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

Percentage Accurate: 67.6% → 90.1%

Time: 29.1s

Alternatives: 24

Speedup: 0.5×

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: 67.6% 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: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(t_1, t - x, x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (- a z))) (t_2 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_2 -4e-272)
     (fma t_1 (- t x) x)
     (if (<= t_2 0.0) (+ t (/ (* (- t x) (- a y)) z)) (+ x (* (- t x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (a - z);
	double t_2 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_2 <= -4e-272) {
		tmp = fma(t_1, (t - x), x);
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(a - z))
	t_2 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -4e-272)
		tmp = fma(t_1, Float64(t - x), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-272], N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -3.99999999999999972e-272

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-*l/ 90.7%

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

      3. fma-def 90.7%

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

   3. Simplified 90.7%

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

   if -3.99999999999999972e-272 < (+.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. +-commutative 4.4%

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

      2. associate-*l/ 4.4%

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

      3. fma-def 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in z around -inf 99.8%

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

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

   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/ 89.1%

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

   3. Simplified 89.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -4 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 57.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -2.45 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-249}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-220}:\\ \;\;\;\;\frac{t}{\frac{z}{y + z}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (- t (/ t (/ z y)))))
   (if (<= a -2.45e-18)
     (- x (* y (/ (- x t) a)))
     (if (<= a -2.25e-120)
       t_1
       (if (<= a 7.6e-293)
         t_2
         (if (<= a 1.2e-249)
           (* (- t x) (/ y (- a z)))
           (if (<= a 6.2e-220)
             (/ t (/ z (+ y z)))
             (if (<= a 3.6e-186)
               t_1
               (if (<= a 2e-153)
                 t_2
                 (if (<= a 1.02e+76) t_1 (- x (/ z (/ a t)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t - (t / (z / y));
	double tmp;
	if (a <= -2.45e-18) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= -2.25e-120) {
		tmp = t_1;
	} else if (a <= 7.6e-293) {
		tmp = t_2;
	} else if (a <= 1.2e-249) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 6.2e-220) {
		tmp = t / (z / (y + z));
	} else if (a <= 3.6e-186) {
		tmp = t_1;
	} else if (a <= 2e-153) {
		tmp = t_2;
	} else if (a <= 1.02e+76) {
		tmp = t_1;
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t - (t / (z / y))
    if (a <= (-2.45d-18)) then
        tmp = x - (y * ((x - t) / a))
    else if (a <= (-2.25d-120)) then
        tmp = t_1
    else if (a <= 7.6d-293) then
        tmp = t_2
    else if (a <= 1.2d-249) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 6.2d-220) then
        tmp = t / (z / (y + z))
    else if (a <= 3.6d-186) then
        tmp = t_1
    else if (a <= 2d-153) then
        tmp = t_2
    else if (a <= 1.02d+76) then
        tmp = t_1
    else
        tmp = x - (z / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t - (t / (z / y));
	double tmp;
	if (a <= -2.45e-18) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= -2.25e-120) {
		tmp = t_1;
	} else if (a <= 7.6e-293) {
		tmp = t_2;
	} else if (a <= 1.2e-249) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 6.2e-220) {
		tmp = t / (z / (y + z));
	} else if (a <= 3.6e-186) {
		tmp = t_1;
	} else if (a <= 2e-153) {
		tmp = t_2;
	} else if (a <= 1.02e+76) {
		tmp = t_1;
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t - (t / (z / y))
	tmp = 0
	if a <= -2.45e-18:
		tmp = x - (y * ((x - t) / a))
	elif a <= -2.25e-120:
		tmp = t_1
	elif a <= 7.6e-293:
		tmp = t_2
	elif a <= 1.2e-249:
		tmp = (t - x) * (y / (a - z))
	elif a <= 6.2e-220:
		tmp = t / (z / (y + z))
	elif a <= 3.6e-186:
		tmp = t_1
	elif a <= 2e-153:
		tmp = t_2
	elif a <= 1.02e+76:
		tmp = t_1
	else:
		tmp = x - (z / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (a <= -2.45e-18)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	elseif (a <= -2.25e-120)
		tmp = t_1;
	elseif (a <= 7.6e-293)
		tmp = t_2;
	elseif (a <= 1.2e-249)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 6.2e-220)
		tmp = Float64(t / Float64(z / Float64(y + z)));
	elseif (a <= 3.6e-186)
		tmp = t_1;
	elseif (a <= 2e-153)
		tmp = t_2;
	elseif (a <= 1.02e+76)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t - (t / (z / y));
	tmp = 0.0;
	if (a <= -2.45e-18)
		tmp = x - (y * ((x - t) / a));
	elseif (a <= -2.25e-120)
		tmp = t_1;
	elseif (a <= 7.6e-293)
		tmp = t_2;
	elseif (a <= 1.2e-249)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 6.2e-220)
		tmp = t / (z / (y + z));
	elseif (a <= 3.6e-186)
		tmp = t_1;
	elseif (a <= 2e-153)
		tmp = t_2;
	elseif (a <= 1.02e+76)
		tmp = t_1;
	else
		tmp = x - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.45e-18], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.25e-120], t$95$1, If[LessEqual[a, 7.6e-293], t$95$2, If[LessEqual[a, 1.2e-249], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-220], N[(t / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-186], t$95$1, If[LessEqual[a, 2e-153], t$95$2, If[LessEqual[a, 1.02e+76], t$95$1, N[(x - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.4500000000000001e-18

   1. Initial program 71.3%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in a around inf 67.0%

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

      1. associate-/l* 79.7%

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

   7. Simplified 79.7%

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

   8. Taylor expanded in y around inf 57.8%

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

      1. associate-*r/ 70.5%

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

   10. Simplified 70.5%

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

   if -2.4500000000000001e-18 < a < -2.25e-120 or 6.20000000000000023e-220 < a < 3.5999999999999998e-186 or 2.00000000000000008e-153 < a < 1.02000000000000007e76

   1. Initial program 74.9%

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

      1. associate-*l/ 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in y around inf 67.0%

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

      1. div-sub 67.0%

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

   7. Simplified 67.0%

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

   if -2.25e-120 < a < 7.6e-293 or 3.5999999999999998e-186 < a < 2.00000000000000008e-153

   1. Initial program 66.6%

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

   5. Taylor expanded in x around 0 68.7%

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

      1. associate-/l* 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in a around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. neg-mul-1 78.0%

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

   10. Simplified 78.0%

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

   11. Taylor expanded in z around 0 78.0%

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

       1. mul-1-neg 78.0%

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

       2. unsub-neg 78.0%

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

       3. associate-/l* 78.0%

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

   13. Simplified 78.0%

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

   if 7.6e-293 < a < 1.20000000000000006e-249

   1. Initial program 78.5%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in y around -inf 89.1%

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

      1. associate-*l/ 89.4%

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

   7. Simplified 89.4%

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

   if 1.20000000000000006e-249 < a < 6.20000000000000023e-220

   1. Initial program 51.1%

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

      1. associate-*l/ 51.9%

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

   3. Simplified 51.9%

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

   5. Taylor expanded in x around 0 84.2%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in a around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

   10. Simplified 83.3%

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

       1. associate-/r/ 43.9%

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

       2. sub-neg 43.9%

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

       3. distribute-lft-in 43.9%

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

       4. add-sqr-sqrt 17.5%

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

       5. sqrt-unprod 60.6%

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

       6. sqr-neg 60.6%

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

       7. sqrt-unprod 43.1%

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

       8. add-sqr-sqrt 60.6%

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

       9. add-sqr-sqrt 17.3%

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

       10. sqrt-unprod 2.6%

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

       11. sqr-neg 2.6%

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

       12. sqrt-unprod 1.5%

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

       13. add-sqr-sqrt 2.4%

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

       14. add-sqr-sqrt 0.9%

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

       15. sqrt-unprod 25.7%

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

       16. sqr-neg 25.7%

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

       17. sqrt-unprod 43.1%

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

       18. add-sqr-sqrt 60.6%

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

   12. Applied egg-rr 60.6%

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

       1. distribute-lft-in 60.6%

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

       2. associate-*l/ 84.2%

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

       3. associate-/l* 100.0%

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

   14. Simplified 100.0%

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

   if 1.02000000000000007e76 < a

   1. Initial program 66.9%

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

      1. associate-/l* 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in t around inf 80.1%

