Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.9% → 90.8%

Time: 16.9s

Alternatives: 21

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: 79.9% 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: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{a - z}{x - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-192)
     t_1
     (if (<= t_1 0.0)
       (+ t (* (- t x) (/ (- a y) z)))
       (- x (/ (- y z) (/ (- a z) (- x t))))))))

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 <= -2e-192) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x - ((y - z) / ((a - z) / (x - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-2d-192)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t + ((t - x) * ((a - y) / z))
    else
        tmp = x - ((y - z) / ((a - z) / (x - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-192) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x - ((y - z) / ((a - z) / (x - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -2e-192:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + ((t - x) * ((a - y) / z))
	else:
		tmp = x - ((y - z) / ((a - z) / (x - t)))
	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 <= -2e-192)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(x - t))));
	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 <= -2e-192)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + ((t - x) * ((a - y) / z));
	else
		tmp = x - ((y - z) / ((a - z) / (x - t)));
	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[LessEqual[t$95$1, -2e-192], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000002e-192

   1. Initial program 93.8%

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

   if -2.0000000000000002e-192 < (+.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 67.9%

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

      1. associate--l+ 67.9%

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

      2. distribute-lft-out-- 67.9%

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

      3. div-sub 67.9%

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

      4. mul-1-neg 67.9%

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

      5. unsub-neg 67.9%

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

      6. distribute-rgt-out-- 68.3%

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

      7. associate-/l* 93.5%

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

   5. Simplified 93.5%

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

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

   1. Initial program 91.4%

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

      1. clear-num 91.4%

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

      2. un-div-inv 92.0%

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

   4. Applied egg-rr 92.0%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-192}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{a - z}{x - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-192} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-192) (not (<= t_1 0.0)))
     t_1
     (+ t (* (- t x) (/ (- a y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-192) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((t - x) * ((a - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-192)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((t - x) * ((a - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-192) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((t - x) * ((a - y) / 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 <= -2e-192) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((t - x) * ((a - y) / 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 <= -2e-192) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / 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 <= -2e-192) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((t - x) * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-192], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $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)))) < -2.0000000000000002e-192 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.5%

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

   if -2.0000000000000002e-192 < (+.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 67.9%

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

      1. associate--l+ 67.9%

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

      2. distribute-lft-out-- 67.9%

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

      3. div-sub 67.9%

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

      4. mul-1-neg 67.9%

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

      5. unsub-neg 67.9%

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

      6. distribute-rgt-out-- 68.3%

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

      7. associate-/l* 93.5%

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

   5. Simplified 93.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-192} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -0.0003:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-177}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-26} \lor \neg \left(a \leq 6.6 \cdot 10^{+59}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -0.0003)
     t_2
     (if (<= a -6.6e-226)
       t_1
       (if (<= a 3.3e-177)
         (* (- t x) (/ y (- a z)))
         (if (<= a 7e-101)
           (* t (/ (- z y) z))
           (if (or (<= a 3e-26) (not (<= a 6.6e+59))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -0.0003) {
		tmp = t_2;
	} else if (a <= -6.6e-226) {
		tmp = t_1;
	} else if (a <= 3.3e-177) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 7e-101) {
		tmp = t * ((z - y) / z);
	} else if ((a <= 3e-26) || !(a <= 6.6e+59)) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * (t / (a - z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-0.0003d0)) then
        tmp = t_2
    else if (a <= (-6.6d-226)) then
        tmp = t_1
    else if (a <= 3.3d-177) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 7d-101) then
        tmp = t * ((z - y) / z)
    else if ((a <= 3d-26) .or. (.not. (a <= 6.6d+59))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -0.0003) {
		tmp = t_2;
	} else if (a <= -6.6e-226) {
		tmp = t_1;
	} else if (a <= 3.3e-177) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 7e-101) {
		tmp = t * ((z - y) / z);
	} else if ((a <= 3e-26) || !(a <= 6.6e+59)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -0.0003:
		tmp = t_2
	elif a <= -6.6e-226:
		tmp = t_1
	elif a <= 3.3e-177:
		tmp = (t - x) * (y / (a - z))
	elif a <= 7e-101:
		tmp = t * ((z - y) / z)
	elif (a <= 3e-26) or not (a <= 6.6e+59):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -0.0003)
		tmp = t_2;
	elseif (a <= -6.6e-226)
		tmp = t_1;
	elseif (a <= 3.3e-177)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 7e-101)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif ((a <= 3e-26) || !(a <= 6.6e+59))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -0.0003)
		tmp = t_2;
	elseif (a <= -6.6e-226)
		tmp = t_1;
	elseif (a <= 3.3e-177)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 7e-101)
		tmp = t * ((z - y) / z);
	elseif ((a <= 3e-26) || ~((a <= 6.6e+59)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0003], t$95$2, If[LessEqual[a, -6.6e-226], t$95$1, If[LessEqual[a, 3.3e-177], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-101], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 3e-26], N[Not[LessEqual[a, 6.6e+59]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.99999999999999974e-4 or 6.99999999999999989e-101 < a < 3.00000000000000012e-26 or 6.5999999999999999e59 < a

   1. Initial program 88.4%

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

      1. clear-num 87.3%

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

      2. un-div-inv 87.4%

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

   4. Applied egg-rr 87.4%

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

   5. Taylor expanded in z around 0 62.5%

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

      1. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   if -2.99999999999999974e-4 < a < -6.6e-226 or 3.00000000000000012e-26 < a < 6.5999999999999999e59

   1. Initial program 80.9%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 72.9%

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

   5. Simplified 72.9%

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

   if -6.6e-226 < a < 3.3e-177

   1. Initial program 71.5%

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

   3. Taylor expanded in y around -inf 71.5%

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

      1. associate-/l* 71.6%

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

      2. *-un-lft-identity 71.6%

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

      3. associate-*l/ 71.5%

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

      4. associate-*r* 75.6%

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

      5. div-inv 75.7%

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

   5. Applied egg-rr 75.7%

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

   if 3.3e-177 < a < 6.99999999999999989e-101

   1. Initial program 64.6%

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

   3. Taylor expanded in t around inf 63.3%

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

   4. Taylor expanded in a around 0 72.1%

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

      1. associate-*r/ 72.1%

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

      2. neg-mul-1 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in z around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

   9. Simplified 72.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0003:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-226}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-177}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-26} \lor \neg \left(a \leq 6.6 \cdot 10^{+59}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;a \leq -0.0028:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-227}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (* t (/ (- z y) z))))
   (if (<= a -0.0028)
     (- x (* y (/ x a)))
     (if (<= a -5.8e-111)
       t_1
       (if (<= a -4.5e-227)
         t_2
         (if (<= a 5.8e-181)
           (* (/ y z) (- x t))
           (if (<= a 4.7e-107)
             t_2
             (if (<= a 1.2e+82) t_1 (* x (- 1.0 (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((z - y) / z);
	double tmp;
	if (a <= -0.0028) {
		tmp = x - (y * (x / a));
	} else if (a <= -5.8e-111) {
		tmp = t_1;
	} else if (a <= -4.5e-227) {
		tmp = t_2;
	} else if (a <= 5.8e-181) {
		tmp = (y / z) * (x - t);
	} else if (a <= 4.7e-107) {
		tmp = t_2;
	} else if (a <= 1.2e+82) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = t * ((z - y) / z)
    if (a <= (-0.0028d0)) then
        tmp = x - (y * (x / a))
    else if (a <= (-5.8d-111)) then
        tmp = t_1
    else if (a <= (-4.5d-227)) then
        tmp = t_2
    else if (a <= 5.8d-181) then
        tmp = (y / z) * (x - t)
    else if (a <= 4.7d-107) then
        tmp = t_2
    else if (a <= 1.2d+82) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = t * ((z - y) / z);
	double tmp;
	if (a <= -0.0028) {
		tmp = x - (y * (x / a));
	} else if (a <= -5.8e-111) {
		tmp = t_1;
	} else if (a <= -4.5e-227) {
		tmp = t_2;
	} else if (a <= 5.8e-181) {
		tmp = (y / z) * (x - t);
	} else if (a <= 4.7e-107) {
		tmp = t_2;
	} else if (a <= 1.2e+82) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = t * ((z - y) / z)
	tmp = 0
	if a <= -0.0028:
		tmp = x - (y * (x / a))
	elif a <= -5.8e-111:
		tmp = t_1
	elif a <= -4.5e-227:
		tmp = t_2
	elif a <= 5.8e-181:
		tmp = (y / z) * (x - t)
	elif a <= 4.7e-107:
		tmp = t_2
	elif a <= 1.2e+82:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (a <= -0.0028)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (a <= -5.8e-111)
		tmp = t_1;
	elseif (a <= -4.5e-227)
		tmp = t_2;
	elseif (a <= 5.8e-181)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 4.7e-107)
		tmp = t_2;
	elseif (a <= 1.2e+82)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = t * ((z - y) / z);
	tmp = 0.0;
	if (a <= -0.0028)
		tmp = x - (y * (x / a));
	elseif (a <= -5.8e-111)
		tmp = t_1;
	elseif (a <= -4.5e-227)
		tmp = t_2;
	elseif (a <= 5.8e-181)
		tmp = (y / z) * (x - t);
	elseif (a <= 4.7e-107)
		tmp = t_2;
	elseif (a <= 1.2e+82)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0028], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.8e-111], t$95$1, If[LessEqual[a, -4.5e-227], t$95$2, If[LessEqual[a, 5.8e-181], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e-107], t$95$2, If[LessEqual[a, 1.2e+82], t$95$1, N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -0.00279999999999999997

