Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 95.6%

Time: 16.0s

Alternatives: 22

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.2% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-306}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- t x) (- z a))))))
   (if (<= t_1 -1e-306)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (fma (- t x) (/ (- y z) (- a z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((t - x) / (z - a)));
	double tmp;
	if (t_1 <= -1e-306) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if (t_1 <= -1e-306)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-306], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $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 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000003e-306

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*l/ 82.9%

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

      3. associate-*r/ 93.4%

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

      4. clear-num 93.3%

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

      5. un-div-inv 94.0%

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

   4. Applied egg-rr 94.0%

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

   if -1.00000000000000003e-306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 78.3%

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

      1. associate--l+ 78.3%

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

      2. distribute-lft-out-- 78.3%

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

      3. div-sub 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. div-sub 78.3%

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

      7. associate-/l* 85.4%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

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

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. remove-double-neg 85.5%

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

      3. unsub-neg 85.5%

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

      4. *-commutative 85.5%

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

      5. associate-*l/ 76.2%

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

      6. associate-/l* 94.6%

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

      7. fma-neg 94.6%

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

      8. remove-double-neg 94.6%

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

   3. Simplified 94.6%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq -1 \cdot 10^{-306}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 46.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-95}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-247}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -2.9e+77)
     x
     (if (<= a -1.7e-15)
       (* t (/ (- y z) a))
       (if (<= a -6.2e-17)
         (/ (* x y) z)
         (if (<= a -1.55e-95)
           t
           (if (<= a 8.2e-280)
             t_1
             (if (<= a 8e-247)
               (* x (/ y z))
               (if (<= a 6e-47)
                 t_1
                 (if (<= a 1.65e+78)
                   (* t (/ y (- a z)))
                   (if (<= a 1.35e+117) t_1 x)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.9e+77) {
		tmp = x;
	} else if (a <= -1.7e-15) {
		tmp = t * ((y - z) / a);
	} else if (a <= -6.2e-17) {
		tmp = (x * y) / z;
	} else if (a <= -1.55e-95) {
		tmp = t;
	} else if (a <= 8.2e-280) {
		tmp = t_1;
	} else if (a <= 8e-247) {
		tmp = x * (y / z);
	} else if (a <= 6e-47) {
		tmp = t_1;
	} else if (a <= 1.65e+78) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.35e+117) {
		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 = t * (1.0d0 - (y / z))
    if (a <= (-2.9d+77)) then
        tmp = x
    else if (a <= (-1.7d-15)) then
        tmp = t * ((y - z) / a)
    else if (a <= (-6.2d-17)) then
        tmp = (x * y) / z
    else if (a <= (-1.55d-95)) then
        tmp = t
    else if (a <= 8.2d-280) then
        tmp = t_1
    else if (a <= 8d-247) then
        tmp = x * (y / z)
    else if (a <= 6d-47) then
        tmp = t_1
    else if (a <= 1.65d+78) then
        tmp = t * (y / (a - z))
    else if (a <= 1.35d+117) 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 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -2.9e+77) {
		tmp = x;
	} else if (a <= -1.7e-15) {
		tmp = t * ((y - z) / a);
	} else if (a <= -6.2e-17) {
		tmp = (x * y) / z;
	} else if (a <= -1.55e-95) {
		tmp = t;
	} else if (a <= 8.2e-280) {
		tmp = t_1;
	} else if (a <= 8e-247) {
		tmp = x * (y / z);
	} else if (a <= 6e-47) {
		tmp = t_1;
	} else if (a <= 1.65e+78) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.35e+117) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -2.9e+77:
		tmp = x
	elif a <= -1.7e-15:
		tmp = t * ((y - z) / a)
	elif a <= -6.2e-17:
		tmp = (x * y) / z
	elif a <= -1.55e-95:
		tmp = t
	elif a <= 8.2e-280:
		tmp = t_1
	elif a <= 8e-247:
		tmp = x * (y / z)
	elif a <= 6e-47:
		tmp = t_1
	elif a <= 1.65e+78:
		tmp = t * (y / (a - z))
	elif a <= 1.35e+117:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -2.9e+77)
		tmp = x;
	elseif (a <= -1.7e-15)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (a <= -6.2e-17)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= -1.55e-95)
		tmp = t;
	elseif (a <= 8.2e-280)
		tmp = t_1;
	elseif (a <= 8e-247)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 6e-47)
		tmp = t_1;
	elseif (a <= 1.65e+78)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 1.35e+117)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -2.9e+77)
		tmp = x;
	elseif (a <= -1.7e-15)
		tmp = t * ((y - z) / a);
	elseif (a <= -6.2e-17)
		tmp = (x * y) / z;
	elseif (a <= -1.55e-95)
		tmp = t;
	elseif (a <= 8.2e-280)
		tmp = t_1;
	elseif (a <= 8e-247)
		tmp = x * (y / z);
	elseif (a <= 6e-47)
		tmp = t_1;
	elseif (a <= 1.65e+78)
		tmp = t * (y / (a - z));
	elseif (a <= 1.35e+117)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+77], x, If[LessEqual[a, -1.7e-15], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e-17], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, -1.55e-95], t, If[LessEqual[a, 8.2e-280], t$95$1, If[LessEqual[a, 8e-247], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-47], t$95$1, If[LessEqual[a, 1.65e+78], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+117], t$95$1, x]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -2.9000000000000002e77 or 1.3500000000000001e117 < a

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 53.8%

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

   if -2.9000000000000002e77 < a < -1.7e-15

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 44.5%

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

   4. Taylor expanded in a around inf 44.5%

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

      1. associate-/l* 51.8%

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

   6. Simplified 51.8%

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

   if -1.7e-15 < a < -6.1999999999999997e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in a around 0 52.8%

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

   if -6.1999999999999997e-17 < a < -1.54999999999999996e-95

   1. Initial program 75.3%

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

   3. Taylor expanded in z around inf 36.1%

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

   if -1.54999999999999996e-95 < a < 8.2000000000000003e-280 or 8.0000000000000002e-247 < a < 6.00000000000000033e-47 or 1.65e78 < a < 1.3500000000000001e117

   1. Initial program 66.0%

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

   3. Taylor expanded in a around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. unsub-neg 49.2%

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

      3. associate-/l* 60.7%

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

      4. div-sub 60.7%

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

      5. sub-neg 60.7%

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

      6. *-inverses 60.7%

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

      7. metadata-eval 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in t around inf 57.9%

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

   if 8.2000000000000003e-280 < a < 8.0000000000000002e-247

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. unsub-neg 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in a around 0 84.8%

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

   if 6.00000000000000033e-47 < a < 1.65e78

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. div-sub 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around inf 36.4%

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

      1. associate-/l* 40.2%

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

   8. Simplified 40.2%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a - z}} \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-306} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -1e-306) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((t - x) / (z - a)))
    if ((t_1 <= (-1d-306)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((t - x) / (z - a)))
	tmp = 0
	if (t_1 <= -1e-306) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if ((t_1 <= -1e-306) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((t - x) / (z - a)));
	tmp = 0.0;
	if ((t_1 <= -1e-306) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-306], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000003e-306 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*l/ 79.5%

