 71.7%

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

      1. expm1-log1p-u 68.5%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot t}{a}\right)\right)} \]

      2. expm1-udef 64.7%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot t}{a}\right)} - 1\right)} \]

      3. associate-/l* 67.0%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{t}}}\right)} - 1\right) \]

   7. Applied egg-rr 67.0%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{t}}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 70.8%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{t}}\right)\right)} \]

      2. expm1-log1p 77.9%

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

      3. associate-/r/ 76.9%

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

      4. *-commutative 76.9%

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

      5. associate-*r/ 71.7%

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

      6. *-commutative 71.7%

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

      7. associate-*r/ 77.9%

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

   9. Simplified 77.9%

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

   if -1.4e83 < a < -6.10000000000000012e-193 or 8.2000000000000002e-151 < a < 8.9999999999999999e69

   1. Initial program 58.7%

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

      1. associate-*l/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in x around 0 43.7%

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

      1. associate-*r/ 61.0%

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

   6. Simplified 61.0%

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

   if -6.10000000000000012e-193 < a < 8.2000000000000002e-151

   1. Initial program 73.5%

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

      1. associate-*l/ 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. *-commutative 72.3%

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

   6. Simplified 72.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 5: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+59}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+203}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ y (/ z (- t x))))))
   (if (<= z -1.8e+154)
     t_1
     (if (<= z 1.95e+59)
       (+ x (* (- t x) (/ y (- a z))))
       (if (<= z 8.8e+203) (+ t (/ (* (- y a) (- x t)) z)) 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 <= -1.8e+154) {
		tmp = t_1;
	} else if (z <= 1.95e+59) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else if (z <= 8.8e+203) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (y / (z / (t - x)))
    if (z <= (-1.8d+154)) then
        tmp = t_1
    else if (z <= 1.95d+59) then
        tmp = x + ((t - x) * (y / (a - z)))
    else if (z <= 8.8d+203) then
        tmp = t + (((y - a) * (x - t)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y / (z / (t - x)));
	double tmp;
	if (z <= -1.8e+154) {
		tmp = t_1;
	} else if (z <= 1.95e+59) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else if (z <= 8.8e+203) {
		tmp = t + (((y - a) * (x - t)) / z);
	} 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 <= -1.8e+154:
		tmp = t_1
	elif z <= 1.95e+59:
		tmp = x + ((t - x) * (y / (a - z)))
	elif z <= 8.8e+203:
		tmp = t + (((y - a) * (x - t)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(y / Float64(z / Float64(t - x))))
	tmp = 0.0
	if (z <= -1.8e+154)
		tmp = t_1;
	elseif (z <= 1.95e+59)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / Float64(a - z))));
	elseif (z <= 8.8e+203)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	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 <= -1.8e+154)
		tmp = t_1;
	elseif (z <= 1.95e+59)
		tmp = x + ((t - x) * (y / (a - z)));
	elseif (z <= 8.8e+203)
		tmp = t + (((y - a) * (x - t)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+154], t$95$1, If[LessEqual[z, 1.95e+59], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+203], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e154 or 8.80000000000000018e203 < z

   1. Initial program 22.6%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in a around 0 22.4%

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

      1. associate-*r/ 22.4%

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

      2. neg-mul-1 22.4%

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

      3. *-commutative 22.4%

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

      4. distribute-rgt-neg-in 22.4%

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

   6. Simplified 22.4%

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

   7. Taylor expanded in y around 0 68.2%

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

      1. +-commutative 68.2%

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

      2. mul-1-neg 68.2%

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

      3. unsub-neg 68.2%

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

      4. associate-/l* 91.8%

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

   9. Simplified 91.8%

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

   if -1.8e154 < z < 1.95000000000000011e59

   1. Initial program 87.0%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around inf 84.0%

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

   if 1.95000000000000011e59 < z < 8.80000000000000018e203

   1. Initial program 33.1%

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

      1. associate-*l/ 61.4%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in z around -inf 73.8%

