Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.9% → 94.9%

Time: 20.4s

Alternatives: 19

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: 80.9% 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: 94.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-274} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-274) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ 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) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-274) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} 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(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-274) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-274], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $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)))) < -9.99999999999999966e-275 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. remove-double-neg 92.9%

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

      3. unsub-neg 92.9%

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

      4. *-commutative 92.9%

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

      5. associate-*l/ 77.5%

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

      6. associate-/l* 95.9%

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

      7. fma-neg 95.9%

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

      8. remove-double-neg 95.9%

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

   3. Simplified 95.9%

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

   if -9.99999999999999966e-275 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in z around inf 89.8%

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

      1. associate--l+ 89.8%

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

      2. distribute-lft-out-- 89.8%

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

      3. div-sub 89.7%

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

      4. mul-1-neg 89.7%

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

      5. unsub-neg 89.7%

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

      6. div-sub 89.8%

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

      7. associate-/l* 94.9%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-274} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-163} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t}{x} + \frac{\left(y - a\right) \cdot \left(1 - \frac{t}{x}\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-163) (not (<= t_1 0.0)))
     t_1
     (* x (+ (/ t x) (/ (* (- y a) (- 1.0 (/ t x))) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-163) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = x * ((t / x) + (((y - a) * (1.0 - (t / x))) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-163)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = x * ((t / x) + (((y - a) * (1.0d0 - (t / x))) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-163) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = x * ((t / x) + (((y - a) * (1.0 - (t / x))) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-163) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = x * ((t / x) + (((y - a) * (1.0 - (t / x))) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-163) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(t / x) + Float64(Float64(Float64(y - a) * Float64(1.0 - Float64(t / x))) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-163) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = x * ((t / x) + (((y - a) * (1.0 - (t / x))) / z));
	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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-163], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(x * N[(N[(t / x), $MachinePrecision] + N[(N[(N[(y - a), $MachinePrecision] * N[(1.0 - N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $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)))) < -4.99999999999999977e-163 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 95.7%

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

   if -4.99999999999999977e-163 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 8.4%

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

   3. Taylor expanded in x around inf 19.9%

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

      1. times-frac 20.2%

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

      2. distribute-rgt-out 20.1%

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

   5. Simplified 20.1%

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

   6. Taylor expanded in z around -inf 91.0%

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

      1. +-commutative 91.0%

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

      2. mul-1-neg 91.0%

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

      3. unsub-neg 91.0%

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

      4. distribute-rgt-out-- 91.0%

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

      5. sub-neg 91.0%

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

      6. metadata-eval 91.0%

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

      7. +-commutative 91.0%

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

   8. Simplified 91.0%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-163} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t}{x} + \frac{\left(y - a\right) \cdot \left(1 - \frac{t}{x}\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+151}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-187}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-236}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* y (/ (- t x) a))))
   (if (<= z -6e+151)
     t
     (if (<= z -4.9e+25)
       (* x (/ (- y a) z))
       (if (<= z -1.15e-67)
         t_1
         (if (<= z -2.4e-110)
           t_2
           (if (<= z -2.9e-168)
             t_1
             (if (<= z -4.4e-187)
               (* t (/ (- y z) a))
               (if (<= z -2.9e-236) t_2 (if (<= z 7.2e+25) t_1 t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (z <= -6e+151) {
		tmp = t;
	} else if (z <= -4.9e+25) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.15e-67) {
		tmp = t_1;
	} else if (z <= -2.4e-110) {
		tmp = t_2;
	} else if (z <= -2.9e-168) {
		tmp = t_1;
	} else if (z <= -4.4e-187) {
		tmp = t * ((y - z) / a);
	} else if (z <= -2.9e-236) {
		tmp = t_2;
	} else if (z <= 7.2e+25) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = y * ((t - x) / a)
    if (z <= (-6d+151)) then
        tmp = t
    else if (z <= (-4.9d+25)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.15d-67)) then
        tmp = t_1
    else if (z <= (-2.4d-110)) then
        tmp = t_2
    else if (z <= (-2.9d-168)) then
        tmp = t_1
    else if (z <= (-4.4d-187)) then
        tmp = t * ((y - z) / a)
    else if (z <= (-2.9d-236)) then
        tmp = t_2
    else if (z <= 7.2d+25) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (z <= -6e+151) {
		tmp = t;
	} else if (z <= -4.9e+25) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.15e-67) {
		tmp = t_1;
	} else if (z <= -2.4e-110) {
		tmp = t_2;
	} else if (z <= -2.9e-168) {
		tmp = t_1;
	} else if (z <= -4.4e-187) {
		tmp = t * ((y - z) / a);
	} else if (z <= -2.9e-236) {
		tmp = t_2;
	} else if (z <= 7.2e+25) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = y * ((t - x) / a)
	tmp = 0
	if z <= -6e+151:
		tmp = t
	elif z <= -4.9e+25:
		tmp = x * ((y - a) / z)
	elif z <= -1.15e-67:
		tmp = t_1
	elif z <= -2.4e-110:
		tmp = t_2
	elif z <= -2.9e-168:
		tmp = t_1
	elif z <= -4.4e-187:
		tmp = t * ((y - z) / a)
	elif z <= -2.9e-236:
		tmp = t_2
	elif z <= 7.2e+25:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -6e+151)
		tmp = t;
	elseif (z <= -4.9e+25)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.15e-67)
		tmp = t_1;
	elseif (z <= -2.4e-110)
		tmp = t_2;
	elseif (z <= -2.9e-168)
		tmp = t_1;
	elseif (z <= -4.4e-187)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= -2.9e-236)
		tmp = t_2;
	elseif (z <= 7.2e+25)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -6e+151)
		tmp = t;
	elseif (z <= -4.9e+25)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.15e-67)
		tmp = t_1;
	elseif (z <= -2.4e-110)
		tmp = t_2;
	elseif (z <= -2.9e-168)
		tmp = t_1;
	elseif (z <= -4.4e-187)
		tmp = t * ((y - z) / a);
	elseif (z <= -2.9e-236)
		tmp = t_2;
	elseif (z <= 7.2e+25)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+151], t, If[LessEqual[z, -4.9e+25], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-67], t$95$1, If[LessEqual[z, -2.4e-110], t$95$2, If[LessEqual[z, -2.9e-168], t$95$1, If[LessEqual[z, -4.4e-187], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-236], t$95$2, If[LessEqual[z, 7.2e+25], t$95$1, t]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.9999999999999998e151 or 7.20000000000000031e25 < z