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

      3. associate-*r/ 94.0%

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

      4. clear-num 94.0%

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

      5. un-div-inv 94.3%

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

   4. Applied egg-rr 94.3%

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

   if -1.00000000000000003e-306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 78.3%

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

      1. associate--l+ 78.3%

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

      2. distribute-lft-out-- 78.3%

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

      3. div-sub 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. div-sub 78.3%

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

      7. associate-/l* 85.4%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq -1 \cdot 10^{-306} \lor \neg \left(x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-306} \lor \neg \left(t\_1 \leq 10^{-230}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- t x) (- z a))))))
   (if (or (<= t_1 -1e-306) (not (<= t_1 1e-230)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 1e-230)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((t - x) / (z - a)))
    if ((t_1 <= (-1d-306)) .or. (.not. (t_1 <= 1d-230))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((t - x) / (z - a)));
	double tmp;
	if ((t_1 <= -1e-306) || !(t_1 <= 1e-230)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((t - x) / (z - a)))
	tmp = 0
	if (t_1 <= -1e-306) or not (t_1 <= 1e-230):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(z - a))))
	tmp = 0.0
	if ((t_1 <= -1e-306) || !(t_1 <= 1e-230))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((t - x) / (z - a)));
	tmp = 0.0;
	if ((t_1 <= -1e-306) || ~((t_1 <= 1e-230)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-306], N[Not[LessEqual[t$95$1, 1e-230]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000003e-306 or 1.00000000000000005e-230 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.3%

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

   if -1.00000000000000003e-306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000005e-230

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. associate--l+ 77.2%

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

      2. distribute-lft-out-- 77.2%

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

      3. div-sub 77.3%

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

      4. mul-1-neg 77.3%

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

      5. unsub-neg 77.3%

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

      6. div-sub 77.2%

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

      7. associate-/l* 83.6%

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

      8. associate-/l* 96.5%

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

      9. distribute-rgt-out-- 96.5%

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

   5. Simplified 96.5%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq -1 \cdot 10^{-306} \lor \neg \left(x - \left(y - z\right) \cdot \frac{t - x}{z - a} \leq 10^{-230}\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{t - x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -6.8e+118)
     x
     (if (<= a 2e-280)
       t_1
       (if (<= a 6.5e-247)
         (* x (/ y z))
         (if (<= a 2.8e-47)
           t_1
           (if (<= a 1.1e+79)
             (* t (/ y (- a z)))
             (if (<= a 3.9e+115) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -6.8e+118) {
		tmp = x;
	} else if (a <= 2e-280) {
		tmp = t_1;
	} else if (a <= 6.5e-247) {
		tmp = x * (y / z);
	} else if (a <= 2.8e-47) {
		tmp = t_1;
	} else if (a <= 1.1e+79) {
		tmp = t * (y / (a - z));
	} else if (a <= 3.9e+115) {
		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 = t * (1.0d0 - (y / z))
    if (a <= (-6.8d+118)) then
        tmp = x
    else if (a <= 2d-280) then
        tmp = t_1
    else if (a <= 6.5d-247) then
        tmp = x * (y / z)
    else if (a <= 2.8d-47) then
        tmp = t_1
    else if (a <= 1.1d+79) then
        tmp = t * (y / (a - z))
    else if (a <= 3.9d+115) 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 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -6.8e+118) {
		tmp = x;
	} else if (a <= 2e-280) {
		tmp = t_1;
	} else if (a <= 6.5e-247) {
		tmp = x * (y / z);
	} else if (a <= 2.8e-47) {
		tmp = t_1;
	} else if (a <= 1.1e+79) {
		tmp = t * (y / (a - z));
	} else if (a <= 3.9e+115) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -6.8e+118:
		tmp = x
	elif a <= 2e-280:
		tmp = t_1
	elif a <= 6.5e-247:
		tmp = x * (y / z)
	elif a <= 2.8e-47:
		tmp = t_1
	elif a <= 1.1e+79:
		tmp = t * (y / (a - z))
	elif a <= 3.9e+115:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -6.8e+118)
		tmp = x;
	elseif (a <= 2e-280)
		tmp = t_1;
	elseif (a <= 6.5e-247)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.8e-47)
		tmp = t_1;
	elseif (a <= 1.1e+79)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 3.9e+115)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -6.8e+118)
		tmp = x;
	elseif (a <= 2e-280)
		tmp = t_1;
	elseif (a <= 6.5e-247)
		tmp = x * (y / z);
	elseif (a <= 2.8e-47)
		tmp = t_1;
	elseif (a <= 1.1e+79)
		tmp = t * (y / (a - z));
	elseif (a <= 3.9e+115)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e+118], x, If[LessEqual[a, 2e-280], t$95$1, If[LessEqual[a, 6.5e-247], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-47], t$95$1, If[LessEqual[a, 1.1e+79], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+115], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.79999999999999973e118 or 3.90000000000000006e115 < a

   1. Initial program 87.5%

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

   3. Taylor expanded in a around inf 56.0%

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

   if -6.79999999999999973e118 < a < 1.9999999999999999e-280 or 6.4999999999999996e-247 < a < 2.79999999999999993e-47 or 1.0999999999999999e79 < a < 3.90000000000000006e115

   1. Initial program 72.3%

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

   3. Taylor expanded in a around 0 42.6%

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

      1. mul-1-neg 42.6%

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

      2. unsub-neg 42.6%

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

      3. associate-/l* 54.0%

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

      4. div-sub 54.0%

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

      5. sub-neg 54.0%

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

      6. *-inverses 54.0%

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

      7. metadata-eval 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in t around inf 50.3%

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

   if 1.9999999999999999e-280 < a < 6.4999999999999996e-247

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. unsub-neg 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in a around 0 84.8%

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

   if 2.79999999999999993e-47 < a < 1.0999999999999999e79

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. div-sub 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around inf 36.4%