   1. Initial program 86.0%

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

      1. clear-num 83.8%

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

      2. un-div-inv 83.8%

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

   4. Applied egg-rr 83.8%

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

   5. Taylor expanded in z around 0 69.9%

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

      1. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in t around 0 65.7%

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

      1. neg-mul-1 65.7%

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

      2. distribute-neg-frac2 65.7%

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

   10. Simplified 65.7%

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

   if -0.00279999999999999997 < a < -5.80000000000000003e-111 or 4.69999999999999998e-107 < a < 1.19999999999999999e82

   1. Initial program 90.0%

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

   3. Taylor expanded in y around inf 63.5%

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

      1. div-sub 65.2%

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

   5. Simplified 65.2%

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

   if -5.80000000000000003e-111 < a < -4.49999999999999993e-227 or 5.7999999999999996e-181 < a < 4.69999999999999998e-107

   1. Initial program 66.2%

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

   3. Taylor expanded in t around inf 76.1%

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

   4. Taylor expanded in a around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in z around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. unsub-neg 71.0%

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

   9. Simplified 71.0%

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

   if -4.49999999999999993e-227 < a < 5.7999999999999996e-181

   1. Initial program 72.8%

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

   3. Taylor expanded in y around -inf 70.9%

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

   4. Taylor expanded in a around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. associate-*r* 69.2%

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

      3. *-commutative 69.2%

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

      4. neg-mul-1 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in y around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*r/ 73.5%

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

      4. distribute-rgt-neg-in 73.5%

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

      5. distribute-frac-neg 73.5%

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

   9. Simplified 73.5%

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

   if 1.19999999999999999e82 < a

   1. Initial program 89.5%

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

      1. clear-num 89.0%

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

      2. un-div-inv 89.1%

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

   4. Applied egg-rr 89.1%

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

   5. Taylor expanded in z around 0 55.4%

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

      1. associate-/l* 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in x around inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

   10. Simplified 66.5%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0028:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -0.00086:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-179}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))) (t_2 (+ x (* (- t x) (/ y a)))))
   (if (<= a -0.00086)
     t_2
     (if (<= a -1.2e-226)
       t_1
       (if (<= a 9e-179)
         (* (- t x) (/ y (- a z)))
         (if (<= a 1.04e-100)
           (* t (/ (- z y) z))
           (if (<= a 2.7e-30)
             (+ x (* y (/ (- t x) a)))
             (if (<= a 1.55e+60) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -0.00086) {
		tmp = t_2;
	} else if (a <= -1.2e-226) {
		tmp = t_1;
	} else if (a <= 9e-179) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.04e-100) {
		tmp = t * ((z - y) / z);
	} else if (a <= 2.7e-30) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 1.55e+60) {
		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 = (y - z) * (t / (a - z))
    t_2 = x + ((t - x) * (y / a))
    if (a <= (-0.00086d0)) then
        tmp = t_2
    else if (a <= (-1.2d-226)) then
        tmp = t_1
    else if (a <= 9d-179) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 1.04d-100) then
        tmp = t * ((z - y) / z)
    else if (a <= 2.7d-30) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= 1.55d+60) 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 = (y - z) * (t / (a - z));
	double t_2 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -0.00086) {
		tmp = t_2;
	} else if (a <= -1.2e-226) {
		tmp = t_1;
	} else if (a <= 9e-179) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 1.04e-100) {
		tmp = t * ((z - y) / z);
	} else if (a <= 2.7e-30) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 1.55e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	t_2 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -0.00086:
		tmp = t_2
	elif a <= -1.2e-226:
		tmp = t_1
	elif a <= 9e-179:
		tmp = (t - x) * (y / (a - z))
	elif a <= 1.04e-100:
		tmp = t * ((z - y) / z)
	elif a <= 2.7e-30:
		tmp = x + (y * ((t - x) / a))
	elif a <= 1.55e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -0.00086)
		tmp = t_2;
	elseif (a <= -1.2e-226)
		tmp = t_1;
	elseif (a <= 9e-179)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 1.04e-100)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (a <= 2.7e-30)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= 1.55e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	t_2 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -0.00086)
		tmp = t_2;
	elseif (a <= -1.2e-226)
		tmp = t_1;
	elseif (a <= 9e-179)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 1.04e-100)
		tmp = t * ((z - y) / z);
	elseif (a <= 2.7e-30)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= 1.55e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00086], t$95$2, If[LessEqual[a, -1.2e-226], t$95$1, If[LessEqual[a, 9e-179], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.04e-100], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-30], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+60], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.59999999999999979e-4 or 1.55e60 < a

   1. Initial program 87.7%

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

   3. Taylor expanded in z around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. associate-/l* 72.8%

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

   5. Simplified 72.8%

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

   if -8.59999999999999979e-4 < a < -1.2e-226 or 2.69999999999999987e-30 < a < 1.55e60

   1. Initial program 80.9%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/l* 72.9%

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

   5. Simplified 72.9%

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

   if -1.2e-226 < a < 8.99999999999999984e-179

   1. Initial program 71.5%

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

   3. Taylor expanded in y around -inf 71.5%

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

      1. associate-/l* 71.6%

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

      2. *-un-lft-identity 71.6%

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

      3. associate-*l/ 71.5%

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

      4. associate-*r* 75.6%

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

      5. div-inv 75.7%

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

   5. Applied egg-rr 75.7%

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

   if 8.99999999999999984e-179 < a < 1.04e-100

   1. Initial program 64.6%

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

   3. Taylor expanded in t around inf 63.3%

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

   4. Taylor expanded in a around 0 72.1%

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

      1. associate-*r/ 72.1%

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

      2. neg-mul-1 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in z around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