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

      1. +-commutative 73.8%

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

      2. sub-neg 73.8%

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

      3. mul-1-neg 73.8%

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

      4. +-commutative 73.8%

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

      5. mul-1-neg 73.8%

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

      6. unsub-neg 73.8%

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

      7. +-commutative 73.8%

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

      8. mul-1-neg 73.8%

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

      9. sub-neg 73.8%

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

      10. distribute-rgt-out-- 74.0%

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

   6. Simplified 74.0%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+154}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+59}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+203}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 6: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-54}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -4.3e+111)
     t_1
     (if (<= z -1.7e-200)
       (* x (- 1.0 (/ y a)))
       (if (<= z 5.8e-54) (+ x (* t (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.3e+111) {
		tmp = t_1;
	} else if (z <= -1.7e-200) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.8e-54) {
		tmp = x + (t * (y / a));
	} 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) / (a - z))
    if (z <= (-4.3d+111)) then
        tmp = t_1
    else if (z <= (-1.7d-200)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 5.8d-54) then
        tmp = x + (t * (y / a))
    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) / (a - z));
	double tmp;
	if (z <= -4.3e+111) {
		tmp = t_1;
	} else if (z <= -1.7e-200) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.8e-54) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -4.3e+111:
		tmp = t_1
	elif z <= -1.7e-200:
		tmp = x * (1.0 - (y / a))
	elif z <= 5.8e-54:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.3e+111)
		tmp = t_1;
	elseif (z <= -1.7e-200)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 5.8e-54)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -4.3e+111)
		tmp = t_1;
	elseif (z <= -1.7e-200)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 5.8e-54)
		tmp = x + (t * (y / a));
	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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+111], t$95$1, If[LessEqual[z, -1.7e-200], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-54], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.29999999999999993e111 or 5.80000000000000029e-54 < z

   1. Initial program 39.3%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in x around 0 38.3%

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

      1. associate-*r/ 66.7%

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

   6. Simplified 66.7%

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

   if -4.29999999999999993e111 < z < -1.7000000000000001e-200

   1. Initial program 84.1%

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

      1. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around 0 64.5%

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

   5. Taylor expanded in t around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. associate-/l* 56.9%

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

      3. distribute-neg-frac 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in x around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. sub-neg 58.4%

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

      3. *-commutative 58.4%

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

   10. Simplified 58.4%

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

   if -1.7000000000000001e-200 < z < 5.80000000000000029e-54

   1. Initial program 92.7%

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

      1. clear-num 92.8%

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

      2. associate-/r/ 92.7%

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

   3. Applied egg-rr 92.7%

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

   4. Taylor expanded in t around inf 79.5%

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

   5. Taylor expanded in z around 0 72.7%

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

      1. associate-*l/ 76.6%

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

   7. Simplified 76.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-54}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 7: 70.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.7e+31)
   (+ x (/ t (/ a (- y z))))
   (if (<= a 6.5e-136)
     (- t (/ y (/ z (- t x))))
     (if (<= a 4.5e+44) (* 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 (a <= -2.7e+31) {
		tmp = x + (t / (a / (y - z)));
	} else if (a <= 6.5e-136) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 4.5e+44) {
		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 (a <= (-2.7d+31)) then
        tmp = x + (t / (a / (y - z)))
    else if (a <= 6.5d-136) then
        tmp = t - (y / (z / (t - x)))
    else if (a <= 4.5d+44) 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 (a <= -2.7e+31) {
		tmp = x + (t / (a / (y - z)));
	} else if (a <= 6.5e-136) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 4.5e+44) {
		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 a <= -2.7e+31:
		tmp = x + (t / (a / (y - z)))
	elif a <= 6.5e-136:
		tmp = t - (y / (z / (t - x)))
	elif a <= 4.5e+44:
		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 (a <= -2.7e+31)
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	elseif (a <= 6.5e-136)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (a <= 4.5e+44)
		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 (a <= -2.7e+31)
		tmp = x + (t / (a / (y - z)));
	elseif (a <= 6.5e-136)
		tmp = t - (y / (z / (t - x)));
	elseif (a <= 4.5e+44)
		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[LessEqual[a, -2.7e+31], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-136], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+44], 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 4 regimes

2. if a < -2.69999999999999986e31

   1. Initial program 79.3%

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

      1. clear-num 79.3%

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

      2. associate-/r/ 79.2%

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

   3. Applied egg-rr 79.2%

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

   4. Taylor expanded in t around inf 79.1%

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

   5. Taylor expanded in a around inf 74.7%

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

      1. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

   if -2.69999999999999986e31 < a < 6.50000000000000011e-136

   1. Initial program 64.8%

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

      1. associate-*l/ 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in a around 0 47.5%