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf 49.4%

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

   if -5.9999999999999998e151 < z < -4.9000000000000001e25

   1. Initial program 74.7%

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

   3. Taylor expanded in x around inf 31.2%

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

      1. mul-1-neg 31.2%

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

      2. unsub-neg 31.2%

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

   5. Simplified 31.2%

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

   6. Taylor expanded in z around inf 37.3%

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

      1. associate-*r/ 37.3%

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

      2. mul-1-neg 37.3%

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

      3. neg-mul-1 37.3%

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

      4. sub-neg 37.3%

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

   8. Simplified 37.3%

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

   9. Taylor expanded in x around 0 31.6%

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

       1. associate-/l* 37.3%

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

   11. Simplified 37.3%

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

   if -4.9000000000000001e25 < z < -1.15e-67 or -2.40000000000000006e-110 < z < -2.8999999999999998e-168 or -2.9e-236 < z < 7.20000000000000031e25

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. unsub-neg 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in z around 0 60.7%

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

   if -1.15e-67 < z < -2.40000000000000006e-110 or -4.40000000000000016e-187 < z < -2.9e-236

   1. Initial program 94.8%

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

   3. Taylor expanded in y around inf 82.1%

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

      1. div-sub 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in a around inf 72.0%

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

   if -2.8999999999999998e-168 < z < -4.40000000000000016e-187

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 45.4%

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

   4. Taylor expanded in a around inf 56.9%

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

      1. associate-/l* 67.8%

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

   6. Simplified 67.8%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+151}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-187}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-227} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-227) (not (<= t_1 0.0)))
     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) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-227) || !(t_1 <= 0.0)) {
		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) / (a - z)))
    if ((t_1 <= (-5d-227)) .or. (.not. (t_1 <= 0.0d0))) 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) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-227) || !(t_1 <= 0.0)) {
		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) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-227) or not (t_1 <= 0.0):
		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(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-227) || !(t_1 <= 0.0))
		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) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-227) || ~((t_1 <= 0.0)))
		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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-227], N[Not[LessEqual[t$95$1, 0.0]], $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)))) < -4.99999999999999961e-227 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.5%

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

   if -4.99999999999999961e-227 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 6.5%