   9. Simplified 72.1%

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

   if 1.04e-100 < a < 2.69999999999999987e-30

   1. Initial program 93.8%

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

      1. clear-num 93.7%

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

      2. un-div-inv 93.9%

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

   4. Applied egg-rr 93.9%

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

   5. Taylor expanded in z around 0 67.7%

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

      1. associate-/l* 67.7%

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

   7. Simplified 67.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00086:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-226}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-179}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+60}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -0.00036:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-38}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -0.00036)
     t_2
     (if (<= a -9.5e-228)
       t_1
       (if (<= a 2.5e-181)
         (* (/ y z) (- x t))
         (if (<= a 5.2e-104)
           t_1
           (if (<= a 9.2e-38)
             (+ x (* y (/ t a)))
             (if (<= a 1.15e+68) 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 <= -0.00036) {
		tmp = t_2;
	} else if (a <= -9.5e-228) {
		tmp = t_1;
	} else if (a <= 2.5e-181) {
		tmp = (y / z) * (x - t);
	} else if (a <= 5.2e-104) {
		tmp = t_1;
	} else if (a <= 9.2e-38) {
		tmp = x + (y * (t / a));
	} else if (a <= 1.15e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-0.00036d0)) then
        tmp = t_2
    else if (a <= (-9.5d-228)) then
        tmp = t_1
    else if (a <= 2.5d-181) then
        tmp = (y / z) * (x - t)
    else if (a <= 5.2d-104) then
        tmp = t_1
    else if (a <= 9.2d-38) then
        tmp = x + (y * (t / a))
    else if (a <= 1.15d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -0.00036) {
		tmp = t_2;
	} else if (a <= -9.5e-228) {
		tmp = t_1;
	} else if (a <= 2.5e-181) {
		tmp = (y / z) * (x - t);
	} else if (a <= 5.2e-104) {
		tmp = t_1;
	} else if (a <= 9.2e-38) {
		tmp = x + (y * (t / a));
	} else if (a <= 1.15e+68) {
		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 <= -0.00036:
		tmp = t_2
	elif a <= -9.5e-228:
		tmp = t_1
	elif a <= 2.5e-181:
		tmp = (y / z) * (x - t)
	elif a <= 5.2e-104:
		tmp = t_1
	elif a <= 9.2e-38:
		tmp = x + (y * (t / a))
	elif a <= 1.15e+68:
		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 <= -0.00036)
		tmp = t_2;
	elseif (a <= -9.5e-228)
		tmp = t_1;
	elseif (a <= 2.5e-181)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 5.2e-104)
		tmp = t_1;
	elseif (a <= 9.2e-38)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (a <= 1.15e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -0.00036)
		tmp = t_2;
	elseif (a <= -9.5e-228)
		tmp = t_1;
	elseif (a <= 2.5e-181)
		tmp = (y / z) * (x - t);
	elseif (a <= 5.2e-104)
		tmp = t_1;
	elseif (a <= 9.2e-38)
		tmp = x + (y * (t / a));
	elseif (a <= 1.15e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00036], t$95$2, If[LessEqual[a, -9.5e-228], t$95$1, If[LessEqual[a, 2.5e-181], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-104], t$95$1, If[LessEqual[a, 9.2e-38], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+68], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.60000000000000023e-4 or 1.15e68 < a

   1. Initial program 87.3%

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

      1. clear-num 86.0%

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

      2. un-div-inv 86.0%

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

   4. Applied egg-rr 86.0%

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

   5. Taylor expanded in z around 0 61.9%

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

      1. associate-/l* 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in x around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unsub-neg 65.4%

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

   10. Simplified 65.4%

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

   if -3.60000000000000023e-4 < a < -9.50000000000000024e-228 or 2.5000000000000001e-181 < a < 5.20000000000000005e-104 or 9.20000000000000007e-38 < a < 1.15e68

   1. Initial program 77.9%

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

   3. Taylor expanded in t around inf 73.8%

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

   4. Taylor expanded in a around 0 60.4%

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

      1. associate-*r/ 60.4%

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

      2. neg-mul-1 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. unsub-neg 60.4%

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

   9. Simplified 60.4%

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

   if -9.50000000000000024e-228 < a < 2.5000000000000001e-181

   1. Initial program 72.8%

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

   3. Taylor expanded in y around -inf 70.9%

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

   4. Taylor expanded in a around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. associate-*r* 69.2%

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

      3. *-commutative 69.2%

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

      4. neg-mul-1 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in y around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*r/ 73.5%

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

      4. distribute-rgt-neg-in 73.5%

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

      5. distribute-frac-neg 73.5%

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

   9. Simplified 73.5%

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

   if 5.20000000000000005e-104 < a < 9.20000000000000007e-38

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 69.9%

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

      1. associate-/l* 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in t around inf 63.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00036:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-228}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-104}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-38}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;a \leq -0.0017:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-180}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-38}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))))
   (if (<= a -0.0017)
     (- x (* y (/ x a)))
     (if (<= a -2.6e-227)
       t_1
       (if (<= a 1.85e-180)
         (* (/ y z) (- x t))
         (if (<= a 1.04e-100)
           t_1
           (if (<= a 9.2e-38)
             (+ x (* y (/ t a)))
             (if (<= a 8.8e+67) t_1 (* x (- 1.0 (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -0.0017) {
		tmp = x - (y * (x / a));
	} else if (a <= -2.6e-227) {
		tmp = t_1;
	} else if (a <= 1.85e-180) {
		tmp = (y / z) * (x - t);
	} else if (a <= 1.04e-100) {
		tmp = t_1;
	} else if (a <= 9.2e-38) {
		tmp = x + (y * (t / a));
	} else if (a <= 8.8e+67) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    if (a <= (-0.0017d0)) then
        tmp = x - (y * (x / a))
    else if (a <= (-2.6d-227)) then
        tmp = t_1
    else if (a <= 1.85d-180) then
        tmp = (y / z) * (x - t)
    else if (a <= 1.04d-100) then
        tmp = t_1
    else if (a <= 9.2d-38) then
        tmp = x + (y * (t / a))
    else if (a <= 8.8d+67) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -0.0017) {
		tmp = x - (y * (x / a));
	} else if (a <= -2.6e-227) {
		tmp = t_1;
	} else if (a <= 1.85e-180) {
		tmp = (y / z) * (x - t);
	} else if (a <= 1.04e-100) {
		tmp = t_1;
	} else if (a <= 9.2e-38) {
		tmp = x + (y * (t / a));
	} else if (a <= 8.8e+67) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	tmp = 0
	if a <= -0.0017:
		tmp = x - (y * (x / a))
	elif a <= -2.6e-227:
		tmp = t_1
	elif a <= 1.85e-180:
		tmp = (y / z) * (x - t)
	elif a <= 1.04e-100:
		tmp = t_1
	elif a <= 9.2e-38:
		tmp = x + (y * (t / a))
	elif a <= 8.8e+67:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (a <= -0.0017)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (a <= -2.6e-227)
		tmp = t_1;
	elseif (a <= 1.85e-180)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 1.04e-100)
		tmp = t_1;
	elseif (a <= 9.2e-38)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (a <= 8.8e+67)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	tmp = 0.0;
	if (a <= -0.0017)
		tmp = x - (y * (x / a));
	elseif (a <= -2.6e-227)
		tmp = t_1;
	elseif (a <= 1.85e-180)
		tmp = (y / z) * (x - t);
	elseif (a <= 1.04e-100)
		tmp = t_1;
	elseif (a <= 9.2e-38)
		tmp = x + (y * (t / a));
	elseif (a <= 8.8e+67)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0017], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-227], t$95$1, If[LessEqual[a, 1.85e-180], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.04e-100], t$95$1, If[LessEqual[a, 9.2e-38], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+67], t$95$1, N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -0.00169999999999999991

   1. Initial program 86.0%

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

      1. clear-num 83.8%

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

      2. un-div-inv 83.8%

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

   4. Applied egg-rr 83.8%

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

   5. Taylor expanded in z around 0 69.9%

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

      1. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in t around 0 65.7%

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

      1. neg-mul-1 65.7%

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

      2. distribute-neg-frac2 65.7%

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

   10. Simplified 65.7%

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

   if -0.00169999999999999991 < a < -2.60000000000000011e-227 or 1.85000000000000008e-180 < a < 1.04e-100 or 9.20000000000000007e-38 < a < 8.8e67

   1. Initial program 77.9%

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

   3. Taylor expanded in t around inf 73.8%

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

   4. Taylor expanded in a around 0 60.4%

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

      1. associate-*r/ 60.4%

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

      2. neg-mul-1 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. unsub-neg 60.4%

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

   9. Simplified 60.4%

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

   if -2.60000000000000011e-227 < a < 1.85000000000000008e-180

   1. Initial program 72.8%

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

   3. Taylor expanded in y around -inf 70.9%

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

   4. Taylor expanded in a around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. associate-*r* 69.2%

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

      3. *-commutative 69.2%

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

      4. neg-mul-1 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in y around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*r/ 73.5%