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

      1. associate-*r/ 47.5%

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

      2. neg-mul-1 47.5%

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

      3. *-commutative 47.5%

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

      4. distribute-rgt-neg-in 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in y around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. associate-/l* 75.8%

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

   9. Simplified 75.8%

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

   if 6.50000000000000011e-136 < a < 4.5e44

   1. Initial program 53.0%

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

      1. associate-*l/ 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in x around 0 41.3%

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

      1. associate-*r/ 65.4%

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

   6. Simplified 65.4%

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

   if 4.5e44 < a

   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/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 77.9%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+156} \lor \neg \left(z \leq 1.7 \cdot 10^{+68}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+156) (not (<= z 1.7e+68)))
   (- t (/ y (/ z (- t x))))
   (+ x (* (- t x) (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+156) || !(z <= 1.7e+68)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * (y / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.1d+156)) .or. (.not. (z <= 1.7d+68))) then
        tmp = t - (y / (z / (t - x)))
    else
        tmp = x + ((t - x) * (y / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+156) || !(z <= 1.7e+68)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+156) or not (z <= 1.7e+68):
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + ((t - x) * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+156) || !(z <= 1.7e+68))
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / 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 <= 1.7e+68)))
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + ((t - x) * (y / (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, 1.7e+68]], $MachinePrecision]], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000002e156 or 1.70000000000000008e68 < z

   1. Initial program 25.2%

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

      1. associate-*l/ 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in a around 0 23.5%

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

      1. associate-*r/ 23.5%

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

      2. neg-mul-1 23.5%

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

      3. *-commutative 23.5%

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

      4. distribute-rgt-neg-in 23.5%

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

   6. Simplified 23.5%

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

   7. Taylor expanded in y around 0 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. associate-/l* 81.1%

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

   9. Simplified 81.1%

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

   if -1.10000000000000002e156 < z < 1.70000000000000008e68

   1. Initial program 86.3%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 83.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+156} \lor \neg \left(z \leq 1.7 \cdot 10^{+68}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 9: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 90000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -4.3e+111)
     t_1
     (if (<= z -2e-196)
       (* x (- 1.0 (/ y a)))
       (if (<= z 90000000000.0) (+ x (* y (/ t a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -4.3e+111) {
		tmp = t_1;
	} else if (z <= -2e-196) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 90000000000.0) {
		tmp = x + (y * (t / a));
	} 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 * (1.0d0 - (y / z))
    if (z <= (-4.3d+111)) then
        tmp = t_1
    else if (z <= (-2d-196)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 90000000000.0d0) then
        tmp = x + (y * (t / a))
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -4.3e+111) {
		tmp = t_1;
	} else if (z <= -2e-196) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 90000000000.0) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -4.3e+111:
		tmp = t_1
	elif z <= -2e-196:
		tmp = x * (1.0 - (y / a))
	elif z <= 90000000000.0:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -4.3e+111)
		tmp = t_1;
	elseif (z <= -2e-196)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 90000000000.0)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -4.3e+111)
		tmp = t_1;
	elseif (z <= -2e-196)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 90000000000.0)
		tmp = x + (y * (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+111], t$95$1, If[LessEqual[z, -2e-196], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 90000000000.0], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.29999999999999993e111 or 9e10 < z

   1. Initial program 34.9%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in a around 0 25.4%

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

      1. associate-*r/ 25.4%

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

      2. neg-mul-1 25.4%

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

      3. *-commutative 25.4%

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

      4. distribute-rgt-neg-in 25.4%

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

   6. Simplified 25.4%

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

   7. Taylor expanded in t around inf 61.5%

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

   if -4.29999999999999993e111 < z < -2.0000000000000001e-196

   1. Initial program 84.1%

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

      1. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around 0 64.5%

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

   5. Taylor expanded in t around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. associate-/l* 56.9%

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

      3. distribute-neg-frac 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in x around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. sub-neg 58.4%

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

      3. *-commutative 58.4%

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

   10. Simplified 58.4%

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

   if -2.0000000000000001e-196 < z < 9e10

   1. Initial program 91.5%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 79.8%

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

   5. Taylor expanded in t around inf 68.6%

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

      1. expm1-log1p-u 57.9%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot t}{a}\right)\right)} \]

