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

Percentage Accurate: 67.9% → 88.3%

Time: 17.1s

Alternatives: 19

Speedup: 0.6×

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: 67.9% 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: 88.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+180} \lor \neg \left(z \leq 1.3 \cdot 10^{+214}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\left(y - a\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.8e+180) (not (<= z 1.3e+214)))
   (+ t (* (- t x) (* (- y a) (/ -1.0 z))))
   (fma (- t x) (/ (- y z) (- a z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.8e+180) || !(z <= 1.3e+214)) {
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.8e+180) || !(z <= 1.3e+214))
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(y - a) * Float64(-1.0 / z))));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.8e+180], N[Not[LessEqual[z, 1.3e+214]], $MachinePrecision]], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000002e180 or 1.29999999999999996e214 < z

   1. Initial program 27.7%

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

      1. associate-/l* 42.5%

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

   3. Simplified 42.5%

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

   5. Taylor expanded in z around inf 66.7%

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

      1. associate--l+ 66.7%

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

      2. associate-*r/ 66.7%

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

      3. associate-*r/ 66.7%

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

      4. mul-1-neg 66.7%

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

      5. div-sub 66.7%

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

      6. mul-1-neg 66.7%

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

      7. distribute-lft-out-- 66.7%

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

      8. associate-*r/ 66.7%

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

      9. mul-1-neg 66.7%

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

      10. unsub-neg 66.7%

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

      11. distribute-rgt-out-- 66.9%

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

   7. Simplified 66.9%

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

      1. div-inv 66.9%

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

   9. Applied egg-rr 66.9%

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

       1. associate-*l* 93.1%

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

   11. Simplified 93.1%

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

   if -7.8000000000000002e180 < z < 1.29999999999999996e214

   1. Initial program 80.2%

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

      1. +-commutative 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-/l* 93.2%

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

      4. fma-define 93.2%

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

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+180} \lor \neg \left(z \leq 1.3 \cdot 10^{+214}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\left(y - a\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 39.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -225:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-20}:\\ \;\;\;\;x - \left(x - t\right)\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-227}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* y (/ (- t x) a))))
   (if (<= a -6.5e+127)
     x
     (if (<= a -2.65e+19)
       t_2
       (if (<= a -225.0)
         t_1
         (if (<= a -9.6e-20)
           (- x (- x t))
           (if (<= a -1.06e-110)
             t_2
             (if (<= a -3.1e-227)
               t
               (if (<= a 3.2e-116) t_1 (if (<= a 1.2e+84) t_2 x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (a <= -6.5e+127) {
		tmp = x;
	} else if (a <= -2.65e+19) {
		tmp = t_2;
	} else if (a <= -225.0) {
		tmp = t_1;
	} else if (a <= -9.6e-20) {
		tmp = x - (x - t);
	} else if (a <= -1.06e-110) {
		tmp = t_2;
	} else if (a <= -3.1e-227) {
		tmp = t;
	} else if (a <= 3.2e-116) {
		tmp = t_1;
	} else if (a <= 1.2e+84) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    t_2 = y * ((t - x) / a)
    if (a <= (-6.5d+127)) then
        tmp = x
    else if (a <= (-2.65d+19)) then
        tmp = t_2
    else if (a <= (-225.0d0)) then
        tmp = t_1
    else if (a <= (-9.6d-20)) then
        tmp = x - (x - t)
    else if (a <= (-1.06d-110)) then
        tmp = t_2
    else if (a <= (-3.1d-227)) then
        tmp = t
    else if (a <= 3.2d-116) then
        tmp = t_1
    else if (a <= 1.2d+84) then
        tmp = t_2
    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 t_1 = x * ((y - a) / z);
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (a <= -6.5e+127) {
		tmp = x;
	} else if (a <= -2.65e+19) {
		tmp = t_2;
	} else if (a <= -225.0) {
		tmp = t_1;
	} else if (a <= -9.6e-20) {
		tmp = x - (x - t);
	} else if (a <= -1.06e-110) {
		tmp = t_2;
	} else if (a <= -3.1e-227) {
		tmp = t;
	} else if (a <= 3.2e-116) {
		tmp = t_1;
	} else if (a <= 1.2e+84) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = y * ((t - x) / a)
	tmp = 0
	if a <= -6.5e+127:
		tmp = x
	elif a <= -2.65e+19:
		tmp = t_2
	elif a <= -225.0:
		tmp = t_1
	elif a <= -9.6e-20:
		tmp = x - (x - t)
	elif a <= -1.06e-110:
		tmp = t_2
	elif a <= -3.1e-227:
		tmp = t
	elif a <= 3.2e-116:
		tmp = t_1
	elif a <= 1.2e+84:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (a <= -6.5e+127)
		tmp = x;
	elseif (a <= -2.65e+19)
		tmp = t_2;
	elseif (a <= -225.0)
		tmp = t_1;
	elseif (a <= -9.6e-20)
		tmp = Float64(x - Float64(x - t));
	elseif (a <= -1.06e-110)
		tmp = t_2;
	elseif (a <= -3.1e-227)
		tmp = t;
	elseif (a <= 3.2e-116)
		tmp = t_1;
	elseif (a <= 1.2e+84)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = y * ((t - x) / a);
	tmp = 0.0;
	if (a <= -6.5e+127)
		tmp = x;
	elseif (a <= -2.65e+19)
		tmp = t_2;
	elseif (a <= -225.0)
		tmp = t_1;
	elseif (a <= -9.6e-20)
		tmp = x - (x - t);
	elseif (a <= -1.06e-110)
		tmp = t_2;
	elseif (a <= -3.1e-227)
		tmp = t;
	elseif (a <= 3.2e-116)
		tmp = t_1;
	elseif (a <= 1.2e+84)
		tmp = t_2;
	else
		tmp = x;
	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[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+127], x, If[LessEqual[a, -2.65e+19], t$95$2, If[LessEqual[a, -225.0], t$95$1, If[LessEqual[a, -9.6e-20], N[(x - N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.06e-110], t$95$2, If[LessEqual[a, -3.1e-227], t, If[LessEqual[a, 3.2e-116], t$95$1, If[LessEqual[a, 1.2e+84], t$95$2, x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.5e127 or 1.2e84 < a

   1. Initial program 66.0%

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

      1. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in a around inf 60.4%

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

   if -6.5e127 < a < -2.65e19 or -9.59999999999999971e-20 < a < -1.0599999999999999e-110 or 3.20000000000000009e-116 < a < 1.2e84

   1. Initial program 78.0%

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

      1. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in z around 0 57.7%

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

   6. Taylor expanded in y around inf 45.5%

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

   7. Taylor expanded in a around 0 46.8%

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

   if -2.65e19 < a < -225 or -3.09999999999999979e-227 < a < 3.20000000000000009e-116