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

   3. Taylor expanded in z around inf 88.4%

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

      1. associate--l+ 88.4%

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

      2. distribute-lft-out-- 88.4%

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

      3. div-sub 88.4%

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

      4. mul-1-neg 88.4%

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

      5. unsub-neg 88.4%

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

      6. div-sub 88.4%

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

      7. associate-/l* 92.9%

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

      8. associate-/l* 95.5%

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

      9. distribute-rgt-out-- 95.5%

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

   5. Simplified 95.5%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-227} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -1.05e+72)
     t
     (if (<= z -1.02e-63)
       x
       (if (<= z -8.5e-240)
         t_1
         (if (<= z 7.4e-112) x (if (<= z 5.2e+85) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -1.05e+72) {
		tmp = t;
	} else if (z <= -1.02e-63) {
		tmp = x;
	} else if (z <= -8.5e-240) {
		tmp = t_1;
	} else if (z <= 7.4e-112) {
		tmp = x;
	} else if (z <= 5.2e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (z <= (-1.05d+72)) then
        tmp = t
    else if (z <= (-1.02d-63)) then
        tmp = x
    else if (z <= (-8.5d-240)) then
        tmp = t_1
    else if (z <= 7.4d-112) then
        tmp = x
    else if (z <= 5.2d+85) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -1.05e+72) {
		tmp = t;
	} else if (z <= -1.02e-63) {
		tmp = x;
	} else if (z <= -8.5e-240) {
		tmp = t_1;
	} else if (z <= 7.4e-112) {
		tmp = x;
	} else if (z <= 5.2e+85) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -1.05e+72:
		tmp = t
	elif z <= -1.02e-63:
		tmp = x
	elif z <= -8.5e-240:
		tmp = t_1
	elif z <= 7.4e-112:
		tmp = x
	elif z <= 5.2e+85:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.05e+72)
		tmp = t;
	elseif (z <= -1.02e-63)
		tmp = x;
	elseif (z <= -8.5e-240)
		tmp = t_1;
	elseif (z <= 7.4e-112)
		tmp = x;
	elseif (z <= 5.2e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -1.05e+72)
		tmp = t;
	elseif (z <= -1.02e-63)
		tmp = x;
	elseif (z <= -8.5e-240)
		tmp = t_1;
	elseif (z <= 7.4e-112)
		tmp = x;
	elseif (z <= 5.2e+85)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+72], t, If[LessEqual[z, -1.02e-63], x, If[LessEqual[z, -8.5e-240], t$95$1, If[LessEqual[z, 7.4e-112], x, If[LessEqual[z, 5.2e+85], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0500000000000001e72 or 5.20000000000000021e85 < z

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf 47.8%

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

   if -1.0500000000000001e72 < z < -1.01999999999999997e-63 or -8.5e-240 < z < 7.3999999999999996e-112

   1. Initial program 93.1%

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

   3. Taylor expanded in a around inf 45.2%

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

   if -1.01999999999999997e-63 < z < -8.5e-240 or 7.3999999999999996e-112 < z < 5.20000000000000021e85

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 63.9%

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

      1. div-sub 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in t around inf 38.1%

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

      1. associate-/l* 46.1%

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

   8. Simplified 46.1%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+151}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -6e+151)
     t
     (if (<= z -6e+25)
       (* x (/ (- y a) z))
       (if (<= z -4e-63)
         t_1
         (if (<= z -1.05e-108)
           (* t (/ y (- a z)))
           (if (<= z 2e+25) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6e+151) {
		tmp = t;
	} else if (z <= -6e+25) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4e-63) {
		tmp = t_1;
	} else if (z <= -1.05e-108) {
		tmp = t * (y / (a - z));
	} else if (z <= 2e+25) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-6d+151)) then
        tmp = t
    else if (z <= (-6d+25)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-4d-63)) then
        tmp = t_1
    else if (z <= (-1.05d-108)) then
        tmp = t * (y / (a - z))
    else if (z <= 2d+25) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -6e+151) {
		tmp = t;
	} else if (z <= -6e+25) {
		tmp = x * ((y - a) / z);
	} else if (z <= -4e-63) {
		tmp = t_1;
	} else if (z <= -1.05e-108) {
		tmp = t * (y / (a - z));
	} else if (z <= 2e+25) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -6e+151:
		tmp = t
	elif z <= -6e+25:
		tmp = x * ((y - a) / z)
	elif z <= -4e-63:
		tmp = t_1
	elif z <= -1.05e-108:
		tmp = t * (y / (a - z))
	elif z <= 2e+25:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -6e+151)
		tmp = t;
	elseif (z <= -6e+25)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -4e-63)
		tmp = t_1;
	elseif (z <= -1.05e-108)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2e+25)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -6e+151)
		tmp = t;
	elseif (z <= -6e+25)
		tmp = x * ((y - a) / z);
	elseif (z <= -4e-63)
		tmp = t_1;
	elseif (z <= -1.05e-108)
		tmp = t * (y / (a - z));
	elseif (z <= 2e+25)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+151], t, If[LessEqual[z, -6e+25], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-63], t$95$1, If[LessEqual[z, -1.05e-108], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+25], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.9999999999999998e151 or 2.00000000000000018e25 < z

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf 49.4%

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

   if -5.9999999999999998e151 < z < -6.00000000000000011e25

   1. Initial program 74.7%

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

   3. Taylor expanded in x around inf 31.2%

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

      1. mul-1-neg 31.2%

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

      2. unsub-neg 31.2%

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

   5. Simplified 31.2%

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

   6. Taylor expanded in z around inf 37.3%

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

      1. associate-*r/ 37.3%

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

      2. mul-1-neg 37.3%

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

      3. neg-mul-1 37.3%

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

      4. sub-neg 37.3%

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

   8. Simplified 37.3%

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

   9. Taylor expanded in x around 0 31.6%

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

       1. associate-/l* 37.3%

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

   11. Simplified 37.3%

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

   if -6.00000000000000011e25 < z < -4.00000000000000027e-63 or -1.05e-108 < z < 2.00000000000000018e25