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

   6. Taylor expanded in a around inf 74.1%

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

   7. Taylor expanded in y around 0 62.8%

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

      1. mul-1-neg 62.8%

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

      2. *-commutative 62.8%

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

      3. associate-*r/ 68.3%

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

      4. unsub-neg 68.3%

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

   9. Simplified 68.3%

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

       1. clear-num 68.5%

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

       2. un-div-inv 68.5%

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

   11. Applied egg-rr 68.5%

       \[\leadsto x - \color{blue}{\frac{z}{\frac{a}{t}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-293}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-249}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-220}:\\ \;\;\;\;\frac{t}{\frac{z}{y + z}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-153}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-249}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-220}:\\ \;\;\;\;\frac{t}{\frac{z}{y + z}}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (- t (/ t (/ z y)))))
   (if (<= a -5.5e-18)
     (- x (* y (/ (- x t) a)))
     (if (<= a -8.8e-120)
       t_1
       (if (<= a 7.6e-293)
         t_2
         (if (<= a 1.3e-249)
           (* (- t x) (/ y (- a z)))
           (if (<= a 6.2e-220)
             (/ t (/ z (+ y z)))
             (if (<= a 1.95e-190)
               t_1
               (if (<= a 3.5e-153)
                 t_2
                 (if (<= a 1.6e+77) t_1 (- x (/ (- z y) (/ a t)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t - (t / (z / y));
	double tmp;
	if (a <= -5.5e-18) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= -8.8e-120) {
		tmp = t_1;
	} else if (a <= 7.6e-293) {
		tmp = t_2;
	} else if (a <= 1.3e-249) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 6.2e-220) {
		tmp = t / (z / (y + z));
	} else if (a <= 1.95e-190) {
		tmp = t_1;
	} else if (a <= 3.5e-153) {
		tmp = t_2;
	} else if (a <= 1.6e+77) {
		tmp = t_1;
	} else {
		tmp = x - ((z - y) / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t - (t / (z / y))
    if (a <= (-5.5d-18)) then
        tmp = x - (y * ((x - t) / a))
    else if (a <= (-8.8d-120)) then
        tmp = t_1
    else if (a <= 7.6d-293) then
        tmp = t_2
    else if (a <= 1.3d-249) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 6.2d-220) then
        tmp = t / (z / (y + z))
    else if (a <= 1.95d-190) then
        tmp = t_1
    else if (a <= 3.5d-153) then
        tmp = t_2
    else if (a <= 1.6d+77) then
        tmp = t_1
    else
        tmp = x - ((z - y) / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t - (t / (z / y));
	double tmp;
	if (a <= -5.5e-18) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= -8.8e-120) {
		tmp = t_1;
	} else if (a <= 7.6e-293) {
		tmp = t_2;
	} else if (a <= 1.3e-249) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 6.2e-220) {
		tmp = t / (z / (y + z));
	} else if (a <= 1.95e-190) {
		tmp = t_1;
	} else if (a <= 3.5e-153) {
		tmp = t_2;
	} else if (a <= 1.6e+77) {
		tmp = t_1;
	} else {
		tmp = x - ((z - y) / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t - (t / (z / y))
	tmp = 0
	if a <= -5.5e-18:
		tmp = x - (y * ((x - t) / a))
	elif a <= -8.8e-120:
		tmp = t_1
	elif a <= 7.6e-293:
		tmp = t_2
	elif a <= 1.3e-249:
		tmp = (t - x) * (y / (a - z))
	elif a <= 6.2e-220:
		tmp = t / (z / (y + z))
	elif a <= 1.95e-190:
		tmp = t_1
	elif a <= 3.5e-153:
		tmp = t_2
	elif a <= 1.6e+77:
		tmp = t_1
	else:
		tmp = x - ((z - y) / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (a <= -5.5e-18)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	elseif (a <= -8.8e-120)
		tmp = t_1;
	elseif (a <= 7.6e-293)
		tmp = t_2;
	elseif (a <= 1.3e-249)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 6.2e-220)
		tmp = Float64(t / Float64(z / Float64(y + z)));
	elseif (a <= 1.95e-190)
		tmp = t_1;
	elseif (a <= 3.5e-153)
		tmp = t_2;
	elseif (a <= 1.6e+77)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(z - y) / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t - (t / (z / y));
	tmp = 0.0;
	if (a <= -5.5e-18)
		tmp = x - (y * ((x - t) / a));
	elseif (a <= -8.8e-120)
		tmp = t_1;
	elseif (a <= 7.6e-293)
		tmp = t_2;
	elseif (a <= 1.3e-249)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 6.2e-220)
		tmp = t / (z / (y + z));
	elseif (a <= 1.95e-190)
		tmp = t_1;
	elseif (a <= 3.5e-153)
		tmp = t_2;
	elseif (a <= 1.6e+77)
		tmp = t_1;
	else
		tmp = x - ((z - y) / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e-18], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.8e-120], t$95$1, If[LessEqual[a, 7.6e-293], t$95$2, If[LessEqual[a, 1.3e-249], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-220], N[(t / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e-190], t$95$1, If[LessEqual[a, 3.5e-153], t$95$2, If[LessEqual[a, 1.6e+77], t$95$1, N[(x - N[(N[(z - y), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -5.5e-18

   1. Initial program 71.3%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in a around inf 67.0%

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

      1. associate-/l* 79.7%

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

   7. Simplified 79.7%

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

   8. Taylor expanded in y around inf 57.8%

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

      1. associate-*r/ 70.5%

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

   10. Simplified 70.5%

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

   if -5.5e-18 < a < -8.8000000000000005e-120 or 6.20000000000000023e-220 < a < 1.94999999999999997e-190 or 3.49999999999999981e-153 < a < 1.6000000000000001e77

   1. Initial program 74.9%

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

      1. associate-*l/ 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in y around inf 67.0%

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

      1. div-sub 67.0%

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

   7. Simplified 67.0%

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

   if -8.8000000000000005e-120 < a < 7.6e-293 or 1.94999999999999997e-190 < a < 3.49999999999999981e-153

   1. Initial program 66.6%

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

   5. Taylor expanded in x around 0 68.7%

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

      1. associate-/l* 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in a around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. neg-mul-1 78.0%

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

   10. Simplified 78.0%

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

   11. Taylor expanded in z around 0 78.0%

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

       1. mul-1-neg 78.0%

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

       2. unsub-neg 78.0%

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

       3. associate-/l* 78.0%

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

   13. Simplified 78.0%

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

   if 7.6e-293 < a < 1.29999999999999988e-249

   1. Initial program 78.5%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in y around -inf 89.1%

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

      1. associate-*l/ 89.4%

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

   7. Simplified 89.4%

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

   if 1.29999999999999988e-249 < a < 6.20000000000000023e-220

   1. Initial program 51.1%

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

      1. associate-*l/ 51.9%

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

   3. Simplified 51.9%

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

   5. Taylor expanded in x around 0 84.2%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in a around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

   10. Simplified 83.3%

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

       1. associate-/r/ 43.9%

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

       2. sub-neg 43.9%

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

       3. distribute-lft-in 43.9%

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

       4. add-sqr-sqrt 17.5%

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

       5. sqrt-unprod 60.6%

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

       6. sqr-neg 60.6%

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

       7. sqrt-unprod 43.1%

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

       8. add-sqr-sqrt 60.6%

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

       9. add-sqr-sqrt 17.3%

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

       10. sqrt-unprod 2.6%

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

       11. sqr-neg 2.6%

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

       12. sqrt-unprod 1.5%

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

       13. add-sqr-sqrt 2.4%

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

       14. add-sqr-sqrt 0.9%

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

       15. sqrt-unprod 25.7%

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

       16. sqr-neg 25.7%

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

       17. sqrt-unprod 43.1%

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

       18. add-sqr-sqrt 60.6%

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

   12. Applied egg-rr 60.6%

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

       1. distribute-lft-in 60.6%

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

       2. associate-*l/ 84.2%

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

       3. associate-/l* 100.0%

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

   14. Simplified 100.0%

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

   if 1.6000000000000001e77 < a

   1. Initial program 66.9%

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

      1. associate-/l* 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in t around inf 80.1%

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

   6. Taylor expanded in a around inf 74.1%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a}{t}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-293}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-249}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-220}:\\ \;\;\;\;\frac{t}{\frac{z}{y + z}}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-190}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-153}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -7 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-212}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-192}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-152}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-65}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -7e-102)
     t_1
     (if (<= a 5.5e-212)
       (/ t (/ z (- z y)))
       (if (<= a 2.45e-192)
         (/ (* x (- y a)) z)
         (if (<= a 2.7e-152)
           (- t (/ t (/ z y)))
           (if (<= a 1.2e-76)
             (* y (/ (- x t) z))
             (if (<= a 5.6e-65)
               (* (- t x) (/ a z))
               (if (<= a 2.35e+82)
                 t_1
                 (if (<= a 8.5e+96) t (- x (/ z (/ a t)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -7e-102) {
		tmp = t_1;
	} else if (a <= 5.5e-212) {
		tmp = t / (z / (z - y));
	} else if (a <= 2.45e-192) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 2.7e-152) {
		tmp = t - (t / (z / y));
	} else if (a <= 1.2e-76) {
		tmp = y * ((x - t) / z);
	} else if (a <= 5.6e-65) {
		tmp = (t - x) * (a / z);
	} else if (a <= 2.35e+82) {
		tmp = t_1;
	} else if (a <= 8.5e+96) {
		tmp = t;
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (a <= (-7d-102)) then
        tmp = t_1
    else if (a <= 5.5d-212) then
        tmp = t / (z / (z - y))
    else if (a <= 2.45d-192) then
        tmp = (x * (y - a)) / z
    else if (a <= 2.7d-152) then
        tmp = t - (t / (z / y))
    else if (a <= 1.2d-76) then
        tmp = y * ((x - t) / z)
    else if (a <= 5.6d-65) then
        tmp = (t - x) * (a / z)
    else if (a <= 2.35d+82) then
        tmp = t_1
    else if (a <= 8.5d+96) then
        tmp = t
    else
        tmp = x - (z / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -7e-102) {
		tmp = t_1;
	} else if (a <= 5.5e-212) {
		tmp = t / (z / (z - y));
	} else if (a <= 2.45e-192) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 2.7e-152) {
		tmp = t - (t / (z / y));
	} else if (a <= 1.2e-76) {
		tmp = y * ((x - t) / z);
	} else if (a <= 5.6e-65) {
		tmp = (t - x) * (a / z);
	} else if (a <= 2.35e+82) {
		tmp = t_1;
	} else if (a <= 8.5e+96) {
		tmp = t;
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -7e-102:
		tmp = t_1
	elif a <= 5.5e-212:
		tmp = t / (z / (z - y))
	elif a <= 2.45e-192:
		tmp = (x * (y - a)) / z
	elif a <= 2.7e-152:
		tmp = t - (t / (z / y))
	elif a <= 1.2e-76:
		tmp = y * ((x - t) / z)
	elif a <= 5.6e-65:
		tmp = (t - x) * (a / z)
	elif a <= 2.35e+82:
		tmp = t_1
	elif a <= 8.5e+96:
		tmp = t
	else:
		tmp = x - (z / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -7e-102)
		tmp = t_1;
	elseif (a <= 5.5e-212)
		tmp = Float64(t / Float64(z / Float64(z - y)));
	elseif (a <= 2.45e-192)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 2.7e-152)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (a <= 1.2e-76)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 5.6e-65)
		tmp = Float64(Float64(t - x) * Float64(a / z));
	elseif (a <= 2.35e+82)
		tmp = t_1;
	elseif (a <= 8.5e+96)
		tmp = t;
	else
		tmp = Float64(x - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -7e-102)
		tmp = t_1;
	elseif (a <= 5.5e-212)
		tmp = t / (z / (z - y));
	elseif (a <= 2.45e-192)
		tmp = (x * (y - a)) / z;
	elseif (a <= 2.7e-152)
		tmp = t - (t / (z / y));
	elseif (a <= 1.2e-76)
		tmp = y * ((x - t) / z);
	elseif (a <= 5.6e-65)
		tmp = (t - x) * (a / z);
	elseif (a <= 2.35e+82)
		tmp = t_1;
	elseif (a <= 8.5e+96)
		tmp = t;
	else
		tmp = x - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e-102], t$95$1, If[LessEqual[a, 5.5e-212], N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e-192], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.7e-152], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-76], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e-65], N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e+82], t$95$1, If[LessEqual[a, 8.5e+96], t, N[(x - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -6.99999999999999973e-102 or 5.6000000000000001e-65 < a < 2.35e82