   1. Initial program 74.4%

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

      1. associate-/l* 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in z around inf 85.9%

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

      1. associate--l+ 85.9%

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

      2. associate-*r/ 85.9%

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

      3. associate-*r/ 85.9%

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

      4. mul-1-neg 85.9%

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

      5. div-sub 86.2%

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

      6. mul-1-neg 86.2%

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

      7. distribute-lft-out-- 86.2%

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

      8. associate-*r/ 86.2%

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

      9. mul-1-neg 86.2%

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

      10. unsub-neg 86.2%

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

      11. distribute-rgt-out-- 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in t around 0 45.2%

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

      1. associate-/l* 46.7%

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

   10. Simplified 46.7%

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

   if -225 < a < -9.59999999999999971e-20

   1. Initial program 78.9%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around inf 46.3%

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

   if -1.0599999999999999e-110 < a < -3.09999999999999979e-227

   1. Initial program 50.1%

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

      1. associate-/l* 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in z around inf 61.5%

      \[\leadsto \color{blue}{t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -225:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-20}:\\ \;\;\;\;x - \left(x - t\right)\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-227}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;a \leq -0.0027:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.24 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= a -0.0027)
     x
     (if (<= a -1.24e-110)
       (* y (/ t a))
       (if (<= a -1.45e-226)
         t
         (if (<= a 3.9e-181)
           t_1
           (if (<= a 1.65e+59) t (if (<= a 1.4e+82) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (a <= -0.0027) {
		tmp = x;
	} else if (a <= -1.24e-110) {
		tmp = y * (t / a);
	} else if (a <= -1.45e-226) {
		tmp = t;
	} else if (a <= 3.9e-181) {
		tmp = t_1;
	} else if (a <= 1.65e+59) {
		tmp = t;
	} else if (a <= 1.4e+82) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (a <= (-0.0027d0)) then
        tmp = x
    else if (a <= (-1.24d-110)) then
        tmp = y * (t / a)
    else if (a <= (-1.45d-226)) then
        tmp = t
    else if (a <= 3.9d-181) then
        tmp = t_1
    else if (a <= 1.65d+59) then
        tmp = t
    else if (a <= 1.4d+82) then
        tmp = t_1
    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 t_1 = x * ((y - a) / z);
	double tmp;
	if (a <= -0.0027) {
		tmp = x;
	} else if (a <= -1.24e-110) {
		tmp = y * (t / a);
	} else if (a <= -1.45e-226) {
		tmp = t;
	} else if (a <= 3.9e-181) {
		tmp = t_1;
	} else if (a <= 1.65e+59) {
		tmp = t;
	} else if (a <= 1.4e+82) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if a <= -0.0027:
		tmp = x
	elif a <= -1.24e-110:
		tmp = y * (t / a)
	elif a <= -1.45e-226:
		tmp = t
	elif a <= 3.9e-181:
		tmp = t_1
	elif a <= 1.65e+59:
		tmp = t
	elif a <= 1.4e+82:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (a <= -0.0027)
		tmp = x;
	elseif (a <= -1.24e-110)
		tmp = Float64(y * Float64(t / a));
	elseif (a <= -1.45e-226)
		tmp = t;
	elseif (a <= 3.9e-181)
		tmp = t_1;
	elseif (a <= 1.65e+59)
		tmp = t;
	elseif (a <= 1.4e+82)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (a <= -0.0027)
		tmp = x;
	elseif (a <= -1.24e-110)
		tmp = y * (t / a);
	elseif (a <= -1.45e-226)
		tmp = t;
	elseif (a <= 3.9e-181)
		tmp = t_1;
	elseif (a <= 1.65e+59)
		tmp = t;
	elseif (a <= 1.4e+82)
		tmp = t_1;
	else
		tmp = x;
	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]}, If[LessEqual[a, -0.0027], x, If[LessEqual[a, -1.24e-110], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.45e-226], t, If[LessEqual[a, 3.9e-181], t$95$1, If[LessEqual[a, 1.65e+59], t, If[LessEqual[a, 1.4e+82], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.0027000000000000001 or 1.4e82 < a

   1. Initial program 70.0%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in a around inf 52.1%

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

   if -0.0027000000000000001 < a < -1.24000000000000006e-110

   1. Initial program 81.0%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around 0 54.0%

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

   6. Taylor expanded in y around inf 46.1%

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

   7. Taylor expanded in t around inf 38.9%

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

   if -1.24000000000000006e-110 < a < -1.45000000000000001e-226 or 3.9e-181 < a < 1.65e59

   1. Initial program 62.0%

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

      1. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 45.5%

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

   if -1.45000000000000001e-226 < a < 3.9e-181 or 1.65e59 < a < 1.4e82

   1. Initial program 76.7%

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

      1. associate-/l* 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in z around inf 82.8%

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

      1. associate--l+ 82.8%

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

      2. associate-*r/ 82.8%

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

      3. associate-*r/ 82.8%

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

      4. mul-1-neg 82.8%

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

      5. div-sub 82.8%

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

      6. mul-1-neg 82.8%

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

      7. distribute-lft-out-- 82.8%

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

      8. associate-*r/ 82.8%

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

      9. mul-1-neg 82.8%

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

      10. unsub-neg 82.8%

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

      11. distribute-rgt-out-- 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in t around 0 46.0%

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

      1. associate-/l* 51.1%

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

   10. Simplified 51.1%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0027:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.24 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -0.00029:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.24 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -0.00029)
     x
     (if (<= a -1.24e-110)
       (* y (/ t a))
       (if (<= a -4e-226)
         t
         (if (<= a 1.9e-180)
           t_1
           (if (<= a 5.5e+60) t (if (<= a 2.2e+82) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -0.00029) {
		tmp = x;
	} else if (a <= -1.24e-110) {
		tmp = y * (t / a);
	} else if (a <= -4e-226) {
		tmp = t;
	} else if (a <= 1.9e-180) {
		tmp = t_1;
	} else if (a <= 5.5e+60) {
		tmp = t;
	} else if (a <= 2.2e+82) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-0.00029d0)) then
        tmp = x
    else if (a <= (-1.24d-110)) then
        tmp = y * (t / a)
    else if (a <= (-4d-226)) then
        tmp = t
    else if (a <= 1.9d-180) then
        tmp = t_1
    else if (a <= 5.5d+60) then
        tmp = t
    else if (a <= 2.2d+82) then
        tmp = t_1
    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 t_1 = x * (y / z);
	double tmp;
	if (a <= -0.00029) {
		tmp = x;
	} else if (a <= -1.24e-110) {
		tmp = y * (t / a);
	} else if (a <= -4e-226) {
		tmp = t;
	} else if (a <= 1.9e-180) {
		tmp = t_1;
	} else if (a <= 5.5e+60) {
		tmp = t;
	} else if (a <= 2.2e+82) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -0.00029:
		tmp = x
	elif a <= -1.24e-110:
		tmp = y * (t / a)
	elif a <= -4e-226:
		tmp = t
	elif a <= 1.9e-180:
		tmp = t_1
	elif a <= 5.5e+60:
		tmp = t
	elif a <= 2.2e+82:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -0.00029)
		tmp = x;
	elseif (a <= -1.24e-110)
		tmp = Float64(y * Float64(t / a));
	elseif (a <= -4e-226)
		tmp = t;
	elseif (a <= 1.9e-180)
		tmp = t_1;
	elseif (a <= 5.5e+60)
		tmp = t;
	elseif (a <= 2.2e+82)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -0.00029)
		tmp = x;
	elseif (a <= -1.24e-110)
		tmp = y * (t / a);
	elseif (a <= -4e-226)
		tmp = t;
	elseif (a <= 1.9e-180)
		tmp = t_1;
	elseif (a <= 5.5e+60)
		tmp = t;
	elseif (a <= 2.2e+82)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00029], x, If[LessEqual[a, -1.24e-110], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4e-226], t, If[LessEqual[a, 1.9e-180], t$95$1, If[LessEqual[a, 5.5e+60], t, If[LessEqual[a, 2.2e+82], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.9e-4 or 2.2000000000000001e82 < a