      2. expm1-udef 53.2%

         \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y \cdot t}{a}\right)} - 1\right)} \]

      3. associate-/l* 54.0%

         \[\leadsto x + \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{t}}}\right)} - 1\right) \]

   7. Applied egg-rr 54.0%

      \[\leadsto x + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{t}}\right)} - 1\right)} \]
   8. Step-by-step derivation

      1. expm1-def 58.8%

         \[\leadsto x + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{t}}\right)\right)} \]

      2. expm1-log1p 70.6%

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

      3. associate-/r/ 73.1%

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

      4. *-commutative 73.1%

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

      5. associate-*r/ 68.6%

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

      6. *-commutative 68.6%

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

      7. associate-*r/ 70.7%

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

   9. Simplified 70.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 90000000000:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 10: 54.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -6.9 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 86000000000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -6.9e+112)
     t_1
     (if (<= z -2.1e-201)
       (* x (- 1.0 (/ y a)))
       (if (<= z 86000000000.0) (+ x (* t (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -6.9e+112) {
		tmp = t_1;
	} else if (z <= -2.1e-201) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 86000000000.0) {
		tmp = x + (t * (y / a));
	} 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 * (1.0d0 - (y / z))
    if (z <= (-6.9d+112)) then
        tmp = t_1
    else if (z <= (-2.1d-201)) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 86000000000.0d0) then
        tmp = x + (t * (y / a))
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -6.9e+112) {
		tmp = t_1;
	} else if (z <= -2.1e-201) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 86000000000.0) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -6.9e+112:
		tmp = t_1
	elif z <= -2.1e-201:
		tmp = x * (1.0 - (y / a))
	elif z <= 86000000000.0:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -6.9e+112)
		tmp = t_1;
	elseif (z <= -2.1e-201)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 86000000000.0)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -6.9e+112)
		tmp = t_1;
	elseif (z <= -2.1e-201)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 86000000000.0)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.9e+112], t$95$1, If[LessEqual[z, -2.1e-201], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 86000000000.0], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8999999999999999e112 or 8.6e10 < z

   1. Initial program 34.9%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in a around 0 25.4%

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

      1. associate-*r/ 25.4%

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

      2. neg-mul-1 25.4%

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

      3. *-commutative 25.4%

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

      4. distribute-rgt-neg-in 25.4%

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

   6. Simplified 25.4%

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

   7. Taylor expanded in t around inf 61.5%

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

   if -6.8999999999999999e112 < z < -2.10000000000000012e-201

   1. Initial program 84.1%

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

      1. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around 0 64.5%

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

   5. Taylor expanded in t around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. associate-/l* 56.9%

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

      3. distribute-neg-frac 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in x around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. sub-neg 58.4%

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

      3. *-commutative 58.4%

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

   10. Simplified 58.4%

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

   if -2.10000000000000012e-201 < z < 8.6e10

   1. Initial program 91.5%

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

      1. clear-num 91.5%

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

      2. associate-/r/ 91.5%

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

   3. Applied egg-rr 91.5%

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

   4. Taylor expanded in t around inf 78.7%

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

   5. Taylor expanded in z around 0 68.6%

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

      1. associate-*l/ 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 86000000000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 11: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+111} \lor \neg \left(z \leq 5.2 \cdot 10^{-54}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.4e+111) (not (<= z 5.2e-54)))
   (* 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 <= -7.4e+111) || !(z <= 5.2e-54)) {
		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 <= (-7.4d+111)) .or. (.not. (z <= 5.2d-54))) 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 <= -7.4e+111) || !(z <= 5.2e-54)) {
		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 <= -7.4e+111) or not (z <= 5.2e-54):
		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 <= -7.4e+111) || !(z <= 5.2e-54))
		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 <= -7.4e+111) || ~((z <= 5.2e-54)))
		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, -7.4e+111], N[Not[LessEqual[z, 5.2e-54]], $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 < -7.4000000000000005e111 or 5.20000000000000004e-54 < z