   1. Initial program 73.4%

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

      1. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in t around inf 64.7%

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

   6. Taylor expanded in z around 0 48.2%

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

   if -6.99999999999999973e-102 < a < 5.49999999999999995e-212

   1. Initial program 69.4%

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

      1. associate-*l/ 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in x around 0 64.9%

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

      1. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in a around 0 67.7%

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

      1. associate-*r/ 67.7%

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

      2. neg-mul-1 67.7%

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

   10. Simplified 67.7%

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

       1. frac-2neg 67.7%

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

       2. div-inv 67.6%

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

       3. remove-double-neg 67.6%

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

       4. sub-neg 67.6%

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

       5. distribute-neg-in 67.6%

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

       6. remove-double-neg 67.6%

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

   12. Applied egg-rr 67.6%

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

       1. associate-*r/ 67.7%

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

       2. *-rgt-identity 67.7%

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

       3. +-commutative 67.7%

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

       4. unsub-neg 67.7%

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

   14. Simplified 67.7%

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

   if 5.49999999999999995e-212 < a < 2.45e-192

   1. Initial program 99.7%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. div-sub 99.7%

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

      5. distribute-lft-out-- 99.7%

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

      6. associate-*r/ 99.7%

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

      7. mul-1-neg 99.7%

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

      8. distribute-rgt-out-- 99.7%

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

      9. unsub-neg 99.7%

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

      10. associate-/l* 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in t around 0 99.7%

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

   if 2.45e-192 < a < 2.69999999999999999e-152

   1. Initial program 36.2%

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

      1. associate-*l/ 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in x around 0 52.5%

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

      1. associate-/l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in a around 0 93.7%

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

      1. associate-*r/ 93.7%

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

      2. neg-mul-1 93.7%

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

   10. Simplified 93.7%

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

   11. Taylor expanded in z around 0 93.7%

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

       1. mul-1-neg 93.7%

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

       2. unsub-neg 93.7%

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

       3. associate-/l* 93.7%

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

   13. Simplified 93.7%

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

   if 2.69999999999999999e-152 < a < 1.20000000000000007e-76

   1. Initial program 82.1%

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

      1. associate-*l/ 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in z around inf 69.8%

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

      1. associate-*r/ 69.8%

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

      2. associate-*r* 69.8%

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

      3. mul-1-neg 69.8%

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

      4. associate-*r/ 69.8%

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

      5. associate-*r* 69.8%

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

      6. mul-1-neg 69.8%

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

   7. Simplified 69.8%

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

   8. Taylor expanded in y around -inf 74.0%

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

      1. div-sub 74.0%

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

      2. associate-*r* 74.0%

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

      3. mul-1-neg 74.0%

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

   10. Simplified 74.0%

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

   if 1.20000000000000007e-76 < a < 5.6000000000000001e-65

   1. Initial program 41.8%

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

      1. associate-*l/ 42.2%

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

   3. Simplified 42.2%

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

   5. Taylor expanded in z around inf 79.7%

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

      1. associate--l+ 79.7%

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

      2. associate-*r/ 79.7%

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

      3. associate-*r/ 79.7%

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

      4. div-sub 79.7%

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

      5. distribute-lft-out-- 79.7%

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

      6. associate-*r/ 79.7%

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

      7. mul-1-neg 79.7%

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

      8. distribute-rgt-out-- 79.7%

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

      9. unsub-neg 79.7%

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

      10. associate-/l* 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in a around inf 81.4%

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

      1. associate-/l* 77.1%

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

      2. associate-/r/ 81.7%

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

   10. Simplified 81.7%

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

   if 2.35e82 < a < 8.50000000000000025e96

   1. Initial program 10.6%

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

      1. associate-*l/ 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in z around inf 100.0%

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

   if 8.50000000000000025e96 < a

   1. Initial program 67.8%

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

      1. associate-/l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in t around inf 80.4%

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

   6. Taylor expanded in a around inf 75.6%

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

   7. Taylor expanded in y around 0 63.6%

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

      1. mul-1-neg 63.6%

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

      2. *-commutative 63.6%

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

      3. associate-*r/ 69.4%

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

      4. unsub-neg 69.4%

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

   9. Simplified 69.4%

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

       1. clear-num 69.6%

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

       2. un-div-inv 69.6%

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

   11. Applied egg-rr 69.6%

       \[\leadsto x - \color{blue}{\frac{z}{\frac{a}{t}}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-212}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-192}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-152}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-65}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+82}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-272} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -4e-272) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -4e-272) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / 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) * (x - t)) / (a - z))
    if ((t_1 <= (-4d-272)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / 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) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -4e-272) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if (t_1 <= -4e-272) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -4e-272) || !(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(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -4e-272) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / 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[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-272], 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[(t - x), $MachinePrecision] * N[(a - y), $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))) < -3.99999999999999972e-272 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 75.6%

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

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   if -3.99999999999999972e-272 < (+.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. +-commutative 4.4%

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

      2. associate-*l/ 4.4%

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

      3. fma-def 4.4%

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

   3. Simplified 4.4%

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

   5. Taylor expanded in z around -inf 99.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -4 \cdot 10^{-272} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.65e+80)
     t
     (if (<= z -4.2e-111)
       t_2
       (if (<= z -1.3e-203)
         t_1
         (if (<= z 1.9e+57)
           t_2
           (if (<= z 1.8e+158) t_1 (if (<= z 2.9e+175) t_2 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.65e+80) {
		tmp = t;
	} else if (z <= -4.2e-111) {
		tmp = t_2;
	} else if (z <= -1.3e-203) {
		tmp = t_1;
	} else if (z <= 1.9e+57) {
		tmp = t_2;
	} else if (z <= 1.8e+158) {
		tmp = t_1;
	} else if (z <= 2.9e+175) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-1.65d+80)) then
        tmp = t
    else if (z <= (-4.2d-111)) then
        tmp = t_2
    else if (z <= (-1.3d-203)) then
        tmp = t_1
    else if (z <= 1.9d+57) then
        tmp = t_2
    else if (z <= 1.8d+158) then
        tmp = t_1
    else if (z <= 2.9d+175) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.65e+80) {
		tmp = t;
	} else if (z <= -4.2e-111) {
		tmp = t_2;
	} else if (z <= -1.3e-203) {
		tmp = t_1;
	} else if (z <= 1.9e+57) {
		tmp = t_2;
	} else if (z <= 1.8e+158) {
		tmp = t_1;
	} else if (z <= 2.9e+175) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.65e+80:
		tmp = t
	elif z <= -4.2e-111:
		tmp = t_2
	elif z <= -1.3e-203:
		tmp = t_1
	elif z <= 1.9e+57:
		tmp = t_2
	elif z <= 1.8e+158:
		tmp = t_1
	elif z <= 2.9e+175:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.65e+80)
		tmp = t;
	elseif (z <= -4.2e-111)
		tmp = t_2;
	elseif (z <= -1.3e-203)
		tmp = t_1;
	elseif (z <= 1.9e+57)
		tmp = t_2;
	elseif (z <= 1.8e+158)
		tmp = t_1;
	elseif (z <= 2.9e+175)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.65e+80)
		tmp = t;
	elseif (z <= -4.2e-111)
		tmp = t_2;
	elseif (z <= -1.3e-203)
		tmp = t_1;
	elseif (z <= 1.9e+57)
		tmp = t_2;
	elseif (z <= 1.8e+158)
		tmp = t_1;
	elseif (z <= 2.9e+175)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+80], t, If[LessEqual[z, -4.2e-111], t$95$2, If[LessEqual[z, -1.3e-203], t$95$1, If[LessEqual[z, 1.9e+57], t$95$2, If[LessEqual[z, 1.8e+158], t$95$1, If[LessEqual[z, 2.9e+175], t$95$2, t]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999995e80 or 2.9e175 < z

   1. Initial program 33.5%

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

      1. associate-*l/ 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in z around inf 52.9%

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

   if -1.64999999999999995e80 < z < -4.1999999999999997e-111 or -1.29999999999999988e-203 < z < 1.8999999999999999e57 or 1.79999999999999994e158 < z < 2.9e175

   1. Initial program 87.9%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in a around inf 69.4%

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

      1. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in y around inf 71.0%

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

   9. Taylor expanded in x around inf 54.0%

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

       1. mul-1-neg 54.0%

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

       2. unsub-neg 54.0%

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

   11. Simplified 54.0%

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

   if -4.1999999999999997e-111 < z < -1.29999999999999988e-203 or 1.8999999999999999e57 < z < 1.79999999999999994e158

   1. Initial program 69.3%

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

      1. associate-*l/ 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in z around inf 65.2%

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

      1. associate-*r/ 65.2%

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

      2. associate-*r* 65.2%

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

      3. mul-1-neg 65.2%

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

      4. associate-*r/ 65.2%

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

      5. associate-*r* 65.2%

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

      6. mul-1-neg 65.2%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in x around inf 48.7%