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

      1. associate-/l* 40.2%

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

   8. Simplified 40.2%

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

Alternative 6: 46.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+116}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-237}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.65e+116)
     x
     (if (<= a 4.6e-280)
       t_1
       (if (<= a 2.7e-237)
         (* x (/ y z))
         (if (<= a 7.6e-47)
           t_1
           (if (<= a 2.8e+74) (* t (/ y a)) (if (<= a 4.8e+115) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.65e+116) {
		tmp = x;
	} else if (a <= 4.6e-280) {
		tmp = t_1;
	} else if (a <= 2.7e-237) {
		tmp = x * (y / z);
	} else if (a <= 7.6e-47) {
		tmp = t_1;
	} else if (a <= 2.8e+74) {
		tmp = t * (y / a);
	} else if (a <= 4.8e+115) {
		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 = t * (1.0d0 - (y / z))
    if (a <= (-1.65d+116)) then
        tmp = x
    else if (a <= 4.6d-280) then
        tmp = t_1
    else if (a <= 2.7d-237) then
        tmp = x * (y / z)
    else if (a <= 7.6d-47) then
        tmp = t_1
    else if (a <= 2.8d+74) then
        tmp = t * (y / a)
    else if (a <= 4.8d+115) 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 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.65e+116) {
		tmp = x;
	} else if (a <= 4.6e-280) {
		tmp = t_1;
	} else if (a <= 2.7e-237) {
		tmp = x * (y / z);
	} else if (a <= 7.6e-47) {
		tmp = t_1;
	} else if (a <= 2.8e+74) {
		tmp = t * (y / a);
	} else if (a <= 4.8e+115) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.65e+116:
		tmp = x
	elif a <= 4.6e-280:
		tmp = t_1
	elif a <= 2.7e-237:
		tmp = x * (y / z)
	elif a <= 7.6e-47:
		tmp = t_1
	elif a <= 2.8e+74:
		tmp = t * (y / a)
	elif a <= 4.8e+115:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -1.65e+116)
		tmp = x;
	elseif (a <= 4.6e-280)
		tmp = t_1;
	elseif (a <= 2.7e-237)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 7.6e-47)
		tmp = t_1;
	elseif (a <= 2.8e+74)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= 4.8e+115)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -1.65e+116)
		tmp = x;
	elseif (a <= 4.6e-280)
		tmp = t_1;
	elseif (a <= 2.7e-237)
		tmp = x * (y / z);
	elseif (a <= 7.6e-47)
		tmp = t_1;
	elseif (a <= 2.8e+74)
		tmp = t * (y / a);
	elseif (a <= 4.8e+115)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+116], x, If[LessEqual[a, 4.6e-280], t$95$1, If[LessEqual[a, 2.7e-237], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e-47], t$95$1, If[LessEqual[a, 2.8e+74], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+115], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.6499999999999999e116 or 4.8000000000000001e115 < a

   1. Initial program 87.5%

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

   3. Taylor expanded in a around inf 56.0%

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

   if -1.6499999999999999e116 < a < 4.5999999999999999e-280 or 2.69999999999999984e-237 < a < 7.60000000000000029e-47 or 2.80000000000000002e74 < a < 4.8000000000000001e115

   1. Initial program 72.3%

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

   3. Taylor expanded in a around 0 42.6%

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

      1. mul-1-neg 42.6%

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

      2. unsub-neg 42.6%

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

      3. associate-/l* 54.0%

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

      4. div-sub 54.0%

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

      5. sub-neg 54.0%

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

      6. *-inverses 54.0%

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

      7. metadata-eval 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in t around inf 50.3%

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

   if 4.5999999999999999e-280 < a < 2.69999999999999984e-237

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. unsub-neg 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in a around 0 84.8%

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

   if 7.60000000000000029e-47 < a < 2.80000000000000002e74

   1. Initial program 81.6%

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

   3. Taylor expanded in x around 0 40.2%

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

   4. Taylor expanded in z around 0 34.0%

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

      1. associate-/l* 37.8%

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

   6. Simplified 37.8%

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

Alternative 7: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -0.061:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-276}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-245}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.12 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.02e+109)
   t
   (if (<= z -0.061)
     (* y (/ x z))
     (if (<= z -1.75e-66)
       (* t (/ y (- z)))
       (if (<= z -4.4e-276)
         x
         (if (<= z 1.66e-245) (* (/ y a) (- x)) (if (<= z 2.12e+99) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.02e+109) {
		tmp = t;
	} else if (z <= -0.061) {
		tmp = y * (x / z);
	} else if (z <= -1.75e-66) {
		tmp = t * (y / -z);
	} else if (z <= -4.4e-276) {
		tmp = x;
	} else if (z <= 1.66e-245) {
		tmp = (y / a) * -x;
	} else if (z <= 2.12e+99) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.02d+109)) then
        tmp = t
    else if (z <= (-0.061d0)) then
        tmp = y * (x / z)
    else if (z <= (-1.75d-66)) then
        tmp = t * (y / -z)
    else if (z <= (-4.4d-276)) then
        tmp = x
    else if (z <= 1.66d-245) then
        tmp = (y / a) * -x
    else if (z <= 2.12d+99) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.02e+109) {
		tmp = t;
	} else if (z <= -0.061) {
		tmp = y * (x / z);
	} else if (z <= -1.75e-66) {
		tmp = t * (y / -z);
	} else if (z <= -4.4e-276) {
		tmp = x;
	} else if (z <= 1.66e-245) {
		tmp = (y / a) * -x;
	} else if (z <= 2.12e+99) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.02e+109:
		tmp = t
	elif z <= -0.061:
		tmp = y * (x / z)
	elif z <= -1.75e-66:
		tmp = t * (y / -z)
	elif z <= -4.4e-276:
		tmp = x
	elif z <= 1.66e-245:
		tmp = (y / a) * -x
	elif z <= 2.12e+99:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.02e+109)
		tmp = t;
	elseif (z <= -0.061)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= -1.75e-66)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (z <= -4.4e-276)
		tmp = x;
	elseif (z <= 1.66e-245)
		tmp = Float64(Float64(y / a) * Float64(-x));
	elseif (z <= 2.12e+99)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.02e+109)
		tmp = t;
	elseif (z <= -0.061)
		tmp = y * (x / z);
	elseif (z <= -1.75e-66)
		tmp = t * (y / -z);
	elseif (z <= -4.4e-276)
		tmp = x;
	elseif (z <= 1.66e-245)
		tmp = (y / a) * -x;
	elseif (z <= 2.12e+99)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.02e+109], t, If[LessEqual[z, -0.061], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.75e-66], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-276], x, If[LessEqual[z, 1.66e-245], N[(N[(y / a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, 2.12e+99], x, t]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.01999999999999994e109 or 2.11999999999999999e99 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 55.9%

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

   if -1.01999999999999994e109 < z < -0.060999999999999999

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. div-sub 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in a around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. distribute-neg-frac2 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in t around 0 48.5%

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

   if -0.060999999999999999 < z < -1.75e-66

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 55.1%

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

      1. div-sub 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in a around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. distribute-neg-frac2 44.4%

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

   8. Simplified 44.4%

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

   9. Taylor expanded in t around inf 39.7%

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

       1. mul-1-neg 39.7%

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

       2. associate-/l* 44.7%

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

       3. distribute-rgt-neg-in 44.7%

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

       4. mul-1-neg 44.7%

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

       5. associate-*r/ 44.7%

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

       6. mul-1-neg 44.7%

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

   11. Simplified 44.7%

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

   if -1.75e-66 < z < -4.39999999999999961e-276 or 1.6599999999999999e-245 < z < 2.11999999999999999e99