   1. Initial program 70.0%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in a around inf 52.1%

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

   if -2.9e-4 < a < -1.24000000000000006e-110

   1. Initial program 81.0%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around 0 54.0%

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

   6. Taylor expanded in y around inf 46.1%

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

   7. Taylor expanded in t around inf 38.9%

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

   if -1.24000000000000006e-110 < a < -3.99999999999999969e-226 or 1.9e-180 < a < 5.5000000000000001e60

   1. Initial program 62.0%

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

      1. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in z around inf 45.5%

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

   if -3.99999999999999969e-226 < a < 1.9e-180 or 5.5000000000000001e60 < a < 2.2000000000000001e82

   1. Initial program 76.7%

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

      1. associate-/l* 74.9%

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

   3. Simplified 74.9%

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

      1. associate-*r/ 76.7%

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

      2. clear-num 76.5%

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

      3. associate-/r* 85.2%

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

   6. Applied egg-rr 85.2%

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

   7. Taylor expanded in t around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. unsub-neg 41.6%

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

      3. associate-/l* 46.8%

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

   9. Simplified 46.8%

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

   10. Taylor expanded in y around inf 48.7%

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

       1. associate-*r/ 48.7%

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

       2. mul-1-neg 48.7%

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

       3. *-commutative 48.7%

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

   12. Simplified 48.7%

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

   13. Taylor expanded in a around 0 45.5%

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

       1. associate-/l* 49.2%

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

   15. Simplified 49.2%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00029:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.24 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-104}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-27} \lor \neg \left(a \leq 2 \cdot 10^{+67}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- x t) (/ (- z y) a)))))
   (if (<= a -1.05e-58)
     t_1
     (if (<= a 5.2e-104)
       (+ t (* y (/ (- x t) z)))
       (if (or (<= a 1.3e-27) (not (<= a 2e+67)))
         t_1
         (* t (/ (- y z) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / a));
	double tmp;
	if (a <= -1.05e-58) {
		tmp = t_1;
	} else if (a <= 5.2e-104) {
		tmp = t + (y * ((x - t) / z));
	} else if ((a <= 1.3e-27) || !(a <= 2e+67)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((x - t) * ((z - y) / a))
    if (a <= (-1.05d-58)) then
        tmp = t_1
    else if (a <= 5.2d-104) then
        tmp = t + (y * ((x - t) / z))
    else if ((a <= 1.3d-27) .or. (.not. (a <= 2d+67))) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / a));
	double tmp;
	if (a <= -1.05e-58) {
		tmp = t_1;
	} else if (a <= 5.2e-104) {
		tmp = t + (y * ((x - t) / z));
	} else if ((a <= 1.3e-27) || !(a <= 2e+67)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) * ((z - y) / a))
	tmp = 0
	if a <= -1.05e-58:
		tmp = t_1
	elif a <= 5.2e-104:
		tmp = t + (y * ((x - t) / z))
	elif (a <= 1.3e-27) or not (a <= 2e+67):
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)))
	tmp = 0.0
	if (a <= -1.05e-58)
		tmp = t_1;
	elseif (a <= 5.2e-104)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif ((a <= 1.3e-27) || !(a <= 2e+67))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((x - t) * ((z - y) / a));
	tmp = 0.0;
	if (a <= -1.05e-58)
		tmp = t_1;
	elseif (a <= 5.2e-104)
		tmp = t + (y * ((x - t) / z));
	elseif ((a <= 1.3e-27) || ~((a <= 2e+67)))
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e-58], t$95$1, If[LessEqual[a, 5.2e-104], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.3e-27], N[Not[LessEqual[a, 2e+67]], $MachinePrecision]], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.04999999999999994e-58 or 5.20000000000000005e-104 < a < 1.30000000000000009e-27 or 1.99999999999999997e67 < a

   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* 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in a around inf 64.1%

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

      1. associate-/l* 76.6%

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

   7. Simplified 76.6%

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

   if -1.04999999999999994e-58 < a < 5.20000000000000005e-104

   1. Initial program 68.4%

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

      1. associate-/l* 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in z around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. associate-*r/ 81.8%

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

      3. associate-*r/ 81.8%

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

      4. mul-1-neg 81.8%

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

      5. div-sub 83.0%

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

      6. mul-1-neg 83.0%

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

      7. distribute-lft-out-- 83.0%

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

      8. associate-*r/ 83.0%

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

      9. mul-1-neg 83.0%

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

      10. unsub-neg 83.0%

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

      11. distribute-rgt-out-- 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in y around inf 81.8%