   1. Initial program 39.3%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in x around 0 38.3%

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

      1. associate-*r/ 66.7%

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

   6. Simplified 66.7%

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

   if -7.4000000000000005e111 < z < 5.20000000000000004e-54

   1. Initial program 89.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 75.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+111} \lor \neg \left(z \leq 5.2 \cdot 10^{-54}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 12: 36.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-196}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e+80)
   x
   (if (<= a -1.1e-196)
     (+ x t)
     (if (<= a 7e-151) (* y (/ x z)) (if (<= a 3.4e+69) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+80) {
		tmp = x;
	} else if (a <= -1.1e-196) {
		tmp = x + t;
	} else if (a <= 7e-151) {
		tmp = y * (x / z);
	} else if (a <= 3.4e+69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5d+80)) then
        tmp = x
    else if (a <= (-1.1d-196)) then
        tmp = x + t
    else if (a <= 7d-151) then
        tmp = y * (x / z)
    else if (a <= 3.4d+69) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+80) {
		tmp = x;
	} else if (a <= -1.1e-196) {
		tmp = x + t;
	} else if (a <= 7e-151) {
		tmp = y * (x / z);
	} else if (a <= 3.4e+69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e+80:
		tmp = x
	elif a <= -1.1e-196:
		tmp = x + t
	elif a <= 7e-151:
		tmp = y * (x / z)
	elif a <= 3.4e+69:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e+80)
		tmp = x;
	elseif (a <= -1.1e-196)
		tmp = Float64(x + t);
	elseif (a <= 7e-151)
		tmp = Float64(y * Float64(x / z));
	elseif (a <= 3.4e+69)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e+80)
		tmp = x;
	elseif (a <= -1.1e-196)
		tmp = x + t;
	elseif (a <= 7e-151)
		tmp = y * (x / z);
	elseif (a <= 3.4e+69)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e+80], x, If[LessEqual[a, -1.1e-196], N[(x + t), $MachinePrecision], If[LessEqual[a, 7e-151], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+69], t, x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.99999999999999961e80 or 3.39999999999999986e69 < a

   1. Initial program 75.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in a around inf 64.5%

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

   if -4.99999999999999961e80 < a < -1.10000000000000007e-196

   1. Initial program 60.9%

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

      1. clear-num 60.9%

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

      2. associate-/r/ 60.9%

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

   3. Applied egg-rr 60.9%

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

   4. Taylor expanded in t around inf 48.0%

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

   5. Taylor expanded in z around inf 42.9%

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

   if -1.10000000000000007e-196 < a < 6.99999999999999991e-151

   1. Initial program 73.0%

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

      1. associate-*l/ 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in a around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. neg-mul-1 63.5%

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

      3. *-commutative 63.5%

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

      4. distribute-rgt-neg-in 63.5%

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

   6. Simplified 63.5%

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

   7. Taylor expanded in x around -inf 52.5%

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

      1. associate-/l* 52.3%

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

   9. Simplified 52.3%

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

   10. Taylor expanded in y around 0 52.5%

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

       1. associate-*r/ 52.4%

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

   12. Simplified 52.4%

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

   if 6.99999999999999991e-151 < a < 3.39999999999999986e69

   1. Initial program 55.0%

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

      1. associate-*l/ 65.7%

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

   3. Simplified 65.7%

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

   4. Taylor expanded in z around inf 36.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-196}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 37.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-196}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e+80)
   x
   (if (<= a -8e-196)
     (+ x t)
     (if (<= a 9.5e-151) (* x (/ y z)) (if (<= a 1.3e+69) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+80) {
		tmp = x;
	} else if (a <= -8e-196) {
		tmp = x + t;
	} else if (a <= 9.5e-151) {
		tmp = x * (y / z);
	} else if (a <= 1.3e+69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5d+80)) then
        tmp = x
    else if (a <= (-8d-196)) then
        tmp = x + t
    else if (a <= 9.5d-151) then
        tmp = x * (y / z)
    else if (a <= 1.3d+69) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+80) {
		tmp = x;
	} else if (a <= -8e-196) {
		tmp = x + t;
	} else if (a <= 9.5e-151) {
		tmp = x * (y / z);
	} else if (a <= 1.3e+69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e+80:
		tmp = x
	elif a <= -8e-196:
		tmp = x + t
	elif a <= 9.5e-151:
		tmp = x * (y / z)
	elif a <= 1.3e+69:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e+80)
		tmp = x;
	elseif (a <= -8e-196)
		tmp = Float64(x + t);
	elseif (a <= 9.5e-151)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.3e+69)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e+80)
		tmp = x;
	elseif (a <= -8e-196)
		tmp = x + t;
	elseif (a <= 9.5e-151)
		tmp = x * (y / z);
	elseif (a <= 1.3e+69)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e+80], x, If[LessEqual[a, -8e-196], N[(x + t), $MachinePrecision], If[LessEqual[a, 9.5e-151], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+69], t, x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.99999999999999961e80 or 1.3000000000000001e69 < a