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in z around 0 57.6%

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

   if -4.00000000000000027e-63 < z < -1.05e-108

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 81.3%

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

      1. div-sub 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in t around inf 58.9%

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

      1. associate-/l* 65.6%

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

   8. Simplified 65.6%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+151}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -4.4e+72)
     t
     (if (<= z -1.3e-58)
       x
       (if (<= z -7e-236)
         t_1
         (if (<= z 8.5e-111)
           x
           (if (<= z 1.75e-28) t_1 (if (<= z 2.6e+14) 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 <= -4.4e+72) {
		tmp = t;
	} else if (z <= -1.3e-58) {
		tmp = x;
	} else if (z <= -7e-236) {
		tmp = t_1;
	} else if (z <= 8.5e-111) {
		tmp = x;
	} else if (z <= 1.75e-28) {
		tmp = t_1;
	} else if (z <= 2.6e+14) {
		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 <= (-4.4d+72)) then
        tmp = t
    else if (z <= (-1.3d-58)) then
        tmp = x
    else if (z <= (-7d-236)) then
        tmp = t_1
    else if (z <= 8.5d-111) then
        tmp = x
    else if (z <= 1.75d-28) then
        tmp = t_1
    else if (z <= 2.6d+14) 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 <= -4.4e+72) {
		tmp = t;
	} else if (z <= -1.3e-58) {
		tmp = x;
	} else if (z <= -7e-236) {
		tmp = t_1;
	} else if (z <= 8.5e-111) {
		tmp = x;
	} else if (z <= 1.75e-28) {
		tmp = t_1;
	} else if (z <= 2.6e+14) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -4.4e+72:
		tmp = t
	elif z <= -1.3e-58:
		tmp = x
	elif z <= -7e-236:
		tmp = t_1
	elif z <= 8.5e-111:
		tmp = x
	elif z <= 1.75e-28:
		tmp = t_1
	elif z <= 2.6e+14:
		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 <= -4.4e+72)
		tmp = t;
	elseif (z <= -1.3e-58)
		tmp = x;
	elseif (z <= -7e-236)
		tmp = t_1;
	elseif (z <= 8.5e-111)
		tmp = x;
	elseif (z <= 1.75e-28)
		tmp = t_1;
	elseif (z <= 2.6e+14)
		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 <= -4.4e+72)
		tmp = t;
	elseif (z <= -1.3e-58)
		tmp = x;
	elseif (z <= -7e-236)
		tmp = t_1;
	elseif (z <= 8.5e-111)
		tmp = x;
	elseif (z <= 1.75e-28)
		tmp = t_1;
	elseif (z <= 2.6e+14)
		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, -4.4e+72], t, If[LessEqual[z, -1.3e-58], x, If[LessEqual[z, -7e-236], t$95$1, If[LessEqual[z, 8.5e-111], x, If[LessEqual[z, 1.75e-28], t$95$1, If[LessEqual[z, 2.6e+14], x, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4e72 or 2.6e14 < z

   1. Initial program 64.0%

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

   3. Taylor expanded in z around inf 45.3%

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

   if -4.4e72 < z < -1.30000000000000003e-58 or -6.99999999999999988e-236 < z < 8.5000000000000003e-111 or 1.75e-28 < z < 2.6e14

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 46.2%

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

   if -1.30000000000000003e-58 < z < -6.99999999999999988e-236 or 8.5000000000000003e-111 < z < 1.75e-28

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 68.3%

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

      1. div-sub 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in t around inf 43.9%

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

   7. Taylor expanded in a around inf 34.2%

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

      1. associate-/l* 45.4%

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

   9. Simplified 45.4%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -2e+72)
     t
     (if (<= z -3.5e-65)
       t_1
       (if (<= z -6.5e-111) (* t (/ y (- a z))) (if (<= z 6e+25) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2e+72) {
		tmp = t;
	} else if (z <= -3.5e-65) {
		tmp = t_1;
	} else if (z <= -6.5e-111) {
		tmp = t * (y / (a - z));
	} else if (z <= 6e+25) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-2d+72)) then
        tmp = t
    else if (z <= (-3.5d-65)) then
        tmp = t_1
    else if (z <= (-6.5d-111)) then
        tmp = t * (y / (a - z))
    else if (z <= 6d+25) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2e+72) {
		tmp = t;
	} else if (z <= -3.5e-65) {
		tmp = t_1;
	} else if (z <= -6.5e-111) {
		tmp = t * (y / (a - z));
	} else if (z <= 6e+25) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2e+72:
		tmp = t
	elif z <= -3.5e-65:
		tmp = t_1
	elif z <= -6.5e-111:
		tmp = t * (y / (a - z))
	elif z <= 6e+25:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2e+72)
		tmp = t;
	elseif (z <= -3.5e-65)
		tmp = t_1;
	elseif (z <= -6.5e-111)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 6e+25)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2e+72)
		tmp = t;
	elseif (z <= -3.5e-65)
		tmp = t_1;
	elseif (z <= -6.5e-111)
		tmp = t * (y / (a - z));
	elseif (z <= 6e+25)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+72], t, If[LessEqual[z, -3.5e-65], t$95$1, If[LessEqual[z, -6.5e-111], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+25], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.99999999999999989e72 or 6.00000000000000011e25 < z