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

      1. associate-/l* 86.7%

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

   10. Simplified 86.7%

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

   if 1.30000000000000009e-27 < a < 1.99999999999999997e67

   1. Initial program 77.9%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around 0 63.0%

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

      1. associate-/l* 77.5%

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

   7. Simplified 77.5%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-58}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-104}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-27} \lor \neg \left(a \leq 2 \cdot 10^{+67}\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -0.0026:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -0.0026)
     x
     (if (<= a -1.45e-226)
       t
       (if (<= a 5.5e-181)
         t_1
         (if (<= a 4.2e+60) t (if (<= a 1e+83) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -0.0026) {
		tmp = x;
	} else if (a <= -1.45e-226) {
		tmp = t;
	} else if (a <= 5.5e-181) {
		tmp = t_1;
	} else if (a <= 4.2e+60) {
		tmp = t;
	} else if (a <= 1e+83) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-0.0026d0)) then
        tmp = x
    else if (a <= (-1.45d-226)) then
        tmp = t
    else if (a <= 5.5d-181) then
        tmp = t_1
    else if (a <= 4.2d+60) then
        tmp = t
    else if (a <= 1d+83) then
        tmp = t_1
    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 t_1 = x * (y / z);
	double tmp;
	if (a <= -0.0026) {
		tmp = x;
	} else if (a <= -1.45e-226) {
		tmp = t;
	} else if (a <= 5.5e-181) {
		tmp = t_1;
	} else if (a <= 4.2e+60) {
		tmp = t;
	} else if (a <= 1e+83) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -0.0026:
		tmp = x
	elif a <= -1.45e-226:
		tmp = t
	elif a <= 5.5e-181:
		tmp = t_1
	elif a <= 4.2e+60:
		tmp = t
	elif a <= 1e+83:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -0.0026)
		tmp = x;
	elseif (a <= -1.45e-226)
		tmp = t;
	elseif (a <= 5.5e-181)
		tmp = t_1;
	elseif (a <= 4.2e+60)
		tmp = t;
	elseif (a <= 1e+83)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -0.0026)
		tmp = x;
	elseif (a <= -1.45e-226)
		tmp = t;
	elseif (a <= 5.5e-181)
		tmp = t_1;
	elseif (a <= 4.2e+60)
		tmp = t;
	elseif (a <= 1e+83)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0026], x, If[LessEqual[a, -1.45e-226], t, If[LessEqual[a, 5.5e-181], t$95$1, If[LessEqual[a, 4.2e+60], t, If[LessEqual[a, 1e+83], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.0025999999999999999 or 1.00000000000000003e83 < a

   1. Initial program 70.0%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in a around inf 52.1%

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

   if -0.0025999999999999999 < a < -1.45000000000000001e-226 or 5.50000000000000033e-181 < a < 4.2000000000000002e60

   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* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in z around inf 38.7%

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

   if -1.45000000000000001e-226 < a < 5.50000000000000033e-181 or 4.2000000000000002e60 < a < 1.00000000000000003e83

   1. Initial program 76.7%

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

      1. associate-/l* 74.9%

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

   3. Simplified 74.9%

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

      1. associate-*r/ 76.7%

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

      2. clear-num 76.5%

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

      3. associate-/r* 85.2%

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

   6. Applied egg-rr 85.2%

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

   7. Taylor expanded in t around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. unsub-neg 41.6%

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

      3. associate-/l* 46.8%

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

   9. Simplified 46.8%

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

   10. Taylor expanded in y around inf 48.7%

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

       1. associate-*r/ 48.7%

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

       2. mul-1-neg 48.7%

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

       3. *-commutative 48.7%

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

   12. Simplified 48.7%

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

   13. Taylor expanded in a around 0 45.5%

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

       1. associate-/l* 49.2%

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

   15. Simplified 49.2%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0026:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 10^{+83}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -0.00175:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-181}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (* x (/ y a)))))
   (if (<= a -0.00175)
     t_2
     (if (<= a -2.7e-226)
       t_1
       (if (<= a 2.2e-181) (/ (* y (- x t)) z) (if (<= a 8.5e+67) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (a <= -0.00175) {
		tmp = t_2;
	} else if (a <= -2.7e-226) {
		tmp = t_1;
	} else if (a <= 2.2e-181) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 8.5e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - (x * (y / a))
    if (a <= (-0.00175d0)) then
        tmp = t_2
    else if (a <= (-2.7d-226)) then
        tmp = t_1
    else if (a <= 2.2d-181) then
        tmp = (y * (x - t)) / z
    else if (a <= 8.5d+67) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (a <= -0.00175) {
		tmp = t_2;
	} else if (a <= -2.7e-226) {
		tmp = t_1;
	} else if (a <= 2.2e-181) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 8.5e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - (x * (y / a))
	tmp = 0
	if a <= -0.00175:
		tmp = t_2
	elif a <= -2.7e-226:
		tmp = t_1
	elif a <= 2.2e-181:
		tmp = (y * (x - t)) / z
	elif a <= 8.5e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (a <= -0.00175)
		tmp = t_2;
	elseif (a <= -2.7e-226)
		tmp = t_1;
	elseif (a <= 2.2e-181)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 8.5e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - (x * (y / a));
	tmp = 0.0;
	if (a <= -0.00175)
		tmp = t_2;
	elseif (a <= -2.7e-226)
		tmp = t_1;
	elseif (a <= 2.2e-181)
		tmp = (y * (x - t)) / z;
	elseif (a <= 8.5e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00175], t$95$2, If[LessEqual[a, -2.7e-226], t$95$1, If[LessEqual[a, 2.2e-181], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 8.5e+67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.00175000000000000004 or 8.50000000000000038e67 < a

   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* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in z around 0 61.9%

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

   6. Taylor expanded in t around 0 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

      3. associate-/l* 65.4%

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

   8. Simplified 65.4%

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

   if -0.00175000000000000004 < a < -2.70000000000000014e-226 or 2.19999999999999997e-181 < a < 8.50000000000000038e67

   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* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in x around 0 57.2%

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

      1. associate-/l* 71.4%

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

   7. Simplified 71.4%

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

   if -2.70000000000000014e-226 < a < 2.19999999999999997e-181

   1. Initial program 77.0%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in z around inf 90.1%

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

      1. associate--l+ 90.1%

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

      2. associate-*r/ 90.1%

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

      3. associate-*r/ 90.1%

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

      4. mul-1-neg 90.1%

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

      5. div-sub 90.1%

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

      6. mul-1-neg 90.1%

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

      7. distribute-lft-out-- 90.1%

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

      8. associate-*r/ 90.1%

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

      9. mul-1-neg 90.1%

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

      10. unsub-neg 90.1%

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

      11. distribute-rgt-out-- 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in y around -inf 69.2%

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

      1. associate-*r/ 69.2%

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

      2. mul-1-neg 69.2%

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

   10. Simplified 69.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00175:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-181}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -0.0023:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (- x (* x (/ y a)))))
   (if (<= a -0.0023)
     t_2
     (if (<= a -6.8e-227)
       t_1
       (if (<= a 4.1e-181)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.45e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (a <= -0.0023) {
		tmp = t_2;
	} else if (a <= -6.8e-227) {
		tmp = t_1;
	} else if (a <= 4.1e-181) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.45e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x - (x * (y / a))
    if (a <= (-0.0023d0)) then
        tmp = t_2
    else if (a <= (-6.8d-227)) then
        tmp = t_1
    else if (a <= 4.1d-181) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.45d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (a <= -0.0023) {
		tmp = t_2;
	} else if (a <= -6.8e-227) {
		tmp = t_1;
	} else if (a <= 4.1e-181) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.45e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x - (x * (y / a))
	tmp = 0
	if a <= -0.0023:
		tmp = t_2
	elif a <= -6.8e-227:
		tmp = t_1
	elif a <= 4.1e-181:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.45e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (a <= -0.0023)
		tmp = t_2;
	elseif (a <= -6.8e-227)
		tmp = t_1;
	elseif (a <= 4.1e-181)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.45e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x - (x * (y / a));
	tmp = 0.0;
	if (a <= -0.0023)
		tmp = t_2;
	elseif (a <= -6.8e-227)
		tmp = t_1;
	elseif (a <= 4.1e-181)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.45e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0023], t$95$2, If[LessEqual[a, -6.8e-227], t$95$1, If[LessEqual[a, 4.1e-181], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.0023 or 1.45000000000000006e68 < a