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

      4. distribute-rgt-neg-in 73.5%

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

      5. distribute-frac-neg 73.5%

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

   9. Simplified 73.5%

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

   if 1.04e-100 < a < 9.20000000000000007e-38

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 69.9%

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

      1. associate-/l* 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in t around inf 63.9%

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

   if 8.8e67 < a

   1. Initial program 88.4%

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

      1. clear-num 88.0%

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

      2. un-div-inv 88.1%

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in z around 0 54.5%

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

      1. associate-/l* 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in x around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

   10. Simplified 65.1%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0017:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-180}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-100}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-38}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -0.00037:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -0.00037)
     x
     (if (<= a -1.15e-110)
       (* y (/ t a))
       (if (<= a -2.6e-226)
         t
         (if (<= a 5.2e-180)
           t_1
           (if (<= a 5.5e+60) t (if (<= a 1.32e+82) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -0.00037) {
		tmp = x;
	} else if (a <= -1.15e-110) {
		tmp = y * (t / a);
	} else if (a <= -2.6e-226) {
		tmp = t;
	} else if (a <= 5.2e-180) {
		tmp = t_1;
	} else if (a <= 5.5e+60) {
		tmp = t;
	} else if (a <= 1.32e+82) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-0.00037d0)) then
        tmp = x
    else if (a <= (-1.15d-110)) then
        tmp = y * (t / a)
    else if (a <= (-2.6d-226)) then
        tmp = t
    else if (a <= 5.2d-180) then
        tmp = t_1
    else if (a <= 5.5d+60) then
        tmp = t
    else if (a <= 1.32d+82) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -0.00037) {
		tmp = x;
	} else if (a <= -1.15e-110) {
		tmp = y * (t / a);
	} else if (a <= -2.6e-226) {
		tmp = t;
	} else if (a <= 5.2e-180) {
		tmp = t_1;
	} else if (a <= 5.5e+60) {
		tmp = t;
	} else if (a <= 1.32e+82) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -0.00037:
		tmp = x
	elif a <= -1.15e-110:
		tmp = y * (t / a)
	elif a <= -2.6e-226:
		tmp = t
	elif a <= 5.2e-180:
		tmp = t_1
	elif a <= 5.5e+60:
		tmp = t
	elif a <= 1.32e+82:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -0.00037)
		tmp = x;
	elseif (a <= -1.15e-110)
		tmp = Float64(y * Float64(t / a));
	elseif (a <= -2.6e-226)
		tmp = t;
	elseif (a <= 5.2e-180)
		tmp = t_1;
	elseif (a <= 5.5e+60)
		tmp = t;
	elseif (a <= 1.32e+82)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -0.00037)
		tmp = x;
	elseif (a <= -1.15e-110)
		tmp = y * (t / a);
	elseif (a <= -2.6e-226)
		tmp = t;
	elseif (a <= 5.2e-180)
		tmp = t_1;
	elseif (a <= 5.5e+60)
		tmp = t;
	elseif (a <= 1.32e+82)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00037], x, If[LessEqual[a, -1.15e-110], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-226], t, If[LessEqual[a, 5.2e-180], t$95$1, If[LessEqual[a, 5.5e+60], t, If[LessEqual[a, 1.32e+82], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.6999999999999999e-4 or 1.32e82 < a

   1. Initial program 87.7%

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

   3. Taylor expanded in a around inf 52.1%

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

   if -3.6999999999999999e-4 < a < -1.1500000000000001e-110

   1. Initial program 88.8%

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

   3. Taylor expanded in x around 0 65.8%

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

      1. *-commutative 65.8%

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

      2. associate-/l* 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in z around 0 38.6%

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

      1. associate-/l* 34.8%

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

   8. Simplified 34.8%

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

      1. clear-num 34.8%

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

      2. un-div-inv 34.8%

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

   10. Applied egg-rr 34.8%

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

       1. associate-/r/ 38.9%

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

   12. Simplified 38.9%

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

   if -1.1500000000000001e-110 < a < -2.5999999999999998e-226 or 5.1999999999999998e-180 < a < 5.5000000000000001e60

   1. Initial program 77.0%

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

   3. Taylor expanded in z around inf 45.5%

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

   if -2.5999999999999998e-226 < a < 5.1999999999999998e-180 or 5.5000000000000001e60 < a < 1.32e82

   1. Initial program 74.9%

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

   3. Taylor expanded in y around -inf 71.6%

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

   4. Taylor expanded in a around 0 66.6%

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

      1. associate-*r/ 66.6%

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

      2. associate-*r* 66.6%

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

      3. *-commutative 66.6%

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

      4. neg-mul-1 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in t around 0 45.5%

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

      1. associate-/l* 49.2%

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

   9. Simplified 49.2%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00037:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -0.00072:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-172}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))))
   (if (<= a -0.00072)
     (- x (* y (/ x a)))
     (if (<= a -5e-226)
       t_1
       (if (<= a 8e-172)
         (* (/ y z) (- x t))
         (if (<= a 3e+60)
           t_1
           (if (<= a 1.15e+82)
             (* y (/ (- t x) (- a z)))
             (* x (- 1.0 (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -0.00072) {
		tmp = x - (y * (x / a));
	} else if (a <= -5e-226) {
		tmp = t_1;
	} else if (a <= 8e-172) {
		tmp = (y / z) * (x - t);
	} else if (a <= 3e+60) {
		tmp = t_1;
	} else if (a <= 1.15e+82) {
		tmp = y * ((t - x) / (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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / (a - z))
    if (a <= (-0.00072d0)) then
        tmp = x - (y * (x / a))
    else if (a <= (-5d-226)) then
        tmp = t_1
    else if (a <= 8d-172) then
        tmp = (y / z) * (x - t)
    else if (a <= 3d+60) then
        tmp = t_1
    else if (a <= 1.15d+82) then
        tmp = y * ((t - x) / (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 t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -0.00072) {
		tmp = x - (y * (x / a));
	} else if (a <= -5e-226) {
		tmp = t_1;
	} else if (a <= 8e-172) {
		tmp = (y / z) * (x - t);
	} else if (a <= 3e+60) {
		tmp = t_1;
	} else if (a <= 1.15e+82) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	tmp = 0
	if a <= -0.00072:
		tmp = x - (y * (x / a))
	elif a <= -5e-226:
		tmp = t_1
	elif a <= 8e-172:
		tmp = (y / z) * (x - t)
	elif a <= 3e+60:
		tmp = t_1
	elif a <= 1.15e+82:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (a <= -0.00072)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (a <= -5e-226)
		tmp = t_1;
	elseif (a <= 8e-172)
		tmp = Float64(Float64(y / z) * Float64(x - t));
	elseif (a <= 3e+60)
		tmp = t_1;
	elseif (a <= 1.15e+82)
		tmp = Float64(y * Float64(Float64(t - x) / 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)
	t_1 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (a <= -0.00072)
		tmp = x - (y * (x / a));
	elseif (a <= -5e-226)
		tmp = t_1;
	elseif (a <= 8e-172)
		tmp = (y / z) * (x - t);
	elseif (a <= 3e+60)
		tmp = t_1;
	elseif (a <= 1.15e+82)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00072], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-226], t$95$1, If[LessEqual[a, 8e-172], N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+60], t$95$1, If[LessEqual[a, 1.15e+82], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.20000000000000045e-4

   1. Initial program 86.0%

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

      1. clear-num 83.8%

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

      2. un-div-inv 83.8%

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

   4. Applied egg-rr 83.8%

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

   5. Taylor expanded in z around 0 69.9%

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

      1. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in t around 0 65.7%

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

      1. neg-mul-1 65.7%

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

      2. distribute-neg-frac2 65.7%

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

   10. Simplified 65.7%

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

   if -7.20000000000000045e-4 < a < -4.9999999999999998e-226 or 8.0000000000000003e-172 < a < 2.9999999999999998e60