   1. Initial program 62.4%

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

   3. Taylor expanded in z around inf 46.3%

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

   if -1.99999999999999989e72 < z < -3.50000000000000005e-65 or -6.49999999999999974e-111 < z < 6.00000000000000011e25

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in z around 0 53.3%

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

   if -3.50000000000000005e-65 < z < -6.49999999999999974e-111

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 81.3%

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

      1. div-sub 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in t around inf 58.9%

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

      1. associate-/l* 65.6%

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

   8. Simplified 65.6%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-295}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -4.4e+38)
     t_2
     (if (<= a -4e-177)
       t_1
       (if (<= a -1.65e-295)
         (* y (/ (- x t) z))
         (if (<= a 8.8e-29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.4e+38) {
		tmp = t_2;
	} else if (a <= -4e-177) {
		tmp = t_1;
	} else if (a <= -1.65e-295) {
		tmp = y * ((x - t) / z);
	} else if (a <= 8.8e-29) {
		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 * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-4.4d+38)) then
        tmp = t_2
    else if (a <= (-4d-177)) then
        tmp = t_1
    else if (a <= (-1.65d-295)) then
        tmp = y * ((x - t) / z)
    else if (a <= 8.8d-29) 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 * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.4e+38) {
		tmp = t_2;
	} else if (a <= -4e-177) {
		tmp = t_1;
	} else if (a <= -1.65e-295) {
		tmp = y * ((x - t) / z);
	} else if (a <= 8.8e-29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -4.4e+38:
		tmp = t_2
	elif a <= -4e-177:
		tmp = t_1
	elif a <= -1.65e-295:
		tmp = y * ((x - t) / z)
	elif a <= 8.8e-29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -4.4e+38)
		tmp = t_2;
	elseif (a <= -4e-177)
		tmp = t_1;
	elseif (a <= -1.65e-295)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (a <= 8.8e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -4.4e+38)
		tmp = t_2;
	elseif (a <= -4e-177)
		tmp = t_1;
	elseif (a <= -1.65e-295)
		tmp = y * ((x - t) / z);
	elseif (a <= 8.8e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.4e+38], t$95$2, If[LessEqual[a, -4e-177], t$95$1, If[LessEqual[a, -1.65e-295], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e-29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.40000000000000013e38 or 8.79999999999999961e-29 < a

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in z around 0 50.3%

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

   if -4.40000000000000013e38 < a < -3.99999999999999981e-177 or -1.6499999999999999e-295 < a < 8.79999999999999961e-29

   1. Initial program 74.1%

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

   3. Taylor expanded in x around 0 61.2%

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

   4. Taylor expanded in a around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. associate-/l* 67.1%

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

      3. distribute-lft-neg-in 67.1%

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

   6. Simplified 67.1%

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

   if -3.99999999999999981e-177 < a < -1.6499999999999999e-295

   1. Initial program 71.7%

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

   3. Taylor expanded in y around inf 61.4%

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

      1. div-sub 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in a around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. distribute-neg-frac2 61.2%

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

   8. Simplified 61.2%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-295}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-259}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -4.1e+38)
     t_2
     (if (<= a -1.04e-175)
       t_1
       (if (<= a -2.55e-259)
         (* (- x t) (/ y z))
         (if (<= a 9.6e-32) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.1e+38) {
		tmp = t_2;
	} else if (a <= -1.04e-175) {
		tmp = t_1;
	} else if (a <= -2.55e-259) {
		tmp = (x - t) * (y / z);
	} else if (a <= 9.6e-32) {
		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 * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-4.1d+38)) then
        tmp = t_2
    else if (a <= (-1.04d-175)) then
        tmp = t_1
    else if (a <= (-2.55d-259)) then
        tmp = (x - t) * (y / z)
    else if (a <= 9.6d-32) 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 * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -4.1e+38) {
		tmp = t_2;
	} else if (a <= -1.04e-175) {
		tmp = t_1;
	} else if (a <= -2.55e-259) {
		tmp = (x - t) * (y / z);
	} else if (a <= 9.6e-32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -4.1e+38:
		tmp = t_2
	elif a <= -1.04e-175:
		tmp = t_1
	elif a <= -2.55e-259:
		tmp = (x - t) * (y / z)
	elif a <= 9.6e-32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -4.1e+38)
		tmp = t_2;
	elseif (a <= -1.04e-175)
		tmp = t_1;
	elseif (a <= -2.55e-259)
		tmp = Float64(Float64(x - t) * Float64(y / z));
	elseif (a <= 9.6e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -4.1e+38)
		tmp = t_2;
	elseif (a <= -1.04e-175)
		tmp = t_1;
	elseif (a <= -2.55e-259)
		tmp = (x - t) * (y / z);
	elseif (a <= 9.6e-32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+38], t$95$2, If[LessEqual[a, -1.04e-175], t$95$1, If[LessEqual[a, -2.55e-259], N[(N[(x - t), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.6e-32], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.1000000000000003e38 or 9.6000000000000005e-32 < a