   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* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in z around 0 61.9%

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

   6. Taylor expanded in t around 0 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

      3. associate-/l* 65.4%

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

   8. Simplified 65.4%

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

   if -0.0023 < a < -6.79999999999999958e-227 or 4.1000000000000001e-181 < a < 1.45000000000000006e68

   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* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in x around 0 57.2%

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

      1. associate-/l* 71.4%

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

   7. Simplified 71.4%

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

   if -6.79999999999999958e-227 < a < 4.1000000000000001e-181

   1. Initial program 77.0%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around inf 72.9%

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

      1. div-sub 72.9%

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

   7. Simplified 72.9%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0023:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -0.00032:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -0.00032)
     t_2
     (if (<= a -3.8e-226)
       t_1
       (if (<= a 6.5e-181)
         (* y (/ (- t x) (- a z)))
         (if (<= a 5.2e+59) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -0.00032) {
		tmp = t_2;
	} else if (a <= -3.8e-226) {
		tmp = t_1;
	} else if (a <= 6.5e-181) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.2e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-0.00032d0)) then
        tmp = t_2
    else if (a <= (-3.8d-226)) then
        tmp = t_1
    else if (a <= 6.5d-181) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 5.2d+59) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -0.00032) {
		tmp = t_2;
	} else if (a <= -3.8e-226) {
		tmp = t_1;
	} else if (a <= 6.5e-181) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.2e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -0.00032:
		tmp = t_2
	elif a <= -3.8e-226:
		tmp = t_1
	elif a <= 6.5e-181:
		tmp = y * ((t - x) / (a - z))
	elif a <= 5.2e+59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -0.00032)
		tmp = t_2;
	elseif (a <= -3.8e-226)
		tmp = t_1;
	elseif (a <= 6.5e-181)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 5.2e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -0.00032)
		tmp = t_2;
	elseif (a <= -3.8e-226)
		tmp = t_1;
	elseif (a <= 6.5e-181)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 5.2e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00032], t$95$2, If[LessEqual[a, -3.8e-226], t$95$1, If[LessEqual[a, 6.5e-181], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.20000000000000026e-4 or 5.19999999999999999e59 < a

   1. Initial program 70.4%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in z around 0 61.9%

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

      1. associate-/l* 71.8%

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

   7. Simplified 71.8%

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

   if -3.20000000000000026e-4 < a < -3.79999999999999981e-226 or 6.4999999999999997e-181 < a < 5.19999999999999999e59

   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* 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in x around 0 57.4%

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

      1. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

   if -3.79999999999999981e-226 < a < 6.4999999999999997e-181

   1. Initial program 77.0%

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

      1. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around inf 72.9%

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

      1. div-sub 72.9%

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

   7. Simplified 72.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00032:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-226}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-111}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- t x) a)))))
   (if (<= a -1.55e-59)
     t_1
     (if (<= a 1.25e-111)
       (+ t (* y (/ (- x t) z)))
       (if (<= a 4.7e+58)
         (* t (/ (- y z) (- a z)))
         (if (<= a 1.15e+82) (* y (/ (- t x) (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -1.55e-59) {
		tmp = t_1;
	} else if (a <= 1.25e-111) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 4.7e+58) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.15e+82) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((t - x) / a))
    if (a <= (-1.55d-59)) then
        tmp = t_1
    else if (a <= 1.25d-111) then
        tmp = t + (y * ((x - t) / z))
    else if (a <= 4.7d+58) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 1.15d+82) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -1.55e-59) {
		tmp = t_1;
	} else if (a <= 1.25e-111) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 4.7e+58) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.15e+82) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -1.55e-59:
		tmp = t_1
	elif a <= 1.25e-111:
		tmp = t + (y * ((x - t) / z))
	elif a <= 4.7e+58:
		tmp = t * ((y - z) / (a - z))
	elif a <= 1.15e+82:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -1.55e-59)
		tmp = t_1;
	elseif (a <= 1.25e-111)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (a <= 4.7e+58)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 1.15e+82)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -1.55e-59)
		tmp = t_1;
	elseif (a <= 1.25e-111)
		tmp = t + (y * ((x - t) / z));
	elseif (a <= 4.7e+58)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 1.15e+82)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e-59], t$95$1, If[LessEqual[a, 1.25e-111], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e+58], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+82], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.55e-59 or 1.14999999999999994e82 < a

   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* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in z around 0 62.1%

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

      1. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

   if -1.55e-59 < a < 1.2500000000000001e-111

   1. Initial program 68.7%

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

      1. associate-/l* 72.7%

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

   3. Simplified 72.7%

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

   5. Taylor expanded in z around inf 81.4%

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

      1. associate--l+ 81.4%

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

      2. associate-*r/ 81.4%

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

      3. associate-*r/ 81.4%

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

      4. mul-1-neg 81.4%

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

      5. div-sub 82.6%

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

      6. mul-1-neg 82.6%

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

      7. distribute-lft-out-- 82.6%

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

      8. associate-*r/ 82.6%

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

      9. mul-1-neg 82.6%

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

      10. unsub-neg 82.6%

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

      11. distribute-rgt-out-- 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in y around inf 81.5%