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

      1. div-sub 48.7%

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

   10. Simplified 48.7%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 46.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+176}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -3e+98)
     t
     (if (<= z -4.2e-111)
       (+ x (/ (* y t) a))
       (if (<= z -6.2e-206)
         t_1
         (if (<= z 4.2e+58)
           t_2
           (if (<= z 2.9e+164) t_1 (if (<= z 2.8e+176) t_2 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3e+98) {
		tmp = t;
	} else if (z <= -4.2e-111) {
		tmp = x + ((y * t) / a);
	} else if (z <= -6.2e-206) {
		tmp = t_1;
	} else if (z <= 4.2e+58) {
		tmp = t_2;
	} else if (z <= 2.9e+164) {
		tmp = t_1;
	} else if (z <= 2.8e+176) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-3d+98)) then
        tmp = t
    else if (z <= (-4.2d-111)) then
        tmp = x + ((y * t) / a)
    else if (z <= (-6.2d-206)) then
        tmp = t_1
    else if (z <= 4.2d+58) then
        tmp = t_2
    else if (z <= 2.9d+164) then
        tmp = t_1
    else if (z <= 2.8d+176) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -3e+98) {
		tmp = t;
	} else if (z <= -4.2e-111) {
		tmp = x + ((y * t) / a);
	} else if (z <= -6.2e-206) {
		tmp = t_1;
	} else if (z <= 4.2e+58) {
		tmp = t_2;
	} else if (z <= 2.9e+164) {
		tmp = t_1;
	} else if (z <= 2.8e+176) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -3e+98:
		tmp = t
	elif z <= -4.2e-111:
		tmp = x + ((y * t) / a)
	elif z <= -6.2e-206:
		tmp = t_1
	elif z <= 4.2e+58:
		tmp = t_2
	elif z <= 2.9e+164:
		tmp = t_1
	elif z <= 2.8e+176:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -3e+98)
		tmp = t;
	elseif (z <= -4.2e-111)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= -6.2e-206)
		tmp = t_1;
	elseif (z <= 4.2e+58)
		tmp = t_2;
	elseif (z <= 2.9e+164)
		tmp = t_1;
	elseif (z <= 2.8e+176)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -3e+98)
		tmp = t;
	elseif (z <= -4.2e-111)
		tmp = x + ((y * t) / a);
	elseif (z <= -6.2e-206)
		tmp = t_1;
	elseif (z <= 4.2e+58)
		tmp = t_2;
	elseif (z <= 2.9e+164)
		tmp = t_1;
	elseif (z <= 2.8e+176)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+98], t, If[LessEqual[z, -4.2e-111], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-206], t$95$1, If[LessEqual[z, 4.2e+58], t$95$2, If[LessEqual[z, 2.9e+164], t$95$1, If[LessEqual[z, 2.8e+176], t$95$2, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.0000000000000001e98 or 2.8000000000000002e176 < z

   1. Initial program 33.0%

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

      1. associate-*l/ 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in z around inf 54.3%

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

   if -3.0000000000000001e98 < z < -4.1999999999999997e-111

   1. Initial program 80.3%

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

      1. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in t around inf 74.8%

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

   6. Taylor expanded in z around 0 48.8%

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

   if -4.1999999999999997e-111 < z < -6.2000000000000005e-206 or 4.20000000000000024e58 < z < 2.8999999999999999e164

   1. Initial program 68.5%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around inf 64.4%

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

      1. associate-*r/ 64.4%

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

      2. associate-*r* 64.4%

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

      3. mul-1-neg 64.4%

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

      4. associate-*r/ 64.4%

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

      5. associate-*r* 64.4%

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

      6. mul-1-neg 64.4%

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

   7. Simplified 64.4%

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

   8. Taylor expanded in x around inf 49.0%

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

      1. div-sub 49.0%

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

   10. Simplified 49.0%

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

   if -6.2000000000000005e-206 < z < 4.20000000000000024e58 or 2.8999999999999999e164 < z < 2.8000000000000002e176

   1. Initial program 91.0%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in a around inf 74.6%

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

      1. associate-/l* 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in y around inf 75.3%

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

   9. Taylor expanded in x around inf 55.3%

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

       1. mul-1-neg 55.3%

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

       2. unsub-neg 55.3%

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

   11. Simplified 55.3%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+98}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.66 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-70}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+40}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.66e-18)
   (- x (* y (/ (- x t) a)))
   (if (<= a -9e-120)
     (* y (/ (- t x) (- a z)))
     (if (<= a 4e-70)
       (- t (/ y (/ z (- t x))))
       (if (<= a 9e+40)
         (/ t (/ (- a z) (- y z)))
         (if (<= a 7.2e+86)
           (* x (+ (/ (- z y) (- a z)) 1.0))
           (- x (/ t (/ (- a z) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.66e-18) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= -9e-120) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 4e-70) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 9e+40) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 7.2e+86) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = x - (t / ((a - z) / 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 (a <= (-1.66d-18)) then
        tmp = x - (y * ((x - t) / a))
    else if (a <= (-9d-120)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 4d-70) then
        tmp = t - (y / (z / (t - x)))
    else if (a <= 9d+40) then
        tmp = t / ((a - z) / (y - z))
    else if (a <= 7.2d+86) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    else
        tmp = x - (t / ((a - z) / 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 (a <= -1.66e-18) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= -9e-120) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 4e-70) {
		tmp = t - (y / (z / (t - x)));
	} else if (a <= 9e+40) {
		tmp = t / ((a - z) / (y - z));
	} else if (a <= 7.2e+86) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = x - (t / ((a - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.66e-18:
		tmp = x - (y * ((x - t) / a))
	elif a <= -9e-120:
		tmp = y * ((t - x) / (a - z))
	elif a <= 4e-70:
		tmp = t - (y / (z / (t - x)))
	elif a <= 9e+40:
		tmp = t / ((a - z) / (y - z))
	elif a <= 7.2e+86:
		tmp = x * (((z - y) / (a - z)) + 1.0)
	else:
		tmp = x - (t / ((a - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.66e-18)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	elseif (a <= -9e-120)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 4e-70)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	elseif (a <= 9e+40)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (a <= 7.2e+86)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a - z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.66e-18)
		tmp = x - (y * ((x - t) / a));
	elseif (a <= -9e-120)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 4e-70)
		tmp = t - (y / (z / (t - x)));
	elseif (a <= 9e+40)
		tmp = t / ((a - z) / (y - z));
	elseif (a <= 7.2e+86)
		tmp = x * (((z - y) / (a - z)) + 1.0);
	else
		tmp = x - (t / ((a - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.66e-18], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9e-120], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-70], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+40], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+86], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.66e-18

   1. Initial program 71.3%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in a around inf 67.0%

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

      1. associate-/l* 79.7%

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

   7. Simplified 79.7%

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

   8. Taylor expanded in y around inf 57.8%

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

      1. associate-*r/ 70.5%

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

   10. Simplified 70.5%

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

   if -1.66e-18 < a < -9e-120

   1. Initial program 82.4%

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

      1. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

   7. Simplified 82.9%

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

   if -9e-120 < a < 3.99999999999999998e-70

   1. Initial program 69.0%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 82.6%

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

      1. associate--l+ 82.6%

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

      2. associate-*r/ 82.6%

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

      3. associate-*r/ 82.6%

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

      4. div-sub 82.6%

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

      5. distribute-lft-out-- 82.6%

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

      6. associate-*r/ 82.6%

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

      7. mul-1-neg 82.6%

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

      8. distribute-rgt-out-- 82.6%

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

      9. unsub-neg 82.6%

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

      10. associate-/l* 86.2%

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

   7. Simplified 86.2%

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

   8. Taylor expanded in y around inf 80.3%

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

      1. associate-/l* 83.7%

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

   10. Simplified 83.7%

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

   if 3.99999999999999998e-70 < a < 9.00000000000000064e40

   1. Initial program 72.5%

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

      1. associate-*l/ 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in x around 0 57.0%

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

      1. associate-/l* 60.8%

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

   7. Simplified 60.8%

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

   if 9.00000000000000064e40 < a < 7.20000000000000011e86

   1. Initial program 70.6%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around inf 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

   7. Simplified 79.0%

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

   if 7.20000000000000011e86 < a

   1. Initial program 66.7%

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

      1. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in t around inf 80.7%

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

   6. Taylor expanded in y around 0 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. associate-/l* 74.6%

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

   8. Simplified 74.6%

      \[\leadsto \color{blue}{\left(-\frac{t}{\frac{a - z}{z}}\right) + x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.66 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-70}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+40}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-223}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{+21}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -2.7e-79)
     t_1
     (if (<= y 1.2e-223)
       (/ t (/ (- z a) z))
       (if (<= y 3.7e-168)
         (+ x (/ (* y t) a))
         (if (<= y 1.14e+21) (- x (* z (/ t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.7e-79) {
		tmp = t_1;
	} else if (y <= 1.2e-223) {
		tmp = t / ((z - a) / z);
	} else if (y <= 3.7e-168) {
		tmp = x + ((y * t) / a);
	} else if (y <= 1.14e+21) {
		tmp = x - (z * (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 = y * ((t - x) / (a - z))
    if (y <= (-2.7d-79)) then
        tmp = t_1
    else if (y <= 1.2d-223) then
        tmp = t / ((z - a) / z)
    else if (y <= 3.7d-168) then
        tmp = x + ((y * t) / a)
    else if (y <= 1.14d+21) then
        tmp = x - (z * (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 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.7e-79) {
		tmp = t_1;
	} else if (y <= 1.2e-223) {
		tmp = t / ((z - a) / z);
	} else if (y <= 3.7e-168) {
		tmp = x + ((y * t) / a);
	} else if (y <= 1.14e+21) {
		tmp = x - (z * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -2.7e-79:
		tmp = t_1
	elif y <= 1.2e-223:
		tmp = t / ((z - a) / z)
	elif y <= 3.7e-168:
		tmp = x + ((y * t) / a)
	elif y <= 1.14e+21:
		tmp = x - (z * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.7e-79)
		tmp = t_1;
	elseif (y <= 1.2e-223)
		tmp = Float64(t / Float64(Float64(z - a) / z));
	elseif (y <= 3.7e-168)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (y <= 1.14e+21)
		tmp = Float64(x - Float64(z * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -2.7e-79)
		tmp = t_1;
	elseif (y <= 1.2e-223)
		tmp = t / ((z - a) / z);
	elseif (y <= 3.7e-168)
		tmp = x + ((y * t) / a);
	elseif (y <= 1.14e+21)
		tmp = x - (z * (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-79], t$95$1, If[LessEqual[y, 1.2e-223], N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-168], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.14e+21], N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7000000000000002e-79 or 1.14e21 < y