   1. Initial program 82.1%

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

   3. Taylor expanded in x around 0 56.4%

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

      1. *-commutative 56.4%

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

      2. associate-/l* 67.3%

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

   5. Simplified 67.3%

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

   if -4.9999999999999998e-226 < a < 8.0000000000000003e-172

   1. Initial program 70.1%

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

   3. Taylor expanded in y around -inf 70.2%

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

   4. Taylor expanded in a around 0 66.8%

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

      1. associate-*r/ 66.8%

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

      2. associate-*r* 66.8%

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

      3. *-commutative 66.8%

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

      4. neg-mul-1 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in y around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. *-commutative 66.8%

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

      3. associate-*r/ 70.9%

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

      4. distribute-rgt-neg-in 70.9%

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

      5. distribute-frac-neg 70.9%

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

   9. Simplified 70.9%

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

   if 2.9999999999999998e60 < a < 1.14999999999999994e82

   1. Initial program 85.5%

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

   3. Taylor expanded in y around inf 85.4%

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

      1. div-sub 85.4%

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

   5. Simplified 85.4%

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

   if 1.14999999999999994e82 < a

   1. Initial program 89.5%

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

      1. clear-num 89.0%

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

      2. un-div-inv 89.1%

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

   4. Applied egg-rr 89.1%

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

   5. Taylor expanded in z around 0 55.4%

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

      1. associate-/l* 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in x around inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. unsub-neg 66.5%

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

   10. Simplified 66.5%

       \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00072:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-226}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-172}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+60}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -0.0026:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= a -0.0026)
     x
     (if (<= a -9e-111)
       t_1
       (if (<= a -6.5e-226)
         t
         (if (<= a 1.02e-199) (* x (/ y z)) (if (<= a 1.65e+68) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -0.0026) {
		tmp = x;
	} else if (a <= -9e-111) {
		tmp = t_1;
	} else if (a <= -6.5e-226) {
		tmp = t;
	} else if (a <= 1.02e-199) {
		tmp = x * (y / z);
	} else if (a <= 1.65e+68) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (a <= (-0.0026d0)) then
        tmp = x
    else if (a <= (-9d-111)) then
        tmp = t_1
    else if (a <= (-6.5d-226)) then
        tmp = t
    else if (a <= 1.02d-199) then
        tmp = x * (y / z)
    else if (a <= 1.65d+68) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -0.0026) {
		tmp = x;
	} else if (a <= -9e-111) {
		tmp = t_1;
	} else if (a <= -6.5e-226) {
		tmp = t;
	} else if (a <= 1.02e-199) {
		tmp = x * (y / z);
	} else if (a <= 1.65e+68) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if a <= -0.0026:
		tmp = x
	elif a <= -9e-111:
		tmp = t_1
	elif a <= -6.5e-226:
		tmp = t
	elif a <= 1.02e-199:
		tmp = x * (y / z)
	elif a <= 1.65e+68:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (a <= -0.0026)
		tmp = x;
	elseif (a <= -9e-111)
		tmp = t_1;
	elseif (a <= -6.5e-226)
		tmp = t;
	elseif (a <= 1.02e-199)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.65e+68)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (a <= -0.0026)
		tmp = x;
	elseif (a <= -9e-111)
		tmp = t_1;
	elseif (a <= -6.5e-226)
		tmp = t;
	elseif (a <= 1.02e-199)
		tmp = x * (y / z);
	elseif (a <= 1.65e+68)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0026], x, If[LessEqual[a, -9e-111], t$95$1, If[LessEqual[a, -6.5e-226], t, If[LessEqual[a, 1.02e-199], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+68], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.0025999999999999999 or 1.65e68 < a

   1. Initial program 87.3%

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

   3. Taylor expanded in a around inf 50.5%

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

   if -0.0025999999999999999 < a < -8.99999999999999987e-111 or 1.02e-199 < a < 1.65e68

   1. Initial program 86.5%

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

   3. Taylor expanded in x around 0 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-/l* 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around inf 38.8%

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

      1. associate-*r/ 41.3%

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

   8. Simplified 41.3%

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

   if -8.99999999999999987e-111 < a < -6.50000000000000033e-226

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf 61.5%

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

   if -6.50000000000000033e-226 < a < 1.02e-199

   1. Initial program 70.3%

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

   3. Taylor expanded in y around -inf 70.4%

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

   4. Taylor expanded in a around 0 68.6%

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

      1. associate-*r/ 68.6%

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

      2. associate-*r* 68.6%

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

      3. *-commutative 68.6%

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

      4. neg-mul-1 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in t around 0 48.2%

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

      1. associate-/l* 50.8%

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

   9. Simplified 50.8%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0026:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-111}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-226}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-100}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-28} \lor \neg \left(a \leq 3.2 \cdot 10^{+65}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ a (- t x))))))
   (if (<= a -1.85e-54)
     t_1
     (if (<= a 1.04e-100)
       (+ t (* y (/ (- x t) z)))
       (if (or (<= a 2.4e-28) (not (<= a 3.2e+65)))
         t_1
         (* (- y z) (/ t (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -1.85e-54) {
		tmp = t_1;
	} else if (a <= 1.04e-100) {
		tmp = t + (y * ((x - t) / z));
	} else if ((a <= 2.4e-28) || !(a <= 3.2e+65)) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (t / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / (a / (t - x)))
    if (a <= (-1.85d-54)) then
        tmp = t_1
    else if (a <= 1.04d-100) then
        tmp = t + (y * ((x - t) / z))
    else if ((a <= 2.4d-28) .or. (.not. (a <= 3.2d+65))) then
        tmp = t_1
    else
        tmp = (y - z) * (t / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -1.85e-54) {
		tmp = t_1;
	} else if (a <= 1.04e-100) {
		tmp = t + (y * ((x - t) / z));
	} else if ((a <= 2.4e-28) || !(a <= 3.2e+65)) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (t / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (a / (t - x)))
	tmp = 0
	if a <= -1.85e-54:
		tmp = t_1
	elif a <= 1.04e-100:
		tmp = t + (y * ((x - t) / z))
	elif (a <= 2.4e-28) or not (a <= 3.2e+65):
		tmp = t_1
	else:
		tmp = (y - z) * (t / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -1.85e-54)
		tmp = t_1;
	elseif (a <= 1.04e-100)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif ((a <= 2.4e-28) || !(a <= 3.2e+65))
		tmp = t_1;
	else
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / (a / (t - x)));
	tmp = 0.0;
	if (a <= -1.85e-54)
		tmp = t_1;
	elseif (a <= 1.04e-100)
		tmp = t + (y * ((x - t) / z));
	elseif ((a <= 2.4e-28) || ~((a <= 3.2e+65)))
		tmp = t_1;
	else
		tmp = (y - z) * (t / (a - 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[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e-54], t$95$1, If[LessEqual[a, 1.04e-100], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 2.4e-28], N[Not[LessEqual[a, 3.2e+65]], $MachinePrecision]], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8500000000000001e-54 or 1.04e-100 < a < 2.4000000000000002e-28 or 3.20000000000000007e65 < a

   1. Initial program 88.0%

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

      1. clear-num 87.0%

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

      2. un-div-inv 87.6%

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

   4. Applied egg-rr 87.6%

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

   5. Taylor expanded in a around inf 75.5%

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

   if -1.8500000000000001e-54 < a < 1.04e-100

   1. Initial program 72.3%

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

   3. Taylor expanded in z around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. distribute-lft-out-- 81.8%

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

      3. div-sub 83.0%

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

      4. mul-1-neg 83.0%

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

      5. unsub-neg 83.0%

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

      6. distribute-rgt-out-- 83.0%

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

      7. associate-/l* 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in y around inf 81.8%