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

      1. associate-/l* 86.4%

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

   10. Simplified 86.4%

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

   if 1.2500000000000001e-111 < a < 4.69999999999999972e58

   1. Initial program 72.9%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around 0 51.9%

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

      1. associate-/l* 68.5%

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

   7. Simplified 68.5%

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

   if 4.69999999999999972e58 < a < 1.14999999999999994e82

   1. Initial program 72.0%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in y around inf 85.4%

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

      1. div-sub 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-111}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0012:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.0012)
   (- x (* x (/ y a)))
   (if (<= a -1.05e-110)
     (* y (/ (- t x) a))
     (if (<= a -3.8e-226)
       t
       (if (<= a 7e-112) (* x (/ (- y a) z)) (+ x (* t (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0012) {
		tmp = x - (x * (y / a));
	} else if (a <= -1.05e-110) {
		tmp = y * ((t - x) / a);
	} else if (a <= -3.8e-226) {
		tmp = t;
	} else if (a <= 7e-112) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.0012d0)) then
        tmp = x - (x * (y / a))
    else if (a <= (-1.05d-110)) then
        tmp = y * ((t - x) / a)
    else if (a <= (-3.8d-226)) then
        tmp = t
    else if (a <= 7d-112) then
        tmp = x * ((y - a) / z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0012) {
		tmp = x - (x * (y / a));
	} else if (a <= -1.05e-110) {
		tmp = y * ((t - x) / a);
	} else if (a <= -3.8e-226) {
		tmp = t;
	} else if (a <= 7e-112) {
		tmp = x * ((y - a) / z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.0012:
		tmp = x - (x * (y / a))
	elif a <= -1.05e-110:
		tmp = y * ((t - x) / a)
	elif a <= -3.8e-226:
		tmp = t
	elif a <= 7e-112:
		tmp = x * ((y - a) / z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.0012)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (a <= -1.05e-110)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= -3.8e-226)
		tmp = t;
	elseif (a <= 7e-112)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.0012)
		tmp = x - (x * (y / a));
	elseif (a <= -1.05e-110)
		tmp = y * ((t - x) / a);
	elseif (a <= -3.8e-226)
		tmp = t;
	elseif (a <= 7e-112)
		tmp = x * ((y - a) / z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.0012], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.05e-110], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-226], t, If[LessEqual[a, 7e-112], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -0.00119999999999999989

   1. Initial program 80.5%

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

      1. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in z around 0 69.9%

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

   6. Taylor expanded in t around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. unsub-neg 60.8%

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

      3. associate-/l* 65.7%

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

   8. Simplified 65.7%

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

   if -0.00119999999999999989 < a < -1.05000000000000001e-110

   1. Initial program 81.0%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around 0 54.0%

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

   6. Taylor expanded in y around inf 46.1%

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

   7. Taylor expanded in a around 0 50.1%

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

   if -1.05000000000000001e-110 < a < -3.79999999999999981e-226

   1. Initial program 50.1%

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

      1. associate-/l* 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in z around inf 61.5%

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

   if -3.79999999999999981e-226 < a < 6.99999999999999988e-112

   1. Initial program 74.2%

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

      1. associate-/l* 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in z around inf 88.4%

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

      1. associate--l+ 88.4%

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

      2. associate-*r/ 88.4%

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

      3. associate-*r/ 88.4%

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

      4. mul-1-neg 88.4%

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

      5. div-sub 88.6%

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

      6. mul-1-neg 88.6%

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

      7. distribute-lft-out-- 88.6%

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

      8. associate-*r/ 88.6%

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

      9. mul-1-neg 88.6%

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

      10. unsub-neg 88.6%

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

      11. distribute-rgt-out-- 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in t around 0 44.7%

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

      1. associate-/l* 46.3%

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

   10. Simplified 46.3%

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

   if 6.99999999999999988e-112 < a

   1. Initial program 65.0%

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

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around 0 52.5%

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

   6. Taylor expanded in t around inf 51.9%

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

      1. associate-/l* 53.0%

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

   8. Simplified 53.0%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0012:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00046:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-112}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.00046)
   (- x (* x (/ y a)))
   (if (<= a -6.6e-111)
     (* y (/ (- t x) a))
     (if (<= a -1.9e-226)
       t
       (if (<= a 3.3e-112) (/ (* y (- x t)) z) (+ x (* t (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00046) {
		tmp = x - (x * (y / a));
	} else if (a <= -6.6e-111) {
		tmp = y * ((t - x) / a);
	} else if (a <= -1.9e-226) {
		tmp = t;
	} else if (a <= 3.3e-112) {
		tmp = (y * (x - t)) / z;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.00046d0)) then
        tmp = x - (x * (y / a))
    else if (a <= (-6.6d-111)) then
        tmp = y * ((t - x) / a)
    else if (a <= (-1.9d-226)) then
        tmp = t
    else if (a <= 3.3d-112) then
        tmp = (y * (x - t)) / z
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00046) {
		tmp = x - (x * (y / a));
	} else if (a <= -6.6e-111) {
		tmp = y * ((t - x) / a);
	} else if (a <= -1.9e-226) {
		tmp = t;
	} else if (a <= 3.3e-112) {
		tmp = (y * (x - t)) / z;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.00046:
		tmp = x - (x * (y / a))
	elif a <= -6.6e-111:
		tmp = y * ((t - x) / a)
	elif a <= -1.9e-226:
		tmp = t
	elif a <= 3.3e-112:
		tmp = (y * (x - t)) / z
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.00046)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (a <= -6.6e-111)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= -1.9e-226)
		tmp = t;
	elseif (a <= 3.3e-112)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.00046)
		tmp = x - (x * (y / a));
	elseif (a <= -6.6e-111)
		tmp = y * ((t - x) / a);
	elseif (a <= -1.9e-226)
		tmp = t;
	elseif (a <= 3.3e-112)
		tmp = (y * (x - t)) / z;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.00046], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.6e-111], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9e-226], t, If[LessEqual[a, 3.3e-112], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.6000000000000001e-4

   1. Initial program 80.5%

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

      1. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in z around 0 69.9%

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

   6. Taylor expanded in t around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. unsub-neg 60.8%

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

      3. associate-/l* 65.7%

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

   8. Simplified 65.7%

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

   if -4.6000000000000001e-4 < a < -6.6e-111

   1. Initial program 81.0%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around 0 54.0%

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

   6. Taylor expanded in y around inf 46.1%

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

   7. Taylor expanded in a around 0 50.1%

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

   if -6.6e-111 < a < -1.89999999999999991e-226

   1. Initial program 50.1%

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

      1. associate-/l* 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in z around inf 61.5%

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

   if -1.89999999999999991e-226 < a < 3.3000000000000001e-112

   1. Initial program 74.2%

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

      1. associate-/l* 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in z around inf 88.4%

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

      1. associate--l+ 88.4%

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

      2. associate-*r/ 88.4%

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

      3. associate-*r/ 88.4%

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

      4. mul-1-neg 88.4%

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

      5. div-sub 88.6%

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

      6. mul-1-neg 88.6%

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

      7. distribute-lft-out-- 88.6%

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

      8. associate-*r/ 88.6%

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

      9. mul-1-neg 88.6%

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

      10. unsub-neg 88.6%

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

      11. distribute-rgt-out-- 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in y around -inf 62.4%