   1. Initial program 68.9%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around inf 68.6%

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

      1. div-sub 69.4%

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

   7. Simplified 69.4%

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

   if -2.7000000000000002e-79 < y < 1.19999999999999993e-223

   1. Initial program 60.0%

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

      1. associate-*l/ 66.3%

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

   3. Simplified 66.3%

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

   5. Taylor expanded in x around 0 53.3%

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

      1. associate-/l* 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in y around 0 51.3%

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

      1. mul-1-neg 51.3%

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

   10. Simplified 51.3%

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

   if 1.19999999999999993e-223 < y < 3.69999999999999997e-168

   1. Initial program 100.0%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in t around inf 89.3%

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

   6. Taylor expanded in z around 0 89.3%

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

   if 3.69999999999999997e-168 < y < 1.14e21

   1. Initial program 80.7%

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

      1. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t around inf 72.5%

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

   6. Taylor expanded in a around inf 57.9%

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

   7. Taylor expanded in y around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-commutative 52.6%

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

      3. associate-*r/ 54.2%

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

      4. unsub-neg 54.2%

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

   9. Simplified 54.2%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-223}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{+21}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-225}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+21}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.9e-79)
   (* y (/ (- t x) (- a z)))
   (if (<= y 1.6e-225)
     (/ t (/ (- z a) z))
     (if (<= y 3.2e-168)
       (+ x (/ (* y t) a))
       (if (<= y 5.2e+21) (- x (* z (/ t a))) (* (- t x) (/ y (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e-79) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= 1.6e-225) {
		tmp = t / ((z - a) / z);
	} else if (y <= 3.2e-168) {
		tmp = x + ((y * t) / a);
	} else if (y <= 5.2e+21) {
		tmp = x - (z * (t / a));
	} else {
		tmp = (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 (y <= (-2.9d-79)) then
        tmp = y * ((t - x) / (a - z))
    else if (y <= 1.6d-225) then
        tmp = t / ((z - a) / z)
    else if (y <= 3.2d-168) then
        tmp = x + ((y * t) / a)
    else if (y <= 5.2d+21) then
        tmp = x - (z * (t / a))
    else
        tmp = (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 (y <= -2.9e-79) {
		tmp = y * ((t - x) / (a - z));
	} else if (y <= 1.6e-225) {
		tmp = t / ((z - a) / z);
	} else if (y <= 3.2e-168) {
		tmp = x + ((y * t) / a);
	} else if (y <= 5.2e+21) {
		tmp = x - (z * (t / a));
	} else {
		tmp = (t - x) * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.9e-79:
		tmp = y * ((t - x) / (a - z))
	elif y <= 1.6e-225:
		tmp = t / ((z - a) / z)
	elif y <= 3.2e-168:
		tmp = x + ((y * t) / a)
	elif y <= 5.2e+21:
		tmp = x - (z * (t / a))
	else:
		tmp = (t - x) * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.9e-79)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (y <= 1.6e-225)
		tmp = Float64(t / Float64(Float64(z - a) / z));
	elseif (y <= 3.2e-168)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (y <= 5.2e+21)
		tmp = Float64(x - Float64(z * Float64(t / a)));
	else
		tmp = 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 (y <= -2.9e-79)
		tmp = y * ((t - x) / (a - z));
	elseif (y <= 1.6e-225)
		tmp = t / ((z - a) / z);
	elseif (y <= 3.2e-168)
		tmp = x + ((y * t) / a);
	elseif (y <= 5.2e+21)
		tmp = x - (z * (t / a));
	else
		tmp = (t - x) * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.9e-79], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-225], N[(t / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-168], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+21], N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.9000000000000001e-79

   1. Initial program 65.4%

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

      1. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in y around inf 56.8%

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

      1. div-sub 58.2%

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

   7. Simplified 58.2%

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

   if -2.9000000000000001e-79 < y < 1.59999999999999987e-225

   1. Initial program 60.0%

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

      1. associate-*l/ 66.3%

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

   3. Simplified 66.3%

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

   5. Taylor expanded in x around 0 53.3%

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

      1. associate-/l* 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in y around 0 51.3%

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

      1. mul-1-neg 51.3%

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

   10. Simplified 51.3%

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

   if 1.59999999999999987e-225 < y < 3.20000000000000006e-168

   1. Initial program 100.0%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in t around inf 89.3%

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

   6. Taylor expanded in z around 0 89.3%

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

   if 3.20000000000000006e-168 < y < 5.2e21

   1. Initial program 80.7%

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

      1. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

   5. Taylor expanded in t around inf 72.5%

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

   6. Taylor expanded in a around inf 57.9%

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

   7. Taylor expanded in y around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-commutative 52.6%

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

      3. associate-*r/ 54.2%

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

      4. unsub-neg 54.2%

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

   9. Simplified 54.2%

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

   if 5.2e21 < y

   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/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in y around -inf 68.9%

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

      1. associate-*l/ 82.4%

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

   7. Simplified 82.4%

      \[\leadsto \color{blue}{\frac{y}{a - z} \cdot \left(t - x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-225}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-168}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+21}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -7 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-186}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ t (/ z y)))))
   (if (<= a -7e-102)
     (+ x (/ (* y t) a))
     (if (<= a 1.18e-212)
       t_1
       (if (<= a 1e-186)
         (* x (/ (- y a) z))
         (if (<= a 4e+44) t_1 (* x (- 1.0 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (a <= -7e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.18e-212) {
		tmp = t_1;
	} else if (a <= 1e-186) {
		tmp = x * ((y - a) / z);
	} else if (a <= 4e+44) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (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) :: t_1
    real(8) :: tmp
    t_1 = t - (t / (z / y))
    if (a <= (-7d-102)) then
        tmp = x + ((y * t) / a)
    else if (a <= 1.18d-212) then
        tmp = t_1
    else if (a <= 1d-186) then
        tmp = x * ((y - a) / z)
    else if (a <= 4d+44) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (a <= -7e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 1.18e-212) {
		tmp = t_1;
	} else if (a <= 1e-186) {
		tmp = x * ((y - a) / z);
	} else if (a <= 4e+44) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t / (z / y))
	tmp = 0
	if a <= -7e-102:
		tmp = x + ((y * t) / a)
	elif a <= 1.18e-212:
		tmp = t_1
	elif a <= 1e-186:
		tmp = x * ((y - a) / z)
	elif a <= 4e+44:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (a <= -7e-102)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 1.18e-212)
		tmp = t_1;
	elseif (a <= 1e-186)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 4e+44)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t / (z / y));
	tmp = 0.0;
	if (a <= -7e-102)
		tmp = x + ((y * t) / a);
	elseif (a <= 1.18e-212)
		tmp = t_1;
	elseif (a <= 1e-186)
		tmp = x * ((y - a) / z);
	elseif (a <= 4e+44)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e-102], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.18e-212], t$95$1, If[LessEqual[a, 1e-186], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+44], t$95$1, N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.99999999999999973e-102

   1. Initial program 72.7%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around inf 66.6%

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

   6. Taylor expanded in z around 0 51.2%

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

   if -6.99999999999999973e-102 < a < 1.17999999999999996e-212 or 9.9999999999999991e-187 < a < 4.0000000000000004e44

   1. Initial program 69.5%

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

      1. associate-*l/ 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in x around 0 58.6%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in a around 0 58.3%

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

      1. associate-*r/ 58.3%

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

      2. neg-mul-1 58.3%

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

   10. Simplified 58.3%

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

   11. Taylor expanded in z around 0 56.3%

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

       1. mul-1-neg 56.3%

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

       2. unsub-neg 56.3%

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

       3. associate-/l* 58.3%

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

   13. Simplified 58.3%

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

   if 1.17999999999999996e-212 < a < 9.9999999999999991e-187

   1. Initial program 99.7%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r/ 99.7%

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

      2. associate-*r* 99.7%

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

      3. mul-1-neg 99.7%

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

      4. associate-*r/ 99.7%

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

      5. associate-*r* 99.7%

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

      6. mul-1-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 99.4%

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

      1. div-sub 99.4%

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

   10. Simplified 99.4%

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

   if 4.0000000000000004e44 < a

   1. Initial program 66.8%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in a around inf 60.9%

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

      1. associate-/l* 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in y around inf 61.8%

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

   9. Taylor expanded in x around inf 52.7%

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

       1. mul-1-neg 52.7%

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

       2. unsub-neg 52.7%

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

   11. Simplified 52.7%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-212}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 10^{-186}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+44}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ t (/ z y)))))
   (if (<= a -6.5e-102)
     (+ x (/ (* y t) a))
     (if (<= a 5.4e-212)
       t_1
       (if (<= a 1.12e-190)
         (* x (/ (- y a) z))
         (if (<= a 7.6e+41) t_1 (- x (* z (/ t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (a <= -6.5e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 5.4e-212) {
		tmp = t_1;
	} else if (a <= 1.12e-190) {
		tmp = x * ((y - a) / z);
	} else if (a <= 7.6e+41) {
		tmp = t_1;
	} else {
		tmp = x - (z * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (t / (z / y))
    if (a <= (-6.5d-102)) then
        tmp = x + ((y * t) / a)
    else if (a <= 5.4d-212) then
        tmp = t_1
    else if (a <= 1.12d-190) then
        tmp = x * ((y - a) / z)
    else if (a <= 7.6d+41) then
        tmp = t_1
    else
        tmp = x - (z * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (a <= -6.5e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 5.4e-212) {
		tmp = t_1;
	} else if (a <= 1.12e-190) {
		tmp = x * ((y - a) / z);
	} else if (a <= 7.6e+41) {
		tmp = t_1;
	} else {
		tmp = x - (z * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t / (z / y))
	tmp = 0
	if a <= -6.5e-102:
		tmp = x + ((y * t) / a)
	elif a <= 5.4e-212:
		tmp = t_1
	elif a <= 1.12e-190:
		tmp = x * ((y - a) / z)
	elif a <= 7.6e+41:
		tmp = t_1
	else:
		tmp = x - (z * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (a <= -6.5e-102)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 5.4e-212)
		tmp = t_1;
	elseif (a <= 1.12e-190)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 7.6e+41)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t / (z / y));
	tmp = 0.0;
	if (a <= -6.5e-102)
		tmp = x + ((y * t) / a);
	elseif (a <= 5.4e-212)
		tmp = t_1;
	elseif (a <= 1.12e-190)
		tmp = x * ((y - a) / z);
	elseif (a <= 7.6e+41)
		tmp = t_1;
	else
		tmp = x - (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e-102], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e-212], t$95$1, If[LessEqual[a, 1.12e-190], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+41], t$95$1, N[(x - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.5000000000000003e-102