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

      1. associate-*r/ 86.7%

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

   8. Simplified 86.7%

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

   if 2.4000000000000002e-28 < a < 3.20000000000000007e65

   1. Initial program 92.5%

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

   3. Taylor expanded in x around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. associate-/l* 77.6%

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

   5. Simplified 77.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-100}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-28} \lor \neg \left(a \leq 3.2 \cdot 10^{+65}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -0.0024:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-227}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= a -0.0024)
     x
     (if (<= a -4e-227)
       t
       (if (<= a 1.26e-180)
         t_1
         (if (<= a 4e+60) t (if (<= a 1.32e+82) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -0.0024) {
		tmp = x;
	} else if (a <= -4e-227) {
		tmp = t;
	} else if (a <= 1.26e-180) {
		tmp = t_1;
	} else if (a <= 4e+60) {
		tmp = t;
	} else if (a <= 1.32e+82) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (a <= (-0.0024d0)) then
        tmp = x
    else if (a <= (-4d-227)) then
        tmp = t
    else if (a <= 1.26d-180) then
        tmp = t_1
    else if (a <= 4d+60) then
        tmp = t
    else if (a <= 1.32d+82) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (a <= -0.0024) {
		tmp = x;
	} else if (a <= -4e-227) {
		tmp = t;
	} else if (a <= 1.26e-180) {
		tmp = t_1;
	} else if (a <= 4e+60) {
		tmp = t;
	} else if (a <= 1.32e+82) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if a <= -0.0024:
		tmp = x
	elif a <= -4e-227:
		tmp = t
	elif a <= 1.26e-180:
		tmp = t_1
	elif a <= 4e+60:
		tmp = t
	elif a <= 1.32e+82:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -0.0024)
		tmp = x;
	elseif (a <= -4e-227)
		tmp = t;
	elseif (a <= 1.26e-180)
		tmp = t_1;
	elseif (a <= 4e+60)
		tmp = t;
	elseif (a <= 1.32e+82)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (a <= -0.0024)
		tmp = x;
	elseif (a <= -4e-227)
		tmp = t;
	elseif (a <= 1.26e-180)
		tmp = t_1;
	elseif (a <= 4e+60)
		tmp = t;
	elseif (a <= 1.32e+82)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0024], x, If[LessEqual[a, -4e-227], t, If[LessEqual[a, 1.26e-180], t$95$1, If[LessEqual[a, 4e+60], t, If[LessEqual[a, 1.32e+82], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.00239999999999999979 or 1.32e82 < a

   1. Initial program 87.7%

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

   3. Taylor expanded in a around inf 52.1%

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

   if -0.00239999999999999979 < a < -3.99999999999999978e-227 or 1.25999999999999997e-180 < a < 3.9999999999999998e60

   1. Initial program 80.4%

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

   3. Taylor expanded in z around inf 38.7%

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

   if -3.99999999999999978e-227 < a < 1.25999999999999997e-180 or 3.9999999999999998e60 < a < 1.32e82

   1. Initial program 74.9%

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

   3. Taylor expanded in y around -inf 71.6%

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

   4. Taylor expanded in a around 0 66.6%

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

      1. associate-*r/ 66.6%

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

      2. associate-*r* 66.6%

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

      3. *-commutative 66.6%

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

      4. neg-mul-1 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in t around 0 45.5%

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

      1. associate-/l* 49.2%

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

   9. Simplified 49.2%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0024:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-227}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+60}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -0.00105:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-174}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))))
   (if (<= a -0.00105)
     (- x (* y (/ x a)))
     (if (<= a -4.8e-227)
       t_1
       (if (<= a 2.5e-174)
         (* (- t x) (/ y (- a z)))
         (if (<= a 8.2e+67) t_1 (* x (- 1.0 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -0.00105) {
		tmp = x - (y * (x / a));
	} else if (a <= -4.8e-227) {
		tmp = t_1;
	} else if (a <= 2.5e-174) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 8.2e+67) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t / (a - z))
    if (a <= (-0.00105d0)) then
        tmp = x - (y * (x / a))
    else if (a <= (-4.8d-227)) then
        tmp = t_1
    else if (a <= 2.5d-174) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 8.2d+67) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (a <= -0.00105) {
		tmp = x - (y * (x / a));
	} else if (a <= -4.8e-227) {
		tmp = t_1;
	} else if (a <= 2.5e-174) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 8.2e+67) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	tmp = 0
	if a <= -0.00105:
		tmp = x - (y * (x / a))
	elif a <= -4.8e-227:
		tmp = t_1
	elif a <= 2.5e-174:
		tmp = (t - x) * (y / (a - z))
	elif a <= 8.2e+67:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (a <= -0.00105)
		tmp = Float64(x - Float64(y * Float64(x / a)));
	elseif (a <= -4.8e-227)
		tmp = t_1;
	elseif (a <= 2.5e-174)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 8.2e+67)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (a <= -0.00105)
		tmp = x - (y * (x / a));
	elseif (a <= -4.8e-227)
		tmp = t_1;
	elseif (a <= 2.5e-174)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 8.2e+67)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00105], N[(x - N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-227], t$95$1, If[LessEqual[a, 2.5e-174], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+67], t$95$1, N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.00104999999999999994

   1. Initial program 86.0%

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

      1. clear-num 83.8%

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

      2. un-div-inv 83.8%

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

   4. Applied egg-rr 83.8%

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

   5. Taylor expanded in z around 0 69.9%

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

      1. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in t around 0 65.7%

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

      1. neg-mul-1 65.7%

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

      2. distribute-neg-frac2 65.7%

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

   10. Simplified 65.7%

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

   if -0.00104999999999999994 < a < -4.7999999999999999e-227 or 2.5000000000000001e-174 < a < 8.19999999999999959e67

   1. Initial program 82.9%

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

   3. Taylor expanded in x around 0 56.2%

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

      1. *-commutative 56.2%

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

      2. associate-/l* 66.6%

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

   5. Simplified 66.6%

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

   if -4.7999999999999999e-227 < a < 2.5000000000000001e-174

   1. Initial program 70.1%

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

   3. Taylor expanded in y around -inf 70.2%

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

      1. associate-/l* 70.3%

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

      2. *-un-lft-identity 70.3%

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

      3. associate-*l/ 70.2%

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

      4. associate-*r* 74.3%

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

      5. div-inv 74.3%

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

   5. Applied egg-rr 74.3%

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

   if 8.19999999999999959e67 < a

   1. Initial program 88.4%

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

      1. clear-num 88.0%

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

      2. un-div-inv 88.1%

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

   4. Applied egg-rr 88.1%

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

   5. Taylor expanded in z around 0 54.5%

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

      1. associate-/l* 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in x around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

   10. Simplified 65.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00105:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-227}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-174}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-100}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+82}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))))
   (if (<= a -2.2e-57)
     t_1
     (if (<= a 1.04e-100)
       (+ t (* y (/ (- x t) z)))
       (if (<= a 8.2e+58)
         (* (- y z) (/ t (- a z)))
         (if (<= a 1.2e+82) (* (- t x) (/ y (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -2.2e-57) {
		tmp = t_1;
	} else if (a <= 1.04e-100) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 8.2e+58) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= 1.2e+82) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) * (y / a))
    if (a <= (-2.2d-57)) then
        tmp = t_1
    else if (a <= 1.04d-100) then
        tmp = t + (y * ((x - t) / z))
    else if (a <= 8.2d+58) then
        tmp = (y - z) * (t / (a - z))
    else if (a <= 1.2d+82) then
        tmp = (t - x) * (y / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -2.2e-57) {
		tmp = t_1;
	} else if (a <= 1.04e-100) {
		tmp = t + (y * ((x - t) / z));
	} else if (a <= 8.2e+58) {
		tmp = (y - z) * (t / (a - z));
	} else if (a <= 1.2e+82) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -2.2e-57:
		tmp = t_1
	elif a <= 1.04e-100:
		tmp = t + (y * ((x - t) / z))
	elif a <= 8.2e+58:
		tmp = (y - z) * (t / (a - z))
	elif a <= 1.2e+82:
		tmp = (t - x) * (y / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -2.2e-57)
		tmp = t_1;
	elseif (a <= 1.04e-100)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (a <= 8.2e+58)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (a <= 1.2e+82)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -2.2e-57)
		tmp = t_1;
	elseif (a <= 1.04e-100)
		tmp = t + (y * ((x - t) / z));
	elseif (a <= 8.2e+58)
		tmp = (y - z) * (t / (a - z));
	elseif (a <= 1.2e+82)
		tmp = (t - x) * (y / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e-57], t$95$1, If[LessEqual[a, 1.04e-100], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.2e+58], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+82], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.19999999999999999e-57 or 1.19999999999999999e82 < a