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

      1. associate-*r/ 62.4%

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

      2. mul-1-neg 62.4%

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

   10. Simplified 62.4%

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

   if 3.3000000000000001e-112 < a

   1. Initial program 65.0%

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

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around 0 52.5%

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

   6. Taylor expanded in t around inf 51.9%

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

      1. associate-/l* 53.0%

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

   8. Simplified 53.0%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00046:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-112}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 88.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+158} \lor \neg \left(z \leq 1.45 \cdot 10^{+214}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\left(y - a\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e+158) (not (<= z 1.45e+214)))
   (+ t (* (- t x) (* (- y a) (/ -1.0 z))))
   (+ x (/ -1.0 (/ (/ (- a z) (- y z)) (- x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+158) || !(z <= 1.45e+214)) {
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	} else {
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.8d+158)) .or. (.not. (z <= 1.45d+214))) then
        tmp = t + ((t - x) * ((y - a) * ((-1.0d0) / z)))
    else
        tmp = x + ((-1.0d0) / (((a - z) / (y - z)) / (x - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+158) || !(z <= 1.45e+214)) {
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	} else {
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e+158) or not (z <= 1.45e+214):
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)))
	else:
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e+158) || !(z <= 1.45e+214))
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(y - a) * Float64(-1.0 / z))));
	else
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(a - z) / Float64(y - z)) / Float64(x - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.8e+158) || ~((z <= 1.45e+214)))
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	else
		tmp = x + (-1.0 / (((a - z) / (y - z)) / (x - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e+158], N[Not[LessEqual[z, 1.45e+214]], $MachinePrecision]], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 / N[(N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7999999999999998e158 or 1.45e214 < z

   1. Initial program 29.8%

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

      1. associate-/l* 47.0%

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

   3. Simplified 47.0%

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

   5. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. associate-*r/ 67.3%

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

      3. associate-*r/ 67.3%

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

      4. mul-1-neg 67.3%

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

      5. div-sub 67.3%

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

      6. mul-1-neg 67.3%

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

      7. distribute-lft-out-- 67.3%

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

      8. associate-*r/ 67.3%

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

      9. mul-1-neg 67.3%

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

      10. unsub-neg 67.3%

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

      11. distribute-rgt-out-- 67.8%

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

   7. Simplified 67.8%

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

      1. div-inv 67.7%

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

   9. Applied egg-rr 67.7%

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

       1. associate-*l* 93.6%

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

   11. Simplified 93.6%

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

   if -6.7999999999999998e158 < z < 1.45e214

   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* 91.2%

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

   3. Simplified 91.2%

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

      1. associate-*r/ 80.7%

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

      2. clear-num 80.6%

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

      3. associate-/r* 93.0%

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

   6. Applied egg-rr 93.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+158} \lor \neg \left(z \leq 1.45 \cdot 10^{+214}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\left(y - a\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{a - z}{y - z}}{x - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+177} \lor \neg \left(z \leq 1.95 \cdot 10^{+214}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\left(y - a\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z - a}{x - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+177) (not (<= z 1.95e+214)))
   (+ t (* (- t x) (* (- y a) (/ -1.0 z))))
   (+ x (/ (- y z) (/ (- z a) (- x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+177) || !(z <= 1.95e+214)) {
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	} else {
		tmp = x + ((y - z) / ((z - a) / (x - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4d+177)) .or. (.not. (z <= 1.95d+214))) then
        tmp = t + ((t - x) * ((y - a) * ((-1.0d0) / z)))
    else
        tmp = x + ((y - z) / ((z - a) / (x - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+177) || !(z <= 1.95e+214)) {
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	} else {
		tmp = x + ((y - z) / ((z - a) / (x - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+177) or not (z <= 1.95e+214):
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)))
	else:
		tmp = x + ((y - z) / ((z - a) / (x - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+177) || !(z <= 1.95e+214))
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(y - a) * Float64(-1.0 / z))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(z - a) / Float64(x - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+177) || ~((z <= 1.95e+214)))
		tmp = t + ((t - x) * ((y - a) * (-1.0 / z)));
	else
		tmp = x + ((y - z) / ((z - a) / (x - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+177], N[Not[LessEqual[z, 1.95e+214]], $MachinePrecision]], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e177 or 1.95000000000000007e214 < z

   1. Initial program 27.3%

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

      1. associate-/l* 43.7%

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

   3. Simplified 43.7%

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

   5. Taylor expanded in z around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. associate-*r/ 65.3%

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

      3. associate-*r/ 65.3%

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

      4. mul-1-neg 65.3%

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

      5. div-sub 65.3%

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

      6. mul-1-neg 65.3%

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

      7. distribute-lft-out-- 65.3%

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

      8. associate-*r/ 65.3%

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

      9. mul-1-neg 65.3%

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

      10. unsub-neg 65.3%

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

      11. distribute-rgt-out-- 65.7%

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

   7. Simplified 65.7%

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

      1. div-inv 65.7%

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

   9. Applied egg-rr 65.7%

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

       1. associate-*l* 93.2%

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

   11. Simplified 93.2%

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

   if -4e177 < z < 1.95000000000000007e214

   1. Initial program 80.5%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

      1. clear-num 91.0%

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

      2. un-div-inv 91.5%

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

   6. Applied egg-rr 91.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+177} \lor \neg \left(z \leq 1.95 \cdot 10^{+214}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \left(\left(y - a\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z - a}{x - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+181}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+204}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+181)
   (+ t (* y (/ (- x t) z)))
   (if (<= z 2.06e+204)
     (- x (* (- y z) (/ (- t x) (- z a))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+181) {
		tmp = t + (y * ((x - t) / z));
	} else if (z <= 2.06e+204) {
		tmp = x - ((y - z) * ((t - x) / (z - a)));
	} 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) :: tmp
    if (z <= (-3.1d+181)) then
        tmp = t + (y * ((x - t) / z))
    else if (z <= 2.06d+204) then
        tmp = x - ((y - z) * ((t - x) / (z - a)))
    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 tmp;
	if (z <= -3.1e+181) {
		tmp = t + (y * ((x - t) / z));
	} else if (z <= 2.06e+204) {
		tmp = x - ((y - z) * ((t - x) / (z - a)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+181:
		tmp = t + (y * ((x - t) / z))
	elif z <= 2.06e+204:
		tmp = x - ((y - z) * ((t - x) / (z - a)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+181)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (z <= 2.06e+204)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(z - a))));
	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)
	tmp = 0.0;
	if (z <= -3.1e+181)
		tmp = t + (y * ((x - t) / z));
	elseif (z <= 2.06e+204)
		tmp = x - ((y - z) * ((t - x) / (z - a)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+181], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.06e+204], N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $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 3 regimes