   1. Initial program 72.7%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around inf 66.6%

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

   6. Taylor expanded in z around 0 51.2%

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

   if -6.5000000000000003e-102 < a < 5.39999999999999962e-212 or 1.12000000000000005e-190 < a < 7.6000000000000003e41

   1. Initial program 69.2%

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

      1. associate-*l/ 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in x around 0 59.1%

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

      1. associate-/l* 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in a around 0 58.8%

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

      1. associate-*r/ 58.8%

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

      2. neg-mul-1 58.8%

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

   10. Simplified 58.8%

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

   11. Taylor expanded in z around 0 56.8%

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

       1. mul-1-neg 56.8%

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

       2. unsub-neg 56.8%

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

       3. associate-/l* 58.8%

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

   13. Simplified 58.8%

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

   if 5.39999999999999962e-212 < a < 1.12000000000000005e-190

   1. Initial program 99.7%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r/ 99.7%

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

      2. associate-*r* 99.7%

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

      3. mul-1-neg 99.7%

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

      4. associate-*r/ 99.7%

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

      5. associate-*r* 99.7%

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

      6. mul-1-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 99.4%

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

      1. div-sub 99.4%

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

   10. Simplified 99.4%

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

   if 7.6000000000000003e41 < a

   1. Initial program 67.3%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around inf 75.1%

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

   6. Taylor expanded in a around inf 69.7%

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

   7. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. *-commutative 58.1%

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

      3. associate-*r/ 63.0%

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

      4. unsub-neg 63.0%

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

   9. Simplified 63.0%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-212}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+41}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ t (/ z y)))))
   (if (<= a -6.8e-102)
     (+ x (/ (* y t) a))
     (if (<= a 2.6e-212)
       t_1
       (if (<= a 1.65e-192)
         (* x (/ (- y a) z))
         (if (<= a 1.6e+39) t_1 (- x (/ z (/ a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (a <= -6.8e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 2.6e-212) {
		tmp = t_1;
	} else if (a <= 1.65e-192) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.6e+39) {
		tmp = t_1;
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (t / (z / y))
    if (a <= (-6.8d-102)) then
        tmp = x + ((y * t) / a)
    else if (a <= 2.6d-212) then
        tmp = t_1
    else if (a <= 1.65d-192) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.6d+39) then
        tmp = t_1
    else
        tmp = x - (z / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (t / (z / y));
	double tmp;
	if (a <= -6.8e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 2.6e-212) {
		tmp = t_1;
	} else if (a <= 1.65e-192) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.6e+39) {
		tmp = t_1;
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (t / (z / y))
	tmp = 0
	if a <= -6.8e-102:
		tmp = x + ((y * t) / a)
	elif a <= 2.6e-212:
		tmp = t_1
	elif a <= 1.65e-192:
		tmp = x * ((y - a) / z)
	elif a <= 1.6e+39:
		tmp = t_1
	else:
		tmp = x - (z / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (a <= -6.8e-102)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 2.6e-212)
		tmp = t_1;
	elseif (a <= 1.65e-192)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.6e+39)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (t / (z / y));
	tmp = 0.0;
	if (a <= -6.8e-102)
		tmp = x + ((y * t) / a);
	elseif (a <= 2.6e-212)
		tmp = t_1;
	elseif (a <= 1.65e-192)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.6e+39)
		tmp = t_1;
	else
		tmp = x - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e-102], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-212], t$95$1, If[LessEqual[a, 1.65e-192], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+39], t$95$1, N[(x - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.80000000000000026e-102

   1. Initial program 72.7%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around inf 66.6%

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

   6. Taylor expanded in z around 0 51.2%

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

   if -6.80000000000000026e-102 < a < 2.6e-212 or 1.64999999999999995e-192 < a < 1.59999999999999996e39

   1. Initial program 69.2%

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

      1. associate-*l/ 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in x around 0 59.1%

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

      1. associate-/l* 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in a around 0 58.8%

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

      1. associate-*r/ 58.8%

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

      2. neg-mul-1 58.8%

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

   10. Simplified 58.8%

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

   11. Taylor expanded in z around 0 56.8%

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

       1. mul-1-neg 56.8%

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

       2. unsub-neg 56.8%

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

       3. associate-/l* 58.8%

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

   13. Simplified 58.8%

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

   if 2.6e-212 < a < 1.64999999999999995e-192

   1. Initial program 99.7%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r/ 99.7%

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

      2. associate-*r* 99.7%

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

      3. mul-1-neg 99.7%

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

      4. associate-*r/ 99.7%

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

      5. associate-*r* 99.7%

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

      6. mul-1-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 99.4%

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

      1. div-sub 99.4%

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

   10. Simplified 99.4%

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

   if 1.59999999999999996e39 < a

   1. Initial program 67.3%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around inf 75.1%

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

   6. Taylor expanded in a around inf 69.7%

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

   7. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. *-commutative 58.1%

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

      3. associate-*r/ 63.0%

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

      4. unsub-neg 63.0%

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

   9. Simplified 63.0%

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

       1. clear-num 63.2%

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

       2. un-div-inv 63.2%

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

   11. Applied egg-rr 63.2%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-212}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+39}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-212}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+41}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e-102)
   (+ x (/ (* y t) a))
   (if (<= a 2.6e-212)
     (/ t (/ z (- z y)))
     (if (<= a 1.65e-192)
       (* x (/ (- y a) z))
       (if (<= a 5.6e+41) (- t (/ t (/ z y))) (- x (/ z (/ a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 2.6e-212) {
		tmp = t / (z / (z - y));
	} else if (a <= 1.65e-192) {
		tmp = x * ((y - a) / z);
	} else if (a <= 5.6e+41) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.35d-102)) then
        tmp = x + ((y * t) / a)
    else if (a <= 2.6d-212) then
        tmp = t / (z / (z - y))
    else if (a <= 1.65d-192) then
        tmp = x * ((y - a) / z)
    else if (a <= 5.6d+41) then
        tmp = t - (t / (z / y))
    else
        tmp = x - (z / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 2.6e-212) {
		tmp = t / (z / (z - y));
	} else if (a <= 1.65e-192) {
		tmp = x * ((y - a) / z);
	} else if (a <= 5.6e+41) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e-102:
		tmp = x + ((y * t) / a)
	elif a <= 2.6e-212:
		tmp = t / (z / (z - y))
	elif a <= 1.65e-192:
		tmp = x * ((y - a) / z)
	elif a <= 5.6e+41:
		tmp = t - (t / (z / y))
	else:
		tmp = x - (z / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e-102)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 2.6e-212)
		tmp = Float64(t / Float64(z / Float64(z - y)));
	elseif (a <= 1.65e-192)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 5.6e+41)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	else
		tmp = Float64(x - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.35e-102)
		tmp = x + ((y * t) / a);
	elseif (a <= 2.6e-212)
		tmp = t / (z / (z - y));
	elseif (a <= 1.65e-192)
		tmp = x * ((y - a) / z);
	elseif (a <= 5.6e+41)
		tmp = t - (t / (z / y));
	else
		tmp = x - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e-102], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-212], N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-192], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+41], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.35e-102

   1. Initial program 72.7%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around inf 66.6%

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

   6. Taylor expanded in z around 0 51.2%

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

   if -1.35e-102 < a < 2.6e-212

   1. Initial program 69.4%

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

      1. associate-*l/ 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in x around 0 64.9%

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

      1. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in a around 0 67.7%

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

      1. associate-*r/ 67.7%

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

      2. neg-mul-1 67.7%

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

   10. Simplified 67.7%

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

       1. frac-2neg 67.7%

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

       2. div-inv 67.6%

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

       3. remove-double-neg 67.6%

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

       4. sub-neg 67.6%

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

       5. distribute-neg-in 67.6%

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

       6. remove-double-neg 67.6%

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

   12. Applied egg-rr 67.6%

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

       1. associate-*r/ 67.7%

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

       2. *-rgt-identity 67.7%

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

       3. +-commutative 67.7%

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

       4. unsub-neg 67.7%

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

   14. Simplified 67.7%

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

   if 2.6e-212 < a < 1.64999999999999995e-192

   1. Initial program 99.7%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r/ 99.7%

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

      2. associate-*r* 99.7%

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

      3. mul-1-neg 99.7%

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

      4. associate-*r/ 99.7%

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

      5. associate-*r* 99.7%

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

      6. mul-1-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 99.4%

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

      1. div-sub 99.4%

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

   10. Simplified 99.4%

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

   if 1.64999999999999995e-192 < a < 5.5999999999999999e41

   1. Initial program 69.1%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in x around 0 51.7%

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

      1. associate-/l* 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in a around 0 47.6%