   1. Initial program 87.7%

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

   3. Taylor expanded in z around 0 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-/l* 72.4%

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

   5. Simplified 72.4%

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

   if -2.19999999999999999e-57 < a < 1.04e-100

   1. Initial program 72.3%

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

   3. Taylor expanded in z around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. distribute-lft-out-- 81.8%

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

      3. div-sub 83.0%

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

      4. mul-1-neg 83.0%

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

      5. unsub-neg 83.0%

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

      6. distribute-rgt-out-- 83.0%

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

      7. associate-/l* 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in y around inf 81.8%

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

      1. associate-*r/ 86.7%

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

   8. Simplified 86.7%

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

   if 1.04e-100 < a < 8.2e58

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 48.2%

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

      1. *-commutative 48.2%

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

      2. associate-/l* 66.1%

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

   5. Simplified 66.1%

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

   if 8.2e58 < a < 1.19999999999999999e82

   1. Initial program 85.5%

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

   3. Taylor expanded in y around -inf 72.1%

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

      1. associate-/l* 85.4%

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

      2. *-un-lft-identity 85.4%

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

      3. associate-*l/ 85.4%

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

      4. associate-*r* 85.6%

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

      5. div-inv 85.8%

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

   5. Applied egg-rr 85.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-57}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-100}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+82}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ \mathbf{if}\;a \leq -0.002:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))))
   (if (<= a -0.002)
     x
     (if (<= a -8.6e-293)
       t_1
       (if (<= a 7.8e-209) (* x (/ y z)) (if (<= a 3.8e+72) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -0.002) {
		tmp = x;
	} else if (a <= -8.6e-293) {
		tmp = t_1;
	} else if (a <= 7.8e-209) {
		tmp = x * (y / z);
	} else if (a <= 3.8e+72) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    if (a <= (-0.002d0)) then
        tmp = x
    else if (a <= (-8.6d-293)) then
        tmp = t_1
    else if (a <= 7.8d-209) then
        tmp = x * (y / z)
    else if (a <= 3.8d+72) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double tmp;
	if (a <= -0.002) {
		tmp = x;
	} else if (a <= -8.6e-293) {
		tmp = t_1;
	} else if (a <= 7.8e-209) {
		tmp = x * (y / z);
	} else if (a <= 3.8e+72) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / z)
	tmp = 0
	if a <= -0.002:
		tmp = x
	elif a <= -8.6e-293:
		tmp = t_1
	elif a <= 7.8e-209:
		tmp = x * (y / z)
	elif a <= 3.8e+72:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (a <= -0.002)
		tmp = x;
	elseif (a <= -8.6e-293)
		tmp = t_1;
	elseif (a <= 7.8e-209)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 3.8e+72)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	tmp = 0.0;
	if (a <= -0.002)
		tmp = x;
	elseif (a <= -8.6e-293)
		tmp = t_1;
	elseif (a <= 7.8e-209)
		tmp = x * (y / z);
	elseif (a <= 3.8e+72)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.002], x, If[LessEqual[a, -8.6e-293], t$95$1, If[LessEqual[a, 7.8e-209], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+72], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2e-3 or 3.80000000000000006e72 < a

   1. Initial program 87.1%

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

   3. Taylor expanded in a around inf 50.9%

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

   if -2e-3 < a < -8.5999999999999996e-293 or 7.8000000000000001e-209 < a < 3.80000000000000006e72

   1. Initial program 82.3%

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

   3. Taylor expanded in t around inf 69.2%

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

   4. Taylor expanded in a around 0 57.5%

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

      1. associate-*r/ 57.5%

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

      2. neg-mul-1 57.5%

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

   6. Simplified 57.5%

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

   7. Taylor expanded in z around 0 57.5%

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

      1. mul-1-neg 57.5%

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

      2. unsub-neg 57.5%

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

   9. Simplified 57.5%

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

   if -8.5999999999999996e-293 < a < 7.8000000000000001e-209

   1. Initial program 61.3%

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

   3. Taylor expanded in y around -inf 68.1%

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

   4. Taylor expanded in a around 0 65.0%

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

      1. associate-*r/ 65.0%

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

      2. associate-*r* 65.0%

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

      3. *-commutative 65.0%

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

      4. neg-mul-1 65.0%

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

   6. Simplified 65.0%

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

   7. Taylor expanded in t around 0 53.5%

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

      1. associate-/l* 57.9%

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

   9. Simplified 57.9%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.002:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-293}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -0.00056:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -0.00056)
     t_2
     (if (<= a -1.25e-284)
       t_1
       (if (<= a 7.2e-210) (* x (/ y z)) (if (<= a 1.4e+68) 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 <= -0.00056) {
		tmp = t_2;
	} else if (a <= -1.25e-284) {
		tmp = t_1;
	} else if (a <= 7.2e-210) {
		tmp = x * (y / z);
	} else if (a <= 1.4e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-0.00056d0)) then
        tmp = t_2
    else if (a <= (-1.25d-284)) then
        tmp = t_1
    else if (a <= 7.2d-210) then
        tmp = x * (y / z)
    else if (a <= 1.4d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -0.00056) {
		tmp = t_2;
	} else if (a <= -1.25e-284) {
		tmp = t_1;
	} else if (a <= 7.2e-210) {
		tmp = x * (y / z);
	} else if (a <= 1.4e+68) {
		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 <= -0.00056:
		tmp = t_2
	elif a <= -1.25e-284:
		tmp = t_1
	elif a <= 7.2e-210:
		tmp = x * (y / z)
	elif a <= 1.4e+68:
		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 <= -0.00056)
		tmp = t_2;
	elseif (a <= -1.25e-284)
		tmp = t_1;
	elseif (a <= 7.2e-210)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.4e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -0.00056)
		tmp = t_2;
	elseif (a <= -1.25e-284)
		tmp = t_1;
	elseif (a <= 7.2e-210)
		tmp = x * (y / z);
	elseif (a <= 1.4e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00056], t$95$2, If[LessEqual[a, -1.25e-284], t$95$1, If[LessEqual[a, 7.2e-210], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.5999999999999995e-4 or 1.4e68 < a

   1. Initial program 87.3%

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

      1. clear-num 86.0%

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

      2. un-div-inv 86.0%

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

   4. Applied egg-rr 86.0%

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

   5. Taylor expanded in z around 0 61.9%

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

      1. associate-/l* 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in x around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unsub-neg 65.4%

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

   10. Simplified 65.4%

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

   if -5.5999999999999995e-4 < a < -1.24999999999999993e-284 or 7.1999999999999998e-210 < a < 1.4e68

   1. Initial program 82.1%

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

   3. Taylor expanded in t around inf 69.7%

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

   4. Taylor expanded in a around 0 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in z around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