2. if z < -3.09999999999999989e181

   1. Initial program 22.4%

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

      1. associate-/l* 45.8%

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

   3. Simplified 45.8%

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

   5. Taylor expanded in z around inf 55.2%

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

      1. associate--l+ 55.2%

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

      2. associate-*r/ 55.2%

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

      3. associate-*r/ 55.2%

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

      4. mul-1-neg 55.2%

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

      5. div-sub 55.2%

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

      6. mul-1-neg 55.2%

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

      7. distribute-lft-out-- 55.2%

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

      8. associate-*r/ 55.2%

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

      9. mul-1-neg 55.2%

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

      10. unsub-neg 55.2%

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

      11. distribute-rgt-out-- 55.4%

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

   7. Simplified 55.4%

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

   8. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 85.0%

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

   10. Simplified 85.0%

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

   if -3.09999999999999989e181 < z < 2.05999999999999996e204

   1. Initial program 80.1%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   if 2.05999999999999996e204 < z

   1. Initial program 42.7%

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

      1. associate-/l* 39.4%

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

   3. Simplified 39.4%

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

   5. Taylor expanded in z around inf 91.8%

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

      1. associate--l+ 91.8%

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

      2. associate-*r/ 91.8%

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

      3. associate-*r/ 91.8%

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

      4. mul-1-neg 91.8%

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

      5. div-sub 91.8%

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

      6. mul-1-neg 91.8%

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

      7. distribute-lft-out-- 91.8%

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

      8. associate-*r/ 91.8%

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

      9. mul-1-neg 91.8%

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

      10. unsub-neg 91.8%

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

      11. distribute-rgt-out-- 92.2%

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

   7. Simplified 92.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+181}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+204}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+177}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+200}:\\ \;\;\;\;x + \frac{y - z}{\frac{z - a}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+177)
   (+ t (* y (/ (- x t) z)))
   (if (<= z 1.08e+200)
     (+ x (/ (- y z) (/ (- z a) (- x t))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+177) {
		tmp = t + (y * ((x - t) / z));
	} else if (z <= 1.08e+200) {
		tmp = x + ((y - z) / ((z - a) / (x - t)));
	} 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) :: tmp
    if (z <= (-2.8d+177)) then
        tmp = t + (y * ((x - t) / z))
    else if (z <= 1.08d+200) then
        tmp = x + ((y - z) / ((z - a) / (x - t)))
    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 tmp;
	if (z <= -2.8e+177) {
		tmp = t + (y * ((x - t) / z));
	} else if (z <= 1.08e+200) {
		tmp = x + ((y - z) / ((z - a) / (x - t)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+177:
		tmp = t + (y * ((x - t) / z))
	elif z <= 1.08e+200:
		tmp = x + ((y - z) / ((z - a) / (x - t)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+177)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (z <= 1.08e+200)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(z - a) / Float64(x - t))));
	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)
	tmp = 0.0;
	if (z <= -2.8e+177)
		tmp = t + (y * ((x - t) / z));
	elseif (z <= 1.08e+200)
		tmp = x + ((y - z) / ((z - a) / (x - t)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+177], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e+200], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(x - t), $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 3 regimes

2. if z < -2.80000000000000002e177

   1. Initial program 22.1%

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

      1. associate-/l* 47.4%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in z around inf 53.5%

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

      1. associate--l+ 53.5%

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

      2. associate-*r/ 53.5%

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

      3. associate-*r/ 53.5%

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

      4. mul-1-neg 53.5%

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

      5. div-sub 53.5%

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

      6. mul-1-neg 53.5%

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

      7. distribute-lft-out-- 53.5%

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

      8. associate-*r/ 53.5%

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

      9. mul-1-neg 53.5%

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

      10. unsub-neg 53.5%

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

      11. distribute-rgt-out-- 54.0%

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

   7. Simplified 54.0%

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

   8. Taylor expanded in y around inf 56.8%

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

      1. associate-/l* 85.4%

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

   10. Simplified 85.4%

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

   if -2.80000000000000002e177 < z < 1.07999999999999996e200

   1. Initial program 80.5%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. clear-num 91.0%

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

      2. un-div-inv 91.4%

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

   6. Applied egg-rr 91.4%

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

   if 1.07999999999999996e200 < z

   1. Initial program 42.7%

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

      1. associate-/l* 39.4%

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

   3. Simplified 39.4%

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

   5. Taylor expanded in z around inf 91.8%

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

      1. associate--l+ 91.8%

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

      2. associate-*r/ 91.8%

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

      3. associate-*r/ 91.8%

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

      4. mul-1-neg 91.8%

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

      5. div-sub 91.8%

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

      6. mul-1-neg 91.8%

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

      7. distribute-lft-out-- 91.8%

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

      8. associate-*r/ 91.8%

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

      9. mul-1-neg 91.8%

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

      10. unsub-neg 91.8%

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

      11. distribute-rgt-out-- 92.2%

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

   7. Simplified 92.2%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+177}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+200}:\\ \;\;\;\;x + \frac{y - z}{\frac{z - a}{x - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+130) t (if (<= z 1.62e+111) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+130) {
		tmp = t;
	} else if (z <= 1.62e+111) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+130)) then
        tmp = t
    else if (z <= 1.62d+111) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+130) {
		tmp = t;
	} else if (z <= 1.62e+111) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+130:
		tmp = t
	elif z <= 1.62e+111:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+130)
		tmp = t;
	elseif (z <= 1.62e+111)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+130)
		tmp = t;
	elseif (z <= 1.62e+111)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+130], t, If[LessEqual[z, 1.62e+111], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999965e130 or 1.61999999999999999e111 < z

   1. Initial program 39.5%

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

      1. associate-/l* 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in z around inf 50.5%

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

   if -8.49999999999999965e130 < z < 1.61999999999999999e111

   1. Initial program 84.2%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 61.8%

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

   6. Taylor expanded in t around inf 54.2%

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

      1. associate-/l* 54.2%

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

   8. Simplified 54.2%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+130}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+111}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0028:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.0028) x (if (<= a 9.5e+67) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0028) {
		tmp = x;
	} else if (a <= 9.5e+67) {
		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 <= (-0.0028d0)) then
        tmp = x
    else if (a <= 9.5d+67) 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 <= -0.0028) {
		tmp = x;
	} else if (a <= 9.5e+67) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.0028:
		tmp = x
	elif a <= 9.5e+67:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.0028)
		tmp = x;
	elseif (a <= 9.5e+67)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.0028)
		tmp = x;
	elseif (a <= 9.5e+67)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.0028], x, If[LessEqual[a, 9.5e+67], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -0.00279999999999999997 or 9.5000000000000002e67 < a

   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* 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in a around inf 50.5%

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

   if -0.00279999999999999997 < a < 9.5000000000000002e67

   1. Initial program 71.6%

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

      1. associate-/l* 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in z around inf 32.3%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0028:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+67}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 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 70.6%

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

   1. associate-/l* 82.4%

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

3. Simplified 82.4%

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

5. Taylor expanded in z around inf 21.8%

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

6. Final simplification 21.8%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 83.9% 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 2024115 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (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))))