   1. Initial program 75.5%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in a around inf 64.5%

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

   if -4.99999999999999961e80 < a < -8.0000000000000004e-196

   1. Initial program 60.9%

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

      1. clear-num 60.9%

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

      2. associate-/r/ 60.9%

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

   3. Applied egg-rr 60.9%

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

   4. Taylor expanded in t around inf 48.0%

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

   5. Taylor expanded in z around inf 42.9%

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

   if -8.0000000000000004e-196 < a < 9.4999999999999996e-151

   1. Initial program 73.0%

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

      1. associate-*l/ 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in a around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. neg-mul-1 63.5%

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

      3. *-commutative 63.5%

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

      4. distribute-rgt-neg-in 63.5%

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

   6. Simplified 63.5%

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

   7. Taylor expanded in x around -inf 52.5%

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

      1. associate-/l* 52.3%

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

   9. Simplified 52.3%

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

       1. associate-/r/ 54.1%

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

   11. Applied egg-rr 54.1%

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

   if 9.4999999999999996e-151 < a < 1.3000000000000001e69

   1. Initial program 55.0%

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

      1. associate-*l/ 65.7%

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

   3. Simplified 65.7%

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

   4. Taylor expanded in z around inf 36.5%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-196}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 48.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+154}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e+154) t (if (<= z 8e+128) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+154) {
		tmp = t;
	} else if (z <= 8e+128) {
		tmp = x * (1.0 - (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 <= (-4.7d+154)) then
        tmp = t
    else if (z <= 8d+128) then
        tmp = x * (1.0d0 - (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 <= -4.7e+154) {
		tmp = t;
	} else if (z <= 8e+128) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e+154:
		tmp = t
	elif z <= 8e+128:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e+154)
		tmp = t;
	elseif (z <= 8e+128)
		tmp = Float64(x * Float64(1.0 - 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 <= -4.7e+154)
		tmp = t;
	elseif (z <= 8e+128)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e+154], t, If[LessEqual[z, 8e+128], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.69999999999999983e154 or 8.0000000000000006e128 < z

   1. Initial program 23.0%

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

      1. associate-*l/ 66.1%

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

   3. Simplified 66.1%

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

   4. Taylor expanded in z around inf 66.6%

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

   if -4.69999999999999983e154 < z < 8.0000000000000006e128

   1. Initial program 83.2%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around 0 67.3%

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

   5. Taylor expanded in t around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. associate-/l* 53.9%

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

      3. distribute-neg-frac 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in x around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. sub-neg 54.8%

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

      3. *-commutative 54.8%

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

   10. Simplified 54.8%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+154}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 38.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.3e+15) x (if (<= a 9.5e+69) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+15) {
		tmp = x;
	} else if (a <= 9.5e+69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.3d+15)) then
        tmp = x
    else if (a <= 9.5d+69) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e+15) {
		tmp = x;
	} else if (a <= 9.5e+69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.3e+15:
		tmp = x
	elif a <= 9.5e+69:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3e+15)
		tmp = x;
	elseif (a <= 9.5e+69)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.3e+15)
		tmp = x;
	elseif (a <= 9.5e+69)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3e+15], x, If[LessEqual[a, 9.5e+69], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e15 or 9.4999999999999995e69 < a

   1. Initial program 76.5%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in a around inf 61.7%

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

   if -1.3e15 < a < 9.4999999999999995e69

   1. Initial program 61.8%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in z around inf 33.7%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 25.2% 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 68.6%

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

   1. associate-*l/ 85.3%

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

3. Simplified 85.3%

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

4. Taylor expanded in z around inf 23.5%

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

5. Final simplification 23.5%

   \[\leadsto t \]

Developer target: 84.6% 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 2023199 
(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))))