   1. Initial program 90.5%

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

   3. Taylor expanded in a around inf 36.2%

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

   if -4.39999999999999961e-276 < z < 1.6599999999999999e-245

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in z around 0 73.6%

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

   7. Taylor expanded in y around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-/l* 52.9%

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

      3. distribute-rgt-neg-in 52.9%

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

      4. distribute-neg-frac2 52.9%

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

   9. Simplified 52.9%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -0.061:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-276}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-245}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.12 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -0.017:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-298}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+110)
   t
   (if (<= z -0.017)
     (* y (/ x z))
     (if (<= z -9e-65)
       (* t (/ y (- z)))
       (if (<= z -4.6e-279)
         x
         (if (<= z 3.25e-298) (/ t (/ a y)) (if (<= z 6.2e+98) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+110) {
		tmp = t;
	} else if (z <= -0.017) {
		tmp = y * (x / z);
	} else if (z <= -9e-65) {
		tmp = t * (y / -z);
	} else if (z <= -4.6e-279) {
		tmp = x;
	} else if (z <= 3.25e-298) {
		tmp = t / (a / y);
	} else if (z <= 6.2e+98) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.9d+110)) then
        tmp = t
    else if (z <= (-0.017d0)) then
        tmp = y * (x / z)
    else if (z <= (-9d-65)) then
        tmp = t * (y / -z)
    else if (z <= (-4.6d-279)) then
        tmp = x
    else if (z <= 3.25d-298) then
        tmp = t / (a / y)
    else if (z <= 6.2d+98) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+110) {
		tmp = t;
	} else if (z <= -0.017) {
		tmp = y * (x / z);
	} else if (z <= -9e-65) {
		tmp = t * (y / -z);
	} else if (z <= -4.6e-279) {
		tmp = x;
	} else if (z <= 3.25e-298) {
		tmp = t / (a / y);
	} else if (z <= 6.2e+98) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+110:
		tmp = t
	elif z <= -0.017:
		tmp = y * (x / z)
	elif z <= -9e-65:
		tmp = t * (y / -z)
	elif z <= -4.6e-279:
		tmp = x
	elif z <= 3.25e-298:
		tmp = t / (a / y)
	elif z <= 6.2e+98:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+110)
		tmp = t;
	elseif (z <= -0.017)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= -9e-65)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (z <= -4.6e-279)
		tmp = x;
	elseif (z <= 3.25e-298)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 6.2e+98)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+110)
		tmp = t;
	elseif (z <= -0.017)
		tmp = y * (x / z);
	elseif (z <= -9e-65)
		tmp = t * (y / -z);
	elseif (z <= -4.6e-279)
		tmp = x;
	elseif (z <= 3.25e-298)
		tmp = t / (a / y);
	elseif (z <= 6.2e+98)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+110], t, If[LessEqual[z, -0.017], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-65], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e-279], x, If[LessEqual[z, 3.25e-298], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+98], x, t]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.9e110 or 6.20000000000000038e98 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 55.9%

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

   if -2.9e110 < z < -0.017000000000000001

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. div-sub 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in a around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. distribute-neg-frac2 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in t around 0 48.5%

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

   if -0.017000000000000001 < z < -8.9999999999999995e-65

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 55.1%

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

      1. div-sub 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in a around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. distribute-neg-frac2 44.4%

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

   8. Simplified 44.4%

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

   9. Taylor expanded in t around inf 39.7%

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

       1. mul-1-neg 39.7%

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

       2. associate-/l* 44.7%

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

       3. distribute-rgt-neg-in 44.7%

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

       4. mul-1-neg 44.7%

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

       5. associate-*r/ 44.7%

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

       6. mul-1-neg 44.7%

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

   11. Simplified 44.7%

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

   if -8.9999999999999995e-65 < z < -4.5999999999999999e-279 or 3.2500000000000001e-298 < z < 6.20000000000000038e98

   1. Initial program 90.7%

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

   3. Taylor expanded in a around inf 35.8%

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

   if -4.5999999999999999e-279 < z < 3.2500000000000001e-298

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 64.8%

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

   4. Taylor expanded in z around 0 64.8%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

      1. clear-num 65.0%

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

      2. div-inv 65.1%

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

   8. Applied egg-rr 65.1%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -0.017:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-298}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -1.6e+109)
     t
     (if (<= z -5.6e-27)
       x
       (if (<= z -2.95e-64)
         t_1
         (if (<= z -3.6e-279)
           x
           (if (<= z 3.4e-294) t_1 (if (<= z 5.5e+98) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.6e+109) {
		tmp = t;
	} else if (z <= -5.6e-27) {
		tmp = x;
	} else if (z <= -2.95e-64) {
		tmp = t_1;
	} else if (z <= -3.6e-279) {
		tmp = x;
	} else if (z <= 3.4e-294) {
		tmp = t_1;
	} else if (z <= 5.5e+98) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-1.6d+109)) then
        tmp = t
    else if (z <= (-5.6d-27)) then
        tmp = x
    else if (z <= (-2.95d-64)) then
        tmp = t_1
    else if (z <= (-3.6d-279)) then
        tmp = x
    else if (z <= 3.4d-294) then
        tmp = t_1
    else if (z <= 5.5d+98) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -1.6e+109) {
		tmp = t;
	} else if (z <= -5.6e-27) {
		tmp = x;
	} else if (z <= -2.95e-64) {
		tmp = t_1;
	} else if (z <= -3.6e-279) {
		tmp = x;
	} else if (z <= 3.4e-294) {
		tmp = t_1;
	} else if (z <= 5.5e+98) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -1.6e+109:
		tmp = t
	elif z <= -5.6e-27:
		tmp = x
	elif z <= -2.95e-64:
		tmp = t_1
	elif z <= -3.6e-279:
		tmp = x
	elif z <= 3.4e-294:
		tmp = t_1
	elif z <= 5.5e+98:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -1.6e+109)
		tmp = t;
	elseif (z <= -5.6e-27)
		tmp = x;
	elseif (z <= -2.95e-64)
		tmp = t_1;
	elseif (z <= -3.6e-279)
		tmp = x;
	elseif (z <= 3.4e-294)
		tmp = t_1;
	elseif (z <= 5.5e+98)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -1.6e+109)
		tmp = t;
	elseif (z <= -5.6e-27)
		tmp = x;
	elseif (z <= -2.95e-64)
		tmp = t_1;
	elseif (z <= -3.6e-279)
		tmp = x;
	elseif (z <= 3.4e-294)
		tmp = t_1;
	elseif (z <= 5.5e+98)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+109], t, If[LessEqual[z, -5.6e-27], x, If[LessEqual[z, -2.95e-64], t$95$1, If[LessEqual[z, -3.6e-279], x, If[LessEqual[z, 3.4e-294], t$95$1, If[LessEqual[z, 5.5e+98], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e109 or 5.49999999999999946e98 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 55.9%

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

   if -1.6000000000000001e109 < z < -5.5999999999999999e-27 or -2.94999999999999997e-64 < z < -3.5999999999999997e-279 or 3.39999999999999981e-294 < z < 5.49999999999999946e98

   1. Initial program 87.5%

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

   3. Taylor expanded in a around inf 35.4%

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

   if -5.5999999999999999e-27 < z < -2.94999999999999997e-64 or -3.5999999999999997e-279 < z < 3.39999999999999981e-294