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in z around 0 50.3%

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

   if -4.1000000000000003e38 < a < -1.03999999999999997e-175 or -2.5499999999999999e-259 < a < 9.6000000000000005e-32

   1. Initial program 72.9%

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

   3. Taylor expanded in x around 0 59.4%

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

   4. Taylor expanded in a around 0 52.5%

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

      1. mul-1-neg 52.5%

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

      2. associate-/l* 65.3%

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

      3. distribute-lft-neg-in 65.3%

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

   6. Simplified 65.3%

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

   if -1.03999999999999997e-175 < a < -2.5499999999999999e-259

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. div-sub 73.8%

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

   5. Simplified 73.8%

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

      1. clear-num 73.8%

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

      2. div-inv 73.8%

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

   7. Applied egg-rr 73.8%

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

      1. associate-/r/ 80.5%

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

   9. Simplified 80.5%

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

   10. Taylor expanded in a around 0 72.9%

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

       1. associate-*r/ 72.9%

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

       2. neg-mul-1 72.9%

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

   12. Simplified 72.9%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.04 \cdot 10^{-175}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-259}:\\ \;\;\;\;\left(x - t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-297}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -3.5e+38)
     t_2
     (if (<= a -5.5e-217)
       t_1
       (if (<= a -9.2e-297)
         (/ (* y (- x t)) z)
         (if (<= a 7.5e-29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -3.5e+38) {
		tmp = t_2;
	} else if (a <= -5.5e-217) {
		tmp = t_1;
	} else if (a <= -9.2e-297) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 7.5e-29) {
		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 * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-3.5d+38)) then
        tmp = t_2
    else if (a <= (-5.5d-217)) then
        tmp = t_1
    else if (a <= (-9.2d-297)) then
        tmp = (y * (x - t)) / z
    else if (a <= 7.5d-29) 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 * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -3.5e+38) {
		tmp = t_2;
	} else if (a <= -5.5e-217) {
		tmp = t_1;
	} else if (a <= -9.2e-297) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 7.5e-29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -3.5e+38:
		tmp = t_2
	elif a <= -5.5e-217:
		tmp = t_1
	elif a <= -9.2e-297:
		tmp = (y * (x - t)) / z
	elif a <= 7.5e-29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -3.5e+38)
		tmp = t_2;
	elseif (a <= -5.5e-217)
		tmp = t_1;
	elseif (a <= -9.2e-297)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 7.5e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -3.5e+38)
		tmp = t_2;
	elseif (a <= -5.5e-217)
		tmp = t_1;
	elseif (a <= -9.2e-297)
		tmp = (y * (x - t)) / z;
	elseif (a <= 7.5e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+38], t$95$2, If[LessEqual[a, -5.5e-217], t$95$1, If[LessEqual[a, -9.2e-297], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 7.5e-29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.50000000000000002e38 or 7.50000000000000006e-29 < a

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in z around 0 50.3%

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

   if -3.50000000000000002e38 < a < -5.49999999999999975e-217 or -9.1999999999999996e-297 < a < 7.50000000000000006e-29

   1. Initial program 75.0%

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

   3. Taylor expanded in x around 0 60.9%

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

   4. Taylor expanded in a around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. associate-/l* 66.5%

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

      3. distribute-lft-neg-in 66.5%

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

   6. Simplified 66.5%

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

   if -5.49999999999999975e-217 < a < -9.1999999999999996e-297

   1. Initial program 66.8%

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

   3. Taylor expanded in y around inf 58.5%

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

      1. div-sub 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in a around 0 70.2%