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

      1. associate-*r/ 47.6%

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

      2. neg-mul-1 47.6%

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

   10. Simplified 47.6%

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

   11. Taylor expanded in z around 0 47.0%

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

       1. mul-1-neg 47.0%

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

       2. unsub-neg 47.0%

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

       3. associate-/l* 47.6%

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

   13. Simplified 47.6%

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

   if 5.5999999999999999e41 < a

   1. Initial program 67.3%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around inf 75.1%

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

   6. Taylor expanded in a around inf 69.7%

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

   7. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. *-commutative 58.1%

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

      3. associate-*r/ 63.0%

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

      4. unsub-neg 63.0%

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

   9. Simplified 63.0%

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

       1. clear-num 63.2%

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

       2. un-div-inv 63.2%

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

   11. Applied egg-rr 63.2%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-212}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+41}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-212}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-192}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+41}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.3e-102)
   (+ x (/ (* y t) a))
   (if (<= a 5.6e-212)
     (/ t (/ z (- z y)))
     (if (<= a 1.65e-192)
       (/ (* x (- y a)) z)
       (if (<= a 8.6e+41) (- t (/ t (/ z y))) (- x (/ z (/ a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 5.6e-212) {
		tmp = t / (z / (z - y));
	} else if (a <= 1.65e-192) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 8.6e+41) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.3d-102)) then
        tmp = x + ((y * t) / a)
    else if (a <= 5.6d-212) then
        tmp = t / (z / (z - y))
    else if (a <= 1.65d-192) then
        tmp = (x * (y - a)) / z
    else if (a <= 8.6d+41) then
        tmp = t - (t / (z / y))
    else
        tmp = x - (z / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e-102) {
		tmp = x + ((y * t) / a);
	} else if (a <= 5.6e-212) {
		tmp = t / (z / (z - y));
	} else if (a <= 1.65e-192) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 8.6e+41) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x - (z / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.3e-102:
		tmp = x + ((y * t) / a)
	elif a <= 5.6e-212:
		tmp = t / (z / (z - y))
	elif a <= 1.65e-192:
		tmp = (x * (y - a)) / z
	elif a <= 8.6e+41:
		tmp = t - (t / (z / y))
	else:
		tmp = x - (z / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.3e-102)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 5.6e-212)
		tmp = Float64(t / Float64(z / Float64(z - y)));
	elseif (a <= 1.65e-192)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 8.6e+41)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	else
		tmp = Float64(x - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.3e-102)
		tmp = x + ((y * t) / a);
	elseif (a <= 5.6e-212)
		tmp = t / (z / (z - y));
	elseif (a <= 1.65e-192)
		tmp = (x * (y - a)) / z;
	elseif (a <= 8.6e+41)
		tmp = t - (t / (z / y));
	else
		tmp = x - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.3e-102], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e-212], N[(t / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-192], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 8.6e+41], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.2999999999999997e-102

   1. Initial program 72.7%

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

      1. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around inf 66.6%

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

   6. Taylor expanded in z around 0 51.2%

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

   if -4.2999999999999997e-102 < a < 5.60000000000000027e-212

   1. Initial program 69.4%

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

      1. associate-*l/ 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in x around 0 64.9%

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

      1. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in a around 0 67.7%

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

      1. associate-*r/ 67.7%

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

      2. neg-mul-1 67.7%

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

   10. Simplified 67.7%

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

       1. frac-2neg 67.7%

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

       2. div-inv 67.6%

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

       3. remove-double-neg 67.6%

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

       4. sub-neg 67.6%

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

       5. distribute-neg-in 67.6%

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

       6. remove-double-neg 67.6%

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

   12. Applied egg-rr 67.6%

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

       1. associate-*r/ 67.7%

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

       2. *-rgt-identity 67.7%

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

       3. +-commutative 67.7%

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

       4. unsub-neg 67.7%

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

   14. Simplified 67.7%

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

   if 5.60000000000000027e-212 < a < 1.64999999999999995e-192

   1. Initial program 99.7%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. div-sub 99.7%

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

      5. distribute-lft-out-- 99.7%

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

      6. associate-*r/ 99.7%

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

      7. mul-1-neg 99.7%

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

      8. distribute-rgt-out-- 99.7%

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

      9. unsub-neg 99.7%

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

      10. associate-/l* 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in t around 0 99.7%

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

   if 1.64999999999999995e-192 < a < 8.60000000000000048e41

   1. Initial program 69.1%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in x around 0 51.7%

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

      1. associate-/l* 60.0%

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

   7. Simplified 60.0%

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

   8. Taylor expanded in a around 0 47.6%

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

      1. associate-*r/ 47.6%

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

      2. neg-mul-1 47.6%

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

   10. Simplified 47.6%

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

   11. Taylor expanded in z around 0 47.0%

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

       1. mul-1-neg 47.0%

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

       2. unsub-neg 47.0%

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

       3. associate-/l* 47.6%

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

   13. Simplified 47.6%

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

   if 8.60000000000000048e41 < a

   1. Initial program 67.3%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around inf 75.1%

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

   6. Taylor expanded in a around inf 69.7%

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

   7. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. *-commutative 58.1%

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

      3. associate-*r/ 63.0%

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

      4. unsub-neg 63.0%

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

   9. Simplified 63.0%

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

       1. clear-num 63.2%

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

       2. un-div-inv 63.2%

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

   11. Applied egg-rr 63.2%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-212}:\\ \;\;\;\;\frac{t}{\frac{z}{z - y}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-192}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+41}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-70}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -8.2e-18)
     t_1
     (if (<= a -1.55e-119)
       (* y (/ (- t x) (- a z)))
       (if (<= a 5e-70) (- t (/ y (/ z (- t x)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -8.2e-18) {
		tmp = t_1;
	} else if (a <= -1.55e-119) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5e-70) {
		tmp = t - (y / (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 = x + ((t - x) / (a / (y - z)))
    if (a <= (-8.2d-18)) then
        tmp = t_1
    else if (a <= (-1.55d-119)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 5d-70) then
        tmp = t - (y / (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 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -8.2e-18) {
		tmp = t_1;
	} else if (a <= -1.55e-119) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5e-70) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -8.2e-18:
		tmp = t_1
	elif a <= -1.55e-119:
		tmp = y * ((t - x) / (a - z))
	elif a <= 5e-70:
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -8.2e-18)
		tmp = t_1;
	elseif (a <= -1.55e-119)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 5e-70)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -8.2e-18)
		tmp = t_1;
	elseif (a <= -1.55e-119)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 5e-70)
		tmp = t - (y / (z / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e-18], t$95$1, If[LessEqual[a, -1.55e-119], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-70], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.1999999999999995e-18 or 4.9999999999999998e-70 < a

   1. Initial program 69.8%

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

      1. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in a around inf 62.3%

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

      1. associate-/l* 75.1%

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

   7. Simplified 75.1%

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

   if -8.1999999999999995e-18 < a < -1.54999999999999989e-119

   1. Initial program 82.4%

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

      1. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

   7. Simplified 82.9%

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

   if -1.54999999999999989e-119 < a < 4.9999999999999998e-70

   1. Initial program 69.0%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 82.6%

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

      1. associate--l+ 82.6%

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

      2. associate-*r/ 82.6%

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

      3. associate-*r/ 82.6%

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

      4. div-sub 82.6%

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

      5. distribute-lft-out-- 82.6%

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

      6. associate-*r/ 82.6%

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

      7. mul-1-neg 82.6%

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

      8. distribute-rgt-out-- 82.6%

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

      9. unsub-neg 82.6%

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

      10. associate-/l* 86.2%

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

   7. Simplified 86.2%

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

   8. Taylor expanded in y around inf 80.3%

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

      1. associate-/l* 83.7%

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

   10. Simplified 83.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-70}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-70}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e-18)
   (+ x (/ (- t x) (/ a (- y z))))
   (if (<= a -1.12e-119)
     (* y (/ (- t x) (- a z)))
     (if (<= a 5.5e-70)
       (- t (/ y (/ z (- t x))))
       (+ x (/ (- y z) (/ (- a z) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e-18) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (a <= -1.12e-119) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.5e-70) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.7d-18)) then
        tmp = x + ((t - x) / (a / (y - z)))
    else if (a <= (-1.12d-119)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 5.5d-70) then
        tmp = t - (y / (z / (t - x)))
    else
        tmp = x + ((y - z) / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e-18) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if (a <= -1.12e-119) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.5e-70) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e-18:
		tmp = x + ((t - x) / (a / (y - z)))
	elif a <= -1.12e-119:
		tmp = y * ((t - x) / (a - z))
	elif a <= 5.5e-70:
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e-18)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	elseif (a <= -1.12e-119)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 5.5e-70)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.7e-18)
		tmp = x + ((t - x) / (a / (y - z)));
	elseif (a <= -1.12e-119)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 5.5e-70)
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e-18], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.12e-119], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-70], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.7000000000000003e-18

   1. Initial program 71.3%

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

      1. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in a around inf 67.0%

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

      1. associate-/l* 79.7%

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

   7. Simplified 79.7%

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

   if -3.7000000000000003e-18 < a < -1.11999999999999998e-119

   1. Initial program 82.4%

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

      1. associate-*l/ 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 82.9%

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

      1. div-sub 82.9%

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

   7. Simplified 82.9%

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

   if -1.11999999999999998e-119 < a < 5.5000000000000001e-70

   1. Initial program 69.0%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 82.6%

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

      1. associate--l+ 82.6%

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

      2. associate-*r/ 82.6%

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

      3. associate-*r/ 82.6%

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

      4. div-sub 82.6%

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

      5. distribute-lft-out-- 82.6%

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

      6. associate-*r/ 82.6%

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

      7. mul-1-neg 82.6%

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

      8. distribute-rgt-out-- 82.6%

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

      9. unsub-neg 82.6%

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

      10. associate-/l* 86.2%

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

   7. Simplified 86.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in y around inf 80.3%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 83.7%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   10. Simplified 83.7%

       \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   if 5.5000000000000001e-70 < a

   1. Initial program 68.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 84.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 72.0%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-70}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-199}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= z -1.05e+94)
     t_1
     (if (<= z -8e-199)
       (+ x (/ (- y z) (/ (- a z) t)))
       (if (<= z 5e-15) (+ x (/ (- t x) (/ a (- y z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -1.05e+94) {
		tmp = t_1;
	} else if (z <= -8e-199) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (z <= 5e-15) {
		tmp = x + ((t - x) / (a / (y - 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 + ((x - t) / (z / (y - a)))
    if (z <= (-1.05d+94)) then
        tmp = t_1
    else if (z <= (-8d-199)) then
        tmp = x + ((y - z) / ((a - z) / t))
    else if (z <= 5d-15) then
        tmp = x + ((t - x) / (a / (y - 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 + ((x - t) / (z / (y - a)));
	double tmp;
	if (z <= -1.05e+94) {
		tmp = t_1;
	} else if (z <= -8e-199) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (z <= 5e-15) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if z <= -1.05e+94:
		tmp = t_1
	elif z <= -8e-199:
		tmp = x + ((y - z) / ((a - z) / t))
	elif z <= 5e-15:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -1.05e+94)
		tmp = t_1;
	elseif (z <= -8e-199)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (z <= 5e-15)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (z <= -1.05e+94)
		tmp = t_1;
	elseif (z <= -8e-199)
		tmp = x + ((y - z) / ((a - z) / t));
	elseif (z <= 5e-15)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+94], t$95$1, If[LessEqual[z, -8e-199], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-15], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999995e94 or 4.99999999999999999e-15 < z