   9. Simplified 57.1%

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

   if -1.24999999999999993e-284 < a < 7.1999999999999998e-210

   1. Initial program 61.3%

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

   3. Taylor expanded in y around -inf 68.1%

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

   4. Taylor expanded in a around 0 65.0%

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

      1. associate-*r/ 65.0%

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

      2. associate-*r* 65.0%

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

      3. *-commutative 65.0%

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

      4. neg-mul-1 65.0%

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

   6. Simplified 65.0%

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

   7. Taylor expanded in t around 0 53.5%

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

      1. associate-/l* 57.9%

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

   9. Simplified 57.9%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00056:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-284}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -0.00075:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -0.00075)
     t_2
     (if (<= a -5.5e-292)
       t_1
       (if (<= a 3.5e-210)
         (* x (/ (- y a) z))
         (if (<= a 1.02e+68) 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 <= -0.00075) {
		tmp = t_2;
	} else if (a <= -5.5e-292) {
		tmp = t_1;
	} else if (a <= 3.5e-210) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.02e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-0.00075d0)) then
        tmp = t_2
    else if (a <= (-5.5d-292)) then
        tmp = t_1
    else if (a <= 3.5d-210) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.02d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -0.00075) {
		tmp = t_2;
	} else if (a <= -5.5e-292) {
		tmp = t_1;
	} else if (a <= 3.5e-210) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.02e+68) {
		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 <= -0.00075:
		tmp = t_2
	elif a <= -5.5e-292:
		tmp = t_1
	elif a <= 3.5e-210:
		tmp = x * ((y - a) / z)
	elif a <= 1.02e+68:
		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 <= -0.00075)
		tmp = t_2;
	elseif (a <= -5.5e-292)
		tmp = t_1;
	elseif (a <= 3.5e-210)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.02e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -0.00075)
		tmp = t_2;
	elseif (a <= -5.5e-292)
		tmp = t_1;
	elseif (a <= 3.5e-210)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.02e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00075], t$95$2, If[LessEqual[a, -5.5e-292], t$95$1, If[LessEqual[a, 3.5e-210], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.5000000000000002e-4 or 1.02e68 < a

   1. Initial program 87.3%

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

      1. clear-num 86.0%

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

      2. un-div-inv 86.0%

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

   4. Applied egg-rr 86.0%

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

   5. Taylor expanded in z around 0 61.9%

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

      1. associate-/l* 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in x around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unsub-neg 65.4%

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

   10. Simplified 65.4%

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

   if -7.5000000000000002e-4 < a < -5.50000000000000006e-292 or 3.50000000000000015e-210 < a < 1.02e68

   1. Initial program 82.1%

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

   3. Taylor expanded in t around inf 69.7%

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

   4. Taylor expanded in a around 0 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in z around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

   9. Simplified 57.1%

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

   if -5.50000000000000006e-292 < a < 3.50000000000000015e-210

   1. Initial program 61.3%

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

   3. Taylor expanded in z around inf 85.3%

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

      1. associate--l+ 85.3%

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

      2. distribute-lft-out-- 85.3%

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

      3. div-sub 85.3%

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

      4. mul-1-neg 85.3%

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

      5. unsub-neg 85.3%

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

      6. distribute-rgt-out-- 85.4%

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

      7. associate-/l* 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in t around 0 54.5%

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

      1. associate-/l* 58.1%

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

   8. Simplified 58.1%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00075:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-292}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -0.0018:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-96}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} + \frac{z}{z - a}\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ a (- t x))))))
   (if (<= a -0.0018)
     t_1
     (if (<= a -1e-96)
       (* t (+ (/ y (- a z)) (/ z (- z a))))
       (if (<= a 1.15e+82) (+ t (* (- t x) (/ (- a y) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -0.0018) {
		tmp = t_1;
	} else if (a <= -1e-96) {
		tmp = t * ((y / (a - z)) + (z / (z - a)));
	} else if (a <= 1.15e+82) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / (a / (t - x)))
    if (a <= (-0.0018d0)) then
        tmp = t_1
    else if (a <= (-1d-96)) then
        tmp = t * ((y / (a - z)) + (z / (z - a)))
    else if (a <= 1.15d+82) then
        tmp = t + ((t - x) * ((a - y) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / (a / (t - x)));
	double tmp;
	if (a <= -0.0018) {
		tmp = t_1;
	} else if (a <= -1e-96) {
		tmp = t * ((y / (a - z)) + (z / (z - a)));
	} else if (a <= 1.15e+82) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / (a / (t - x)))
	tmp = 0
	if a <= -0.0018:
		tmp = t_1
	elif a <= -1e-96:
		tmp = t * ((y / (a - z)) + (z / (z - a)))
	elif a <= 1.15e+82:
		tmp = t + ((t - x) * ((a - y) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -0.0018)
		tmp = t_1;
	elseif (a <= -1e-96)
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) + Float64(z / Float64(z - a))));
	elseif (a <= 1.15e+82)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / (a / (t - x)));
	tmp = 0.0;
	if (a <= -0.0018)
		tmp = t_1;
	elseif (a <= -1e-96)
		tmp = t * ((y / (a - z)) + (z / (z - a)));
	elseif (a <= 1.15e+82)
		tmp = t + ((t - x) * ((a - y) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0018], t$95$1, If[LessEqual[a, -1e-96], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+82], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.0018 or 1.14999999999999994e82 < a

   1. Initial program 87.8%

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

      1. clear-num 86.4%

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

      2. un-div-inv 86.5%

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in a around inf 79.2%

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

   if -0.0018 < a < -9.9999999999999991e-97

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 78.2%

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

   if -9.9999999999999991e-97 < a < 1.14999999999999994e82

   1. Initial program 76.4%

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

   3. Taylor expanded in z around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. distribute-lft-out-- 72.4%

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

      3. div-sub 73.3%

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

      4. mul-1-neg 73.3%

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

      5. unsub-neg 73.3%

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

      6. distribute-rgt-out-- 74.1%

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

      7. associate-/l* 81.2%

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

   5. Simplified 81.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0018:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-96}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} + \frac{z}{z - a}\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-58} \lor \neg \left(a \leq 1.15 \cdot 10^{+82}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.2e-58) (not (<= a 1.15e+82)))
   (+ x (/ (- y z) (/ a (- t x))))
   (+ t (* (- t x) (/ (- a y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e-58) || !(a <= 1.15e+82)) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t + ((t - x) * ((a - y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.2d-58)) .or. (.not. (a <= 1.15d+82))) then
        tmp = x + ((y - z) / (a / (t - x)))
    else
        tmp = t + ((t - x) * ((a - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e-58) || !(a <= 1.15e+82)) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else {
		tmp = t + ((t - x) * ((a - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.2e-58) or not (a <= 1.15e+82):
		tmp = x + ((y - z) / (a / (t - x)))
	else:
		tmp = t + ((t - x) * ((a - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.2e-58) || !(a <= 1.15e+82))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.2e-58) || ~((a <= 1.15e+82)))
		tmp = x + ((y - z) / (a / (t - x)));
	else
		tmp = t + ((t - x) * ((a - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.2e-58], N[Not[LessEqual[a, 1.15e+82]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.20000000000000006e-58 or 1.14999999999999994e82 < a

   1. Initial program 87.7%

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

      1. clear-num 86.5%

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

      2. un-div-inv 87.2%

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

   4. Applied egg-rr 87.2%

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

   5. Taylor expanded in a around inf 76.9%

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

   if -2.20000000000000006e-58 < a < 1.14999999999999994e82

   1. Initial program 77.1%

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

   3. Taylor expanded in z around inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. distribute-lft-out-- 71.8%

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

      3. div-sub 72.7%

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

      4. mul-1-neg 72.7%

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

      5. unsub-neg 72.7%

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

      6. distribute-rgt-out-- 73.5%

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

      7. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-58} \lor \neg \left(a \leq 1.15 \cdot 10^{+82}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00062:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+67}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.00062) x (if (<= a 8.5e+67) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00062) {
		tmp = x;
	} else if (a <= 8.5e+67) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.00062d0)) then
        tmp = x
    else if (a <= 8.5d+67) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00062) {
		tmp = x;
	} else if (a <= 8.5e+67) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.00062:
		tmp = x
	elif a <= 8.5e+67:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.00062)
		tmp = x;
	elseif (a <= 8.5e+67)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.00062)
		tmp = x;
	elseif (a <= 8.5e+67)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.00062], x, If[LessEqual[a, 8.5e+67], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.2e-4 or 8.50000000000000038e67 < a

   1. Initial program 87.3%

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

   3. Taylor expanded in a around inf 50.5%

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

   if -6.2e-4 < a < 8.50000000000000038e67

   1. Initial program 78.4%

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

   3. Taylor expanded in z around inf 32.3%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00062:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+67}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 25.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = t
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return t;
}

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 82.4%

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

3. Taylor expanded in z around inf 21.8%

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

4. Final simplification 21.8%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024115 
(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)))))