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

      1. associate-*r/ 70.2%

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

      2. neg-mul-1 70.2%

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

      3. distribute-rgt-neg-in 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-217}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-297}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.56e+72)
     t_1
     (if (<= z -9.5e+23)
       (* y (/ (- t x) (- a z)))
       (if (<= z 2.5e+21) (+ 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 <= -1.56e+72) {
		tmp = t_1;
	} else if (z <= -9.5e+23) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 2.5e+21) {
		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 <= (-1.56d+72)) then
        tmp = t_1
    else if (z <= (-9.5d+23)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 2.5d+21) 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 <= -1.56e+72) {
		tmp = t_1;
	} else if (z <= -9.5e+23) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 2.5e+21) {
		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 <= -1.56e+72:
		tmp = t_1
	elif z <= -9.5e+23:
		tmp = y * ((t - x) / (a - z))
	elif z <= 2.5e+21:
		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 <= -1.56e+72)
		tmp = t_1;
	elseif (z <= -9.5e+23)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 2.5e+21)
		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 <= -1.56e+72)
		tmp = t_1;
	elseif (z <= -9.5e+23)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 2.5e+21)
		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, -1.56e+72], t$95$1, If[LessEqual[z, -9.5e+23], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+21], 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 < -1.56e72 or 2.5e21 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in x around 0 43.3%

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

      1. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   if -1.56e72 < z < -9.50000000000000038e23

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf 74.9%

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

      1. div-sub 74.9%

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

   5. Simplified 74.9%

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

   if -9.50000000000000038e23 < z < 2.5e21

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 70.9%

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

      1. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+24}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -4.2e+71)
     t_1
     (if (<= z -1.15e+24)
       (/ (- t x) (/ (- a z) y))
       (if (<= z 2.8e+21) (+ 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 <= -4.2e+71) {
		tmp = t_1;
	} else if (z <= -1.15e+24) {
		tmp = (t - x) / ((a - z) / y);
	} else if (z <= 2.8e+21) {
		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 <= (-4.2d+71)) then
        tmp = t_1
    else if (z <= (-1.15d+24)) then
        tmp = (t - x) / ((a - z) / y)
    else if (z <= 2.8d+21) 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 <= -4.2e+71) {
		tmp = t_1;
	} else if (z <= -1.15e+24) {
		tmp = (t - x) / ((a - z) / y);
	} else if (z <= 2.8e+21) {
		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 <= -4.2e+71:
		tmp = t_1
	elif z <= -1.15e+24:
		tmp = (t - x) / ((a - z) / y)
	elif z <= 2.8e+21:
		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 <= -4.2e+71)
		tmp = t_1;
	elseif (z <= -1.15e+24)
		tmp = Float64(Float64(t - x) / Float64(Float64(a - z) / y));
	elseif (z <= 2.8e+21)
		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 <= -4.2e+71)
		tmp = t_1;
	elseif (z <= -1.15e+24)
		tmp = (t - x) / ((a - z) / y);
	elseif (z <= 2.8e+21)
		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, -4.2e+71], t$95$1, If[LessEqual[z, -1.15e+24], N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+21], 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 < -4.19999999999999978e71 or 2.8e21 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in x around 0 43.3%

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

      1. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   if -4.19999999999999978e71 < z < -1.15e24

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf 74.9%

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

      1. div-sub 74.9%

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

   5. Simplified 74.9%

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

      1. clear-num 74.7%

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

      2. div-inv 74.9%

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

   7. Applied egg-rr 74.9%

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

      1. associate-/r/ 74.9%

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

   9. Simplified 74.9%

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

       1. *-commutative 74.9%

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

       2. clear-num 74.7%

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

       3. un-div-inv 75.0%

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

   11. Applied egg-rr 75.0%

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

   if -1.15e24 < z < 2.8e21

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 70.9%

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

      1. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+24}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.9e+38)
     t_1
     (if (<= a -5e-96) t (if (<= a 4.8e-7) (* y (/ (- x t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.9e+38) {
		tmp = t_1;
	} else if (a <= -5e-96) {
		tmp = t;
	} else if (a <= 4.8e-7) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (a <= (-1.9d+38)) then
        tmp = t_1
    else if (a <= (-5d-96)) then
        tmp = t
    else if (a <= 4.8d-7) then
        tmp = y * ((x - t) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.9e+38) {
		tmp = t_1;
	} else if (a <= -5e-96) {
		tmp = t;
	} else if (a <= 4.8e-7) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.9e+38:
		tmp = t_1
	elif a <= -5e-96:
		tmp = t
	elif a <= 4.8e-7:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.9e+38)
		tmp = t_1;
	elseif (a <= -5e-96)
		tmp = t;
	elseif (a <= 4.8e-7)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.9e+38)
		tmp = t_1;
	elseif (a <= -5e-96)
		tmp = t;
	elseif (a <= 4.8e-7)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+38], t$95$1, If[LessEqual[a, -5e-96], t, If[LessEqual[a, 4.8e-7], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999e38 or 4.79999999999999957e-7 < a

   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 inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. unsub-neg 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in z around 0 51.3%