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 66.1%

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

   4. Taylor expanded in z around 0 53.9%

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

      1. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

Alternative 10: 54.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-234}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (+ x (* y (/ t a)))))
   (if (<= a -2.2e-66)
     t_2
     (if (<= a -5.4e-273)
       t_1
       (if (<= a 2.8e-234) (/ (* y (- x t)) z) (if (<= a 2.2e-42) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -2.2e-66) {
		tmp = t_2;
	} else if (a <= -5.4e-273) {
		tmp = t_1;
	} else if (a <= 2.8e-234) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 2.2e-42) {
		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 * (1.0d0 - (y / z))
    t_2 = x + (y * (t / a))
    if (a <= (-2.2d-66)) then
        tmp = t_2
    else if (a <= (-5.4d-273)) then
        tmp = t_1
    else if (a <= 2.8d-234) then
        tmp = (y * (x - t)) / z
    else if (a <= 2.2d-42) 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 * (1.0 - (y / z));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -2.2e-66) {
		tmp = t_2;
	} else if (a <= -5.4e-273) {
		tmp = t_1;
	} else if (a <= 2.8e-234) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 2.2e-42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (y * (t / a))
	tmp = 0
	if a <= -2.2e-66:
		tmp = t_2
	elif a <= -5.4e-273:
		tmp = t_1
	elif a <= 2.8e-234:
		tmp = (y * (x - t)) / z
	elif a <= 2.2e-42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -2.2e-66)
		tmp = t_2;
	elseif (a <= -5.4e-273)
		tmp = t_1;
	elseif (a <= 2.8e-234)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 2.2e-42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (y * (t / a));
	tmp = 0.0;
	if (a <= -2.2e-66)
		tmp = t_2;
	elseif (a <= -5.4e-273)
		tmp = t_1;
	elseif (a <= 2.8e-234)
		tmp = (y * (x - t)) / z;
	elseif (a <= 2.2e-42)
		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[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e-66], t$95$2, If[LessEqual[a, -5.4e-273], t$95$1, If[LessEqual[a, 2.8e-234], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.2e-42], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2000000000000001e-66 or 2.20000000000000005e-42 < a

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l/ 76.1%

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

      3. associate-*r/ 91.5%

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

      4. clear-num 91.4%

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

      5. un-div-inv 91.5%

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

   4. Applied egg-rr 91.5%

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

   5. Taylor expanded in z around 0 69.4%

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

   6. Taylor expanded in t around inf 56.4%

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

      1. *-commutative 56.4%

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

      2. associate-*r/ 56.5%

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

   8. Simplified 56.5%

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

   if -2.2000000000000001e-66 < a < -5.39999999999999969e-273 or 2.7999999999999999e-234 < a < 2.20000000000000005e-42

   1. Initial program 67.8%

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

   3. Taylor expanded in a around 0 44.6%

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

      1. mul-1-neg 44.6%

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

      2. unsub-neg 44.6%

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

      3. associate-/l* 56.3%

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

      4. div-sub 56.3%

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

      5. sub-neg 56.3%

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

      6. *-inverses 56.3%

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

      7. metadata-eval 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in t around inf 54.6%

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

   if -5.39999999999999969e-273 < a < 2.7999999999999999e-234

   1. Initial program 68.6%

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

   3. Taylor expanded in y around inf 68.0%

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

      1. div-sub 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in a around 0 74.8%

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

      1. associate-*r/ 74.8%

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

      2. neg-mul-1 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

   8. Simplified 74.8%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-234}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (+ x (* y (/ t a)))))
   (if (<= a -1.12e-66)
     t_2
     (if (<= a 6.3e-290)
       t_1
       (if (<= a 5.8e-233)
         (* y (/ (- x t) z))
         (if (<= a 2.65e-42) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -1.12e-66) {
		tmp = t_2;
	} else if (a <= 6.3e-290) {
		tmp = t_1;
	} else if (a <= 5.8e-233) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.65e-42) {
		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 * (1.0d0 - (y / z))
    t_2 = x + (y * (t / a))
    if (a <= (-1.12d-66)) then
        tmp = t_2
    else if (a <= 6.3d-290) then
        tmp = t_1
    else if (a <= 5.8d-233) then
        tmp = y * ((x - t) / z)
    else if (a <= 2.65d-42) 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 * (1.0 - (y / z));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -1.12e-66) {
		tmp = t_2;
	} else if (a <= 6.3e-290) {
		tmp = t_1;
	} else if (a <= 5.8e-233) {
		tmp = y * ((x - t) / z);
	} else if (a <= 2.65e-42) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (y * (t / a))
	tmp = 0
	if a <= -1.12e-66:
		tmp = t_2
	elif a <= 6.3e-290:
		tmp = t_1
	elif a <= 5.8e-233:
		tmp = y * ((x - t) / z)
	elif a <= 2.65e-42:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -1.12e-66)
		tmp = t_2;
	elseif (a <= 6.3e-290)
		tmp = t_1;
	elseif (a <= 5.8e-233)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 2.65e-42)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (y * (t / a));
	tmp = 0.0;
	if (a <= -1.12e-66)
		tmp = t_2;
	elseif (a <= 6.3e-290)
		tmp = t_1;
	elseif (a <= 5.8e-233)
		tmp = y * ((x - t) / z);
	elseif (a <= 2.65e-42)
		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[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.12e-66], t$95$2, If[LessEqual[a, 6.3e-290], t$95$1, If[LessEqual[a, 5.8e-233], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e-42], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12000000000000004e-66 or 2.65e-42 < a

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l/ 76.1%

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

      3. associate-*r/ 91.5%

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

      4. clear-num 91.4%

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

      5. un-div-inv 91.5%

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

   4. Applied egg-rr 91.5%

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

   5. Taylor expanded in z around 0 69.4%

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

   6. Taylor expanded in t around inf 56.4%

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

      1. *-commutative 56.4%

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

      2. associate-*r/ 56.5%

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

   8. Simplified 56.5%

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

   if -1.12000000000000004e-66 < a < 6.2999999999999998e-290 or 5.79999999999999964e-233 < a < 2.65e-42

   1. Initial program 65.7%

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

   3. Taylor expanded in a around 0 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

      3. associate-/l* 59.1%

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

      4. div-sub 59.1%

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

      5. sub-neg 59.1%

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

      6. *-inverses 59.1%

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

      7. metadata-eval 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in t around inf 55.1%