   1. Initial program 46.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 67.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.9%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 66.9%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 66.9%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 66.9%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 66.9%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 66.9%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 66.9%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 66.9%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 67.9%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 67.9%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 77.8%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   if -1.04999999999999995e94 < z < -7.99999999999999986e-199

   1. Initial program 84.7%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 72.0%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   if -7.99999999999999986e-199 < z < 4.99999999999999999e-15

   1. Initial program 89.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. Add Preprocessing

   5. Taylor expanded in a around inf 78.9%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 87.5%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a}{y - z}}} \]

   7. Simplified 87.5%

      \[\leadsto \color{blue}{x + \frac{t - x}{\frac{a}{y - z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-199}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-70}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e-18)
   (- x (* y (/ (- x t) a)))
   (if (<= a -1.5e-119)
     (* y (/ (- t x) (- a z)))
     (if (<= a 5.5e-70) (- t (/ y (/ z (- t x)))) (- x (/ (- z y) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-18) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= -1.5e-119) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.5e-70) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x - ((z - y) / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.8d-18)) then
        tmp = x - (y * ((x - t) / a))
    else if (a <= (-1.5d-119)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 5.5d-70) then
        tmp = t - (y / (z / (t - x)))
    else
        tmp = x - ((z - y) / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-18) {
		tmp = x - (y * ((x - t) / a));
	} else if (a <= -1.5e-119) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.5e-70) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x - ((z - y) / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e-18:
		tmp = x - (y * ((x - t) / a))
	elif a <= -1.5e-119:
		tmp = y * ((t - x) / (a - z))
	elif a <= 5.5e-70:
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x - ((z - y) / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e-18)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	elseif (a <= -1.5e-119)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 5.5e-70)
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x - Float64(Float64(z - y) / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.8e-18)
		tmp = x - (y * ((x - t) / a));
	elseif (a <= -1.5e-119)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 5.5e-70)
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x - ((z - y) / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e-18], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-119], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-70], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - y), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.80000000000000005e-18

   1. Initial program 71.3%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 67.0%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 79.7%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a}{y - z}}} \]

   7. Simplified 79.7%

      \[\leadsto \color{blue}{x + \frac{t - x}{\frac{a}{y - z}}} \]

   8. Taylor expanded in y around inf 57.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(t - x\right)}{a}} \]
   9. Step-by-step derivation

      1. associate-*r/ 70.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   10. Simplified 70.5%

       \[\leadsto x + \color{blue}{y \cdot \frac{t - x}{a}} \]

   if -1.80000000000000005e-18 < a < -1.5000000000000001e-119

   1. Initial program 82.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 82.6%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   6. Step-by-step derivation

      1. div-sub 82.9%

         \[\leadsto y \cdot \color{blue}{\frac{t - x}{a - z}} \]

   7. Simplified 82.9%

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z}} \]

   if -1.5000000000000001e-119 < a < 5.5000000000000001e-70

   1. Initial program 69.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 77.0%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 77.0%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 82.6%

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}} \]
   6. Step-by-step derivation

      1. associate--l+ 82.6%

         \[\leadsto \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]

      2. associate-*r/ 82.6%

         \[\leadsto t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]

      3. associate-*r/ 82.6%

         \[\leadsto t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]

      4. div-sub 82.6%

         \[\leadsto t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]

      5. distribute-lft-out-- 82.6%

         \[\leadsto t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]

      6. associate-*r/ 82.6%

         \[\leadsto t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]

      7. mul-1-neg 82.6%

         \[\leadsto t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]

      8. distribute-rgt-out-- 82.6%

         \[\leadsto t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

      9. unsub-neg 82.6%

         \[\leadsto \color{blue}{t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}} \]

      10. associate-/l* 86.2%

          \[\leadsto t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

   7. Simplified 86.2%

      \[\leadsto \color{blue}{t - \frac{t - x}{\frac{z}{y - a}}} \]

   8. Taylor expanded in y around inf 80.3%

      \[\leadsto t - \color{blue}{\frac{y \cdot \left(t - x\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 83.7%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   10. Simplified 83.7%

       \[\leadsto t - \color{blue}{\frac{y}{\frac{z}{t - x}}} \]

   if 5.5000000000000001e-70 < a

   1. Initial program 68.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 84.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 72.0%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in a around inf 64.1%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a}{t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-70}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+79) t (if (<= z 4.6e+112) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+79) {
		tmp = t;
	} else if (z <= 4.6e+112) {
		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 <= (-8.5d+79)) then
        tmp = t
    else if (z <= 4.6d+112) 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 <= -8.5e+79) {
		tmp = t;
	} else if (z <= 4.6e+112) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+79:
		tmp = t
	elif z <= 4.6e+112:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+79)
		tmp = t;
	elseif (z <= 4.6e+112)
		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 <= -8.5e+79)
		tmp = t;
	elseif (z <= 4.6e+112)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+79], t, If[LessEqual[z, 4.6e+112], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999998e79 or 4.5999999999999999e112 < z

   1. Initial program 38.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 62.5%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 62.5%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 49.0%

      \[\leadsto \color{blue}{t} \]

   if -8.4999999999999998e79 < z < 4.5999999999999999e112

   1. Initial program 86.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 63.6%

      \[\leadsto \color{blue}{x + \frac{\left(t - x\right) \cdot \left(y - z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 71.4%

         \[\leadsto x + \color{blue}{\frac{t - x}{\frac{a}{y - z}}} \]

   7. Simplified 71.4%

      \[\leadsto \color{blue}{x + \frac{t - x}{\frac{a}{y - z}}} \]

   8. Taylor expanded in y around inf 65.5%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y}}} \]

   9. Taylor expanded in x around inf 48.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y}{a}\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 48.9%

          \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{y}{a}\right)}\right) \]

       2. unsub-neg 48.9%

          \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y}{a}\right)} \]

   11. Simplified 48.9%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+154} \lor \neg \left(y \leq 4.5 \cdot 10^{+89}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.8e+154) (not (<= y 4.5e+89))) (* t (/ y a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.8e+154) || !(y <= 4.5e+89)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.8d+154)) .or. (.not. (y <= 4.5d+89))) then
        tmp = t * (y / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.8e+154) || !(y <= 4.5e+89)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.8e+154) or not (y <= 4.5e+89):
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.8e+154) || !(y <= 4.5e+89))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.8e+154) || ~((y <= 4.5e+89)))
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.8e+154], N[Not[LessEqual[y, 4.5e+89]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999998e154 or 4.5e89 < y

   1. Initial program 70.8%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 54.0%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]

   6. Taylor expanded in z around 0 28.3%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-*r/ 34.9%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   8. Simplified 34.9%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   if -3.7999999999999998e154 < y < 4.5e89

   1. Initial program 70.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 74.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 74.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.8%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 38.7%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+154} \lor \neg \left(y \leq 4.5 \cdot 10^{+89}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+155}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+91}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.1e+155)
   (/ t (/ a y))
   (if (<= y 3.05e+91) (+ x t) (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+155) {
		tmp = t / (a / y);
	} else if (y <= 3.05e+91) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.1d+155)) then
        tmp = t / (a / y)
    else if (y <= 3.05d+91) then
        tmp = x + t
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+155) {
		tmp = t / (a / y);
	} else if (y <= 3.05e+91) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.1e+155:
		tmp = t / (a / y)
	elif y <= 3.05e+91:
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.1e+155)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 3.05e+91)
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.1e+155)
		tmp = t / (a / y);
	elseif (y <= 3.05e+91)
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.1e+155], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e+91], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1000000000000001e155

   1. Initial program 67.4%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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. Add Preprocessing

   5. Taylor expanded in x around 0 39.8%

      \[\leadsto \color{blue}{\frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 56.0%

         \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   7. Simplified 56.0%

      \[\leadsto \color{blue}{\frac{t}{\frac{a - z}{y - z}}} \]

   8. Taylor expanded in z around 0 43.0%

      \[\leadsto \frac{t}{\color{blue}{\frac{a}{y}}} \]

   if -1.1000000000000001e155 < y < 3.05e91

   1. Initial program 70.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-/l* 74.3%

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

   3. Simplified 74.3%

      \[\leadsto \color{blue}{x + \frac{y - z}{\frac{a - z}{t - x}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.8%

      \[\leadsto x + \frac{y - z}{\color{blue}{\frac{a - z}{t}}} \]

   6. Taylor expanded in z around inf 38.7%

      \[\leadsto x + \color{blue}{t} \]

   if 3.05e91 < y

   1. Initial program 72.5%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 52.9%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]

   6. Taylor expanded in z around 0 24.1%

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-*r/ 30.8%

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]

   8. Simplified 30.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+155}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+91}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{+40}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e-27) x (if (<= a 1e+40) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e-27) {
		tmp = x;
	} else if (a <= 1e+40) {
		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 <= (-1.95d-27)) then
        tmp = x
    else if (a <= 1d+40) 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 <= -1.95e-27) {
		tmp = x;
	} else if (a <= 1e+40) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.95e-27:
		tmp = x
	elif a <= 1e+40:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e-27)
		tmp = x;
	elseif (a <= 1e+40)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.95e-27)
		tmp = x;
	elseif (a <= 1e+40)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e-27], x, If[LessEqual[a, 1e+40], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.94999999999999986e-27 or 1.00000000000000003e40 < a

   1. Initial program 70.1%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.2%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 41.8%

      \[\leadsto \color{blue}{x} \]

   if -1.94999999999999986e-27 < a < 1.00000000000000003e40

   1. Initial program 70.6%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 77.7%

         \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 33.5%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{+40}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.6% 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 70.3%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
2. Step-by-step derivation

   1. associate-*l/ 83.4%

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z} \cdot \left(t - x\right)} \]

3. Simplified 83.4%

   \[\leadsto \color{blue}{x + \frac{y - z}{a - z} \cdot \left(t - x\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 21.9%

   \[\leadsto \color{blue}{t} \]

6. Final simplification 21.9%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 84.2% accurate, 0.6× 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 2024019 
(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))))