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

   if -1.8999999999999999e38 < a < -4.99999999999999995e-96

   1. Initial program 61.7%

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

   3. Taylor expanded in z around inf 42.8%

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

   if -4.99999999999999995e-96 < a < 4.79999999999999957e-7

   1. Initial program 76.8%

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

   3. Taylor expanded in y around inf 59.6%

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

      1. div-sub 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in a around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-neg-frac2 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-96}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -122 \lor \neg \left(z \leq 2.8 \cdot 10^{+21}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -122.0) (not (<= z 2.8e+21)))
   (+ t (* (/ (- t x) z) (- a y)))
   (+ x (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -122.0) || !(z <= 2.8e+21)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-122.0d0)) .or. (.not. (z <= 2.8d+21))) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + (y * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -122.0) || !(z <= 2.8e+21)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -122.0) or not (z <= 2.8e+21):
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -122.0) || !(z <= 2.8e+21))
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -122.0) || ~((z <= 2.8e+21)))
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -122.0], N[Not[LessEqual[z, 2.8e+21]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -122 or 2.8e21 < z

   1. Initial program 65.3%

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

   3. Taylor expanded in z around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. distribute-lft-out-- 65.9%

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

      3. div-sub 65.9%

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

      4. mul-1-neg 65.9%

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

      5. unsub-neg 65.9%

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

      6. div-sub 65.9%

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

      7. associate-/l* 73.6%

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

      8. associate-/l* 79.9%

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

      9. distribute-rgt-out-- 80.0%

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

   5. Simplified 80.0%

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

   if -122 < z < 2.8e21

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 71.7%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -122 \lor \neg \left(z \leq 2.8 \cdot 10^{+21}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-23} \lor \neg \left(t \leq 3 \cdot 10^{-85}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.1e-23) (not (<= t 3e-85)))
   (* t (/ (- y z) (- a z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.1e-23) || !(t <= 3e-85)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.1d-23)) .or. (.not. (t <= 3d-85))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.1e-23) || !(t <= 3e-85)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.1e-23) or not (t <= 3e-85):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.1e-23) || !(t <= 3e-85))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.1e-23) || ~((t <= 3e-85)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.1e-23], N[Not[LessEqual[t, 3e-85]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.10000000000000011e-23 or 3.00000000000000022e-85 < t

   1. Initial program 85.5%

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

   3. Taylor expanded in x around 0 51.0%

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

      1. associate-/l* 72.1%

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

   5. Simplified 72.1%

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

   if -5.10000000000000011e-23 < t < 3.00000000000000022e-85

   1. Initial program 71.9%

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

   3. Taylor expanded in x around inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in z around 0 52.7%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-23} \lor \neg \left(t \leq 3 \cdot 10^{-85}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.2e+102)
   (* y (/ (- t x) (- a z)))
   (if (<= x 1.3e+19) (* t (/ (- y z) (- a z))) (* x (+ (/ (- z y) a) 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.2e+102) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 1.3e+19) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (((z - y) / a) + 1.0);
	}
	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 (x <= (-1.2d+102)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= 1.3d+19) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * (((z - y) / a) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.2e+102) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 1.3e+19) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * (((z - y) / a) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.2e+102:
		tmp = y * ((t - x) / (a - z))
	elif x <= 1.3e+19:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * (((z - y) / a) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.2e+102)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= 1.3e+19)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.2e+102)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= 1.3e+19)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * (((z - y) / a) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.2e+102], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+19], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.19999999999999997e102

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf 55.4%

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

      1. div-sub 62.5%

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

   5. Simplified 62.5%

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

   if -1.19999999999999997e102 < x < 1.3e19

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0 53.6%

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

      1. associate-/l* 68.2%

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

   5. Simplified 68.2%

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

   if 1.3e19 < x

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in a around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

   8. Simplified 53.0%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 68000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.1e+71) t (if (<= z 68000000000000.0) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.1e+71) {
		tmp = t;
	} else if (z <= 68000000000000.0) {
		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 <= (-4.1d+71)) then
        tmp = t
    else if (z <= 68000000000000.0d0) 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 <= -4.1e+71) {
		tmp = t;
	} else if (z <= 68000000000000.0) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.1e+71:
		tmp = t
	elif z <= 68000000000000.0:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.1e+71)
		tmp = t;
	elseif (z <= 68000000000000.0)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.1e+71)
		tmp = t;
	elseif (z <= 68000000000000.0)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.1e+71], t, If[LessEqual[z, 68000000000000.0], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1000000000000002e71 or 6.8e13 < z

   1. Initial program 64.0%

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

   3. Taylor expanded in z around inf 45.3%

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

   if -4.1000000000000002e71 < z < 6.8e13

   1. Initial program 93.6%

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

   3. Taylor expanded in a around inf 34.1%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 68000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 24.8% 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 79.7%

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

3. Taylor expanded in z around inf 24.7%

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

4. Final simplification 24.7%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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)))))