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

   if 6.2999999999999998e-290 < a < 5.79999999999999964e-233

   1. Initial program 89.9%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. div-sub 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in a around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-neg-frac2 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-66}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (+ x (* y (/ t a)))))
   (if (<= a -2.05e-66)
     t_2
     (if (<= a 6.8e-280)
       t_1
       (if (<= a 7e-241) (* x (/ y z)) (if (<= a 1.7e-44) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -2.05e-66) {
		tmp = t_2;
	} else if (a <= 6.8e-280) {
		tmp = t_1;
	} else if (a <= 7e-241) {
		tmp = x * (y / z);
	} else if (a <= 1.7e-44) {
		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 * (1.0d0 - (y / z))
    t_2 = x + (y * (t / a))
    if (a <= (-2.05d-66)) then
        tmp = t_2
    else if (a <= 6.8d-280) then
        tmp = t_1
    else if (a <= 7d-241) then
        tmp = x * (y / z)
    else if (a <= 1.7d-44) 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 * (1.0 - (y / z));
	double t_2 = x + (y * (t / a));
	double tmp;
	if (a <= -2.05e-66) {
		tmp = t_2;
	} else if (a <= 6.8e-280) {
		tmp = t_1;
	} else if (a <= 7e-241) {
		tmp = x * (y / z);
	} else if (a <= 1.7e-44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (y * (t / a))
	tmp = 0
	if a <= -2.05e-66:
		tmp = t_2
	elif a <= 6.8e-280:
		tmp = t_1
	elif a <= 7e-241:
		tmp = x * (y / z)
	elif a <= 1.7e-44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -2.05e-66)
		tmp = t_2;
	elseif (a <= 6.8e-280)
		tmp = t_1;
	elseif (a <= 7e-241)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.7e-44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (y * (t / a));
	tmp = 0.0;
	if (a <= -2.05e-66)
		tmp = t_2;
	elseif (a <= 6.8e-280)
		tmp = t_1;
	elseif (a <= 7e-241)
		tmp = x * (y / z);
	elseif (a <= 1.7e-44)
		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[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.05e-66], t$95$2, If[LessEqual[a, 6.8e-280], t$95$1, If[LessEqual[a, 7e-241], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.04999999999999999e-66 or 1.70000000000000008e-44 < a

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l/ 76.1%

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

      3. associate-*r/ 91.5%

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

      4. clear-num 91.4%

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

      5. un-div-inv 91.5%

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

   4. Applied egg-rr 91.5%

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

   5. Taylor expanded in z around 0 69.4%

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

   6. Taylor expanded in t around inf 56.4%

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

      1. *-commutative 56.4%

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

      2. associate-*r/ 56.5%

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

   8. Simplified 56.5%

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

   if -2.04999999999999999e-66 < a < 6.7999999999999995e-280 or 6.9999999999999998e-241 < a < 1.70000000000000008e-44

   1. Initial program 66.4%

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

   3. Taylor expanded in a around 0 48.3%

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

      1. mul-1-neg 48.3%

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

      2. unsub-neg 48.3%

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

      3. associate-/l* 59.9%

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

      4. div-sub 59.9%

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

      5. sub-neg 59.9%

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

      6. *-inverses 59.9%

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

      7. metadata-eval 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in t around inf 56.0%

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

   if 6.7999999999999995e-280 < a < 6.9999999999999998e-241

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. unsub-neg 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in a around 0 84.8%

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

Alternative 13: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -2.2e-66)
     t_2
     (if (<= a 6e-280)
       t_1
       (if (<= a 2.05e-241) (* x (/ y z)) (if (<= a 8.8e-49) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.2e-66) {
		tmp = t_2;
	} else if (a <= 6e-280) {
		tmp = t_1;
	} else if (a <= 2.05e-241) {
		tmp = x * (y / z);
	} else if (a <= 8.8e-49) {
		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 * (1.0d0 - (y / z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-2.2d-66)) then
        tmp = t_2
    else if (a <= 6d-280) then
        tmp = t_1
    else if (a <= 2.05d-241) then
        tmp = x * (y / z)
    else if (a <= 8.8d-49) 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 * (1.0 - (y / z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -2.2e-66) {
		tmp = t_2;
	} else if (a <= 6e-280) {
		tmp = t_1;
	} else if (a <= 2.05e-241) {
		tmp = x * (y / z);
	} else if (a <= 8.8e-49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -2.2e-66:
		tmp = t_2
	elif a <= 6e-280:
		tmp = t_1
	elif a <= 2.05e-241:
		tmp = x * (y / z)
	elif a <= 8.8e-49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -2.2e-66)
		tmp = t_2;
	elseif (a <= 6e-280)
		tmp = t_1;
	elseif (a <= 2.05e-241)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 8.8e-49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -2.2e-66)
		tmp = t_2;
	elseif (a <= 6e-280)
		tmp = t_1;
	elseif (a <= 2.05e-241)
		tmp = x * (y / z);
	elseif (a <= 8.8e-49)
		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[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e-66], t$95$2, If[LessEqual[a, 6e-280], t$95$1, If[LessEqual[a, 2.05e-241], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e-49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2000000000000001e-66 or 8.79999999999999959e-49 < a

   1. Initial program 85.6%

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

   3. Taylor expanded in x around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. unsub-neg 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in z around 0 52.8%

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

   if -2.2000000000000001e-66 < a < 5.99999999999999974e-280 or 2.0499999999999999e-241 < a < 8.79999999999999959e-49

   1. Initial program 66.3%

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

   3. Taylor expanded in a around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. unsub-neg 48.7%

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

      3. associate-/l* 60.7%

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

      4. div-sub 60.7%

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

      5. sub-neg 60.7%

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

      6. *-inverses 60.7%

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

      7. metadata-eval 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in t around inf 56.7%

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

   if 5.99999999999999974e-280 < a < 2.0499999999999999e-241

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. unsub-neg 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in a around 0 84.8%

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

Alternative 14: 37.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-296}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e+110)
   t
   (if (<= z -1.5e-66)
     (* x (/ y z))
     (if (<= z -3.5e-279)
       x
       (if (<= z 1.9e-296) (/ t (/ a y)) (if (<= z 4.6e+109) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+110) {
		tmp = t;
	} else if (z <= -1.5e-66) {
		tmp = x * (y / z);
	} else if (z <= -3.5e-279) {
		tmp = x;
	} else if (z <= 1.9e-296) {
		tmp = t / (a / y);
	} else if (z <= 4.6e+109) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.6d+110)) then
        tmp = t
    else if (z <= (-1.5d-66)) then
        tmp = x * (y / z)
    else if (z <= (-3.5d-279)) then
        tmp = x
    else if (z <= 1.9d-296) then
        tmp = t / (a / y)
    else if (z <= 4.6d+109) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+110) {
		tmp = t;
	} else if (z <= -1.5e-66) {
		tmp = x * (y / z);
	} else if (z <= -3.5e-279) {
		tmp = x;
	} else if (z <= 1.9e-296) {
		tmp = t / (a / y);
	} else if (z <= 4.6e+109) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e+110:
		tmp = t
	elif z <= -1.5e-66:
		tmp = x * (y / z)
	elif z <= -3.5e-279:
		tmp = x
	elif z <= 1.9e-296:
		tmp = t / (a / y)
	elif z <= 4.6e+109:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e+110)
		tmp = t;
	elseif (z <= -1.5e-66)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -3.5e-279)
		tmp = x;
	elseif (z <= 1.9e-296)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 4.6e+109)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e+110)
		tmp = t;
	elseif (z <= -1.5e-66)
		tmp = x * (y / z);
	elseif (z <= -3.5e-279)
		tmp = x;
	elseif (z <= 1.9e-296)
		tmp = t / (a / y);
	elseif (z <= 4.6e+109)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e+110], t, If[LessEqual[z, -1.5e-66], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-279], x, If[LessEqual[z, 1.9e-296], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+109], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5999999999999997e110 or 4.60000000000000021e109 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 55.9%

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

   if -3.5999999999999997e110 < z < -1.5000000000000001e-66

   1. Initial program 79.4%

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

   3. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in a around 0 37.0%

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

   if -1.5000000000000001e-66 < z < -3.5000000000000001e-279 or 1.9000000000000001e-296 < z < 4.60000000000000021e109

   1. Initial program 90.7%

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

   3. Taylor expanded in a around inf 35.8%

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

   if -3.5000000000000001e-279 < z < 1.9000000000000001e-296

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 64.8%

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

   4. Taylor expanded in z around 0 64.8%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

      1. clear-num 65.0%

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

      2. div-inv 65.1%

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

   8. Applied egg-rr 65.1%

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

Alternative 15: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.16 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+110)
   t
   (if (<= z -9e-66)
     (* x (/ y z))
     (if (<= z -9.8e-278)
       x
       (if (<= z 3.05e-295) (* t (/ y a)) (if (<= z 2.16e+102) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+110) {
		tmp = t;
	} else if (z <= -9e-66) {
		tmp = x * (y / z);
	} else if (z <= -9.8e-278) {
		tmp = x;
	} else if (z <= 3.05e-295) {
		tmp = t * (y / a);
	} else if (z <= 2.16e+102) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+110)) then
        tmp = t
    else if (z <= (-9d-66)) then
        tmp = x * (y / z)
    else if (z <= (-9.8d-278)) then
        tmp = x
    else if (z <= 3.05d-295) then
        tmp = t * (y / a)
    else if (z <= 2.16d+102) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+110) {
		tmp = t;
	} else if (z <= -9e-66) {
		tmp = x * (y / z);
	} else if (z <= -9.8e-278) {
		tmp = x;
	} else if (z <= 3.05e-295) {
		tmp = t * (y / a);
	} else if (z <= 2.16e+102) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+110:
		tmp = t
	elif z <= -9e-66:
		tmp = x * (y / z)
	elif z <= -9.8e-278:
		tmp = x
	elif z <= 3.05e-295:
		tmp = t * (y / a)
	elif z <= 2.16e+102:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+110)
		tmp = t;
	elseif (z <= -9e-66)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -9.8e-278)
		tmp = x;
	elseif (z <= 3.05e-295)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 2.16e+102)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+110)
		tmp = t;
	elseif (z <= -9e-66)
		tmp = x * (y / z);
	elseif (z <= -9.8e-278)
		tmp = x;
	elseif (z <= 3.05e-295)
		tmp = t * (y / a);
	elseif (z <= 2.16e+102)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+110], t, If[LessEqual[z, -9e-66], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.8e-278], x, If[LessEqual[z, 3.05e-295], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.16e+102], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e110 or 2.16000000000000005e102 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 55.9%

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

   if -1.3e110 < z < -8.9999999999999995e-66

   1. Initial program 79.4%

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

   3. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in a around 0 37.0%

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

   if -8.9999999999999995e-66 < z < -9.8000000000000004e-278 or 3.04999999999999987e-295 < z < 2.16000000000000005e102

   1. Initial program 90.7%

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

   3. Taylor expanded in a around inf 35.8%

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

   if -9.8000000000000004e-278 < z < 3.04999999999999987e-295

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 64.8%

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

   4. Taylor expanded in z around 0 64.8%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

Alternative 16: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+45}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.12e+109)
     t_1
     (if (<= z -6.5e-6)
       (* y (/ (- t x) (- a z)))
       (if (<= z 1.05e+45) (- x (/ (- x t) (/ a y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.12e+109) {
		tmp = t_1;
	} else if (z <= -6.5e-6) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.05e+45) {
		tmp = x - ((x - t) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-1.12d+109)) then
        tmp = t_1
    else if (z <= (-6.5d-6)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.05d+45) then
        tmp = x - ((x - t) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.12e+109) {
		tmp = t_1;
	} else if (z <= -6.5e-6) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.05e+45) {
		tmp = x - ((x - t) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.12e+109:
		tmp = t_1
	elif z <= -6.5e-6:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.05e+45:
		tmp = x - ((x - t) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.12e+109)
		tmp = t_1;
	elseif (z <= -6.5e-6)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.05e+45)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.12e+109)
		tmp = t_1;
	elseif (z <= -6.5e-6)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.05e+45)
		tmp = x - ((x - t) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+109], t$95$1, If[LessEqual[z, -6.5e-6], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+45], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1199999999999999e109 or 1.04999999999999997e45 < z

   1. Initial program 62.3%

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

   3. Taylor expanded in x around 0 40.6%

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

      1. associate-/l* 66.1%

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

   5. Simplified 66.1%

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

   if -1.1199999999999999e109 < z < -6.4999999999999996e-6

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. div-sub 69.7%

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

   5. Simplified 69.7%

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

   if -6.4999999999999996e-6 < z < 1.04999999999999997e45

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

      2. associate-*l/ 89.4%

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

      3. associate-*r/ 92.7%

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

      4. clear-num 92.6%

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

      5. un-div-inv 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in z around 0 72.2%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+45}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.00085:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.3e+109)
     t_1
     (if (<= z -0.00085)
       (* y (/ (- t x) (- a z)))
       (if (<= z 1.22e+45) (+ x (* y (/ (- t x) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.3e+109) {
		tmp = t_1;
	} else if (z <= -0.00085) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.22e+45) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-1.3d+109)) then
        tmp = t_1
    else if (z <= (-0.00085d0)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.22d+45) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.3e+109) {
		tmp = t_1;
	} else if (z <= -0.00085) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.22e+45) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.3e+109:
		tmp = t_1
	elif z <= -0.00085:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.22e+45:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.3e+109)
		tmp = t_1;
	elseif (z <= -0.00085)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.22e+45)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.3e+109)
		tmp = t_1;
	elseif (z <= -0.00085)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.22e+45)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+109], t$95$1, If[LessEqual[z, -0.00085], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+45], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2999999999999999e109 or 1.21999999999999997e45 < z

   1. Initial program 62.3%

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

   3. Taylor expanded in x around 0 40.6%

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

      1. associate-/l* 66.1%

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

   5. Simplified 66.1%

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

   if -1.2999999999999999e109 < z < -8.49999999999999953e-4

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. div-sub 69.7%

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

   5. Simplified 69.7%

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

   if -8.49999999999999953e-4 < z < 1.21999999999999997e45

   1. Initial program 88.7%

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

   3. Taylor expanded in z around 0 67.6%

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

      1. associate-/l* 69.2%

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

   5. Simplified 69.2%

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

Alternative 18: 57.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-101}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -9.2e+37)
     t_1
     (if (<= t 8e-159)
       (* x (- 1.0 (/ y a)))
       (if (<= t 1.15e-101) (/ (* x (- y a)) z) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -9.2e+37) {
		tmp = t_1;
	} else if (t <= 8e-159) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 1.15e-101) {
		tmp = (x * (y - 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 = t * ((y - z) / (a - z))
    if (t <= (-9.2d+37)) then
        tmp = t_1
    else if (t <= 8d-159) then
        tmp = x * (1.0d0 - (y / a))
    else if (t <= 1.15d-101) then
        tmp = (x * (y - 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 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -9.2e+37) {
		tmp = t_1;
	} else if (t <= 8e-159) {
		tmp = x * (1.0 - (y / a));
	} else if (t <= 1.15e-101) {
		tmp = (x * (y - a)) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -9.2e+37:
		tmp = t_1
	elif t <= 8e-159:
		tmp = x * (1.0 - (y / a))
	elif t <= 1.15e-101:
		tmp = (x * (y - a)) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -9.2e+37)
		tmp = t_1;
	elseif (t <= 8e-159)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (t <= 1.15e-101)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -9.2e+37)
		tmp = t_1;
	elseif (t <= 8e-159)
		tmp = x * (1.0 - (y / a));
	elseif (t <= 1.15e-101)
		tmp = (x * (y - a)) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+37], t$95$1, If[LessEqual[t, 8e-159], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-101], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.2000000000000001e37 or 1.15e-101 < t

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0 52.3%

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

      1. associate-/l* 70.1%

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

   5. Simplified 70.1%

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

   if -9.2000000000000001e37 < t < 7.99999999999999991e-159

   1. Initial program 72.8%

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

   3. Taylor expanded in x around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. unsub-neg 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in z around 0 57.1%

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

   if 7.99999999999999991e-159 < t < 1.15e-101

   1. Initial program 46.2%

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

   3. Taylor expanded in z around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. distribute-lft-out-- 72.4%

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

      3. div-sub 72.6%

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

      4. mul-1-neg 72.6%

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

      5. unsub-neg 72.6%

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

      6. div-sub 72.4%

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

      7. associate-/l* 67.5%

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

      8. associate-/l* 61.6%

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

      9. distribute-rgt-out-- 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around 0 61.9%

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

Alternative 19: 70.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-66} \lor \neg \left(a \leq 8.6 \cdot 10^{-50}\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.3e-66) (not (<= a 8.6e-50)))
   (- x (/ (- x t) (/ a y)))
   (+ t (* (/ (- t x) z) (- a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-66) || !(a <= 8.6e-50)) {
		tmp = x - ((x - t) / (a / y));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.3d-66)) .or. (.not. (a <= 8.6d-50))) then
        tmp = x - ((x - t) / (a / y))
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-66) || !(a <= 8.6e-50)) {
		tmp = x - ((x - t) / (a / y));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.3e-66) or not (a <= 8.6e-50):
		tmp = x - ((x - t) / (a / y))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.3e-66) || !(a <= 8.6e-50))
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / y)));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.3e-66) || ~((a <= 8.6e-50)))
		tmp = x - ((x - t) / (a / y));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.3e-66], N[Not[LessEqual[a, 8.6e-50]], $MachinePrecision]], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2999999999999999e-66 or 8.59999999999999995e-50 < a

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-*l/ 76.6%

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

      3. associate-*r/ 91.6%

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

      4. clear-num 91.6%

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

      5. un-div-inv 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in z around 0 69.4%

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

   if -1.2999999999999999e-66 < a < 8.59999999999999995e-50

   1. Initial program 67.9%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. associate--l+ 83.1%

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

      2. distribute-lft-out-- 83.1%

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

      3. div-sub 83.1%

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

      4. mul-1-neg 83.1%

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

      5. unsub-neg 83.1%

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

      6. div-sub 83.1%

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

      7. associate-/l* 80.5%

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

      8. associate-/l* 74.6%

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

      9. distribute-rgt-out-- 80.6%

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

   5. Simplified 80.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-66} \lor \neg \left(a \leq 8.6 \cdot 10^{-50}\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-66} \lor \neg \left(a \leq 7.2 \cdot 10^{-51}\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.2e-66) (not (<= a 7.2e-51)))
   (- x (/ (- x t) (/ a y)))
   (+ t (/ (* y (- x t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e-66) || !(a <= 7.2e-51)) {
		tmp = x - ((x - t) / (a / y));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.2d-66)) .or. (.not. (a <= 7.2d-51))) then
        tmp = x - ((x - t) / (a / y))
    else
        tmp = t + ((y * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e-66) || !(a <= 7.2e-51)) {
		tmp = x - ((x - t) / (a / y));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.2e-66) or not (a <= 7.2e-51):
		tmp = x - ((x - t) / (a / y))
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.2e-66) || !(a <= 7.2e-51))
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / y)));
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.2e-66) || ~((a <= 7.2e-51)))
		tmp = x - ((x - t) / (a / y));
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.2e-66], N[Not[LessEqual[a, 7.2e-51]], $MachinePrecision]], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2000000000000001e-66 or 7.2000000000000001e-51 < a

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-*l/ 76.6%

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

      3. associate-*r/ 91.6%

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

      4. clear-num 91.6%

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

      5. un-div-inv 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in z around 0 69.4%

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

   if -2.2000000000000001e-66 < a < 7.2000000000000001e-51

   1. Initial program 67.9%

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

   3. Taylor expanded in z around inf 83.1%

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

      1. associate--l+ 83.1%

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

      2. distribute-lft-out-- 83.1%

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

      3. div-sub 83.1%

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

      4. mul-1-neg 83.1%

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

      5. unsub-neg 83.1%

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

      6. div-sub 83.1%

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

      7. associate-/l* 80.5%

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

      8. associate-/l* 74.6%

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

      9. distribute-rgt-out-- 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around inf 79.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-66} \lor \neg \left(a \leq 7.2 \cdot 10^{-51}\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+109) t (if (<= z 1.42e+99) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+109) {
		tmp = t;
	} else if (z <= 1.42e+99) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d+109)) then
        tmp = t
    else if (z <= 1.42d+99) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+109) {
		tmp = t;
	} else if (z <= 1.42e+99) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+109:
		tmp = t
	elif z <= 1.42e+99:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+109)
		tmp = t;
	elseif (z <= 1.42e+99)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+109)
		tmp = t;
	elseif (z <= 1.42e+99)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+109], t, If[LessEqual[z, 1.42e+99], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000005e109 or 1.42000000000000004e99 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 55.9%

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

   if -1.15000000000000005e109 < z < 1.42000000000000004e99

   1. Initial program 87.4%

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

   3. Taylor expanded in a around inf 31.9%

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

Alternative 22: 25.3% 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 78.3%

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

3. Taylor expanded in z around inf 22.3%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024087 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))