Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.9% → 95.0%

Time: 19.3s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}

Python

def code(x, y, z, t, a):
	return x + ((y - z) * ((t - x) / (a - z)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y - z) * ((t - x) / (a - z)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y - z) * ((t - x) / (a - z)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}

Python

def code(x, y, z, t, a):
	return x + ((y - z) * ((t - x) / (a - z)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y - z) * ((t - x) / (a - z)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-283} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -4e-283) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -4e-283) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -4e-283) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-283], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.99999999999999979e-283 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.3%

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

      1. +-commutative 90.3%

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

      2. remove-double-neg 90.3%

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

      3. unsub-neg 90.3%

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

      4. *-commutative 90.3%

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

      5. associate-*l/ 77.0%

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

      6. associate-/l* 93.5%

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

      7. fma-neg 93.6%

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

      8. remove-double-neg 93.6%

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

   3. Simplified 93.6%

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

   if -3.99999999999999979e-283 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 80.1%

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

      1. associate--l+ 80.1%

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

      2. distribute-lft-out-- 80.1%

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

      3. div-sub 80.1%

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

      4. mul-1-neg 80.1%

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

      5. unsub-neg 80.1%

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

      6. div-sub 80.1%

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

      7. associate-/l* 84.1%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-283} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-86} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-86) (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 <= -1e-86) || !(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 <= (-1d-86)) .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 <= -1e-86) || !(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 <= -1e-86) 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 <= -1e-86) || !(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 <= -1e-86) || ~((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, -1e-86], 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)))) < -1.00000000000000008e-86 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 -1.00000000000000008e-86 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 24.4%

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

      1. clear-num 24.5%

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

      2. un-div-inv 24.3%

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

   4. Applied egg-rr 24.3%

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

   5. Taylor expanded in z around inf 73.4%

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

      1. associate--l+ 73.4%

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

      2. associate-*r/ 73.4%

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

      3. associate-*r/ 73.4%

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

      4. div-sub 73.4%

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

      5. distribute-lft-out-- 73.4%

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

      6. distribute-rgt-out-- 73.4%

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

      7. associate-*r/ 73.4%

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

      8. distribute-rgt-out-- 73.4%

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

      9. mul-1-neg 73.4%

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

      10. distribute-rgt-out-- 73.4%

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

      11. unsub-neg 73.4%

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

      12. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-86} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-86} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-86) (not (<= t_1 0.0)))
     (+ x (/ (- y z) (/ (- a z) (- t x))))
     (+ 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 <= -1e-86) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) / ((a - z) / (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-86)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((y - z) / ((a - z) / (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 t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-86) || !(t_1 <= 0.0)) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} 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 <= -1e-86) or not (t_1 <= 0.0):
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	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 <= -1e-86) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / 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)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-86) || ~((t_1 <= 0.0)))
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	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, -1e-86], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / 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 (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000008e-86 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
   3. Step-by-step derivation

      1. clear-num 92.5%

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

      2. un-div-inv 92.6%

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

   4. Applied egg-rr 92.6%

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

   if -1.00000000000000008e-86 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 24.4%

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

      1. clear-num 24.5%

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

      2. un-div-inv 24.3%

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

   4. Applied egg-rr 24.3%

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

   5. Taylor expanded in z around inf 73.4%

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

      1. associate--l+ 73.4%

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

      2. associate-*r/ 73.4%

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

      3. associate-*r/ 73.4%

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

      4. div-sub 73.4%

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

      5. distribute-lft-out-- 73.4%

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

      6. distribute-rgt-out-- 73.4%

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

      7. associate-*r/ 73.4%

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

      8. distribute-rgt-out-- 73.4%

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

      9. mul-1-neg 73.4%

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

      10. distribute-rgt-out-- 73.4%

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

      11. unsub-neg 73.4%

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

      12. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-86} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t - y \cdot \frac{t - x}{z}\\ t_3 := x + \left(t - x\right) \cdot \frac{y - z}{a}\\ t_4 := y \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{-8}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{t\_4}{a - z}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{t\_4}{a}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z))))
        (t_2 (- t (* y (/ (- t x) z))))
        (t_3 (+ x (* (- t x) (/ (- y z) a))))
        (t_4 (* y (- t x))))
   (if (<= a -1.35e-8)
     t_3
     (if (<= a -2.7e-74)
       t_2
       (if (<= a -7.5e-204)
         (/ t_4 (- a z))
         (if (<= a -2.6e-259)
           t_1
           (if (<= a 2.45e-96)
             t_2
             (if (<= a 1.05e-67)
               (+ x (/ t_4 a))
               (if (<= a 1.95e+14) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t - (y * ((t - x) / z));
	double t_3 = x + ((t - x) * ((y - z) / a));
	double t_4 = y * (t - x);
	double tmp;
	if (a <= -1.35e-8) {
		tmp = t_3;
	} else if (a <= -2.7e-74) {
		tmp = t_2;
	} else if (a <= -7.5e-204) {
		tmp = t_4 / (a - z);
	} else if (a <= -2.6e-259) {
		tmp = t_1;
	} else if (a <= 2.45e-96) {
		tmp = t_2;
	} else if (a <= 1.05e-67) {
		tmp = x + (t_4 / a);
	} else if (a <= 1.95e+14) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = t - (y * ((t - x) / z))
    t_3 = x + ((t - x) * ((y - z) / a))
    t_4 = y * (t - x)
    if (a <= (-1.35d-8)) then
        tmp = t_3
    else if (a <= (-2.7d-74)) then
        tmp = t_2
    else if (a <= (-7.5d-204)) then
        tmp = t_4 / (a - z)
    else if (a <= (-2.6d-259)) then
        tmp = t_1
    else if (a <= 2.45d-96) then
        tmp = t_2
    else if (a <= 1.05d-67) then
        tmp = x + (t_4 / a)
    else if (a <= 1.95d+14) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = t - (y * ((t - x) / z));
	double t_3 = x + ((t - x) * ((y - z) / a));
	double t_4 = y * (t - x);
	double tmp;
	if (a <= -1.35e-8) {
		tmp = t_3;
	} else if (a <= -2.7e-74) {
		tmp = t_2;
	} else if (a <= -7.5e-204) {
		tmp = t_4 / (a - z);
	} else if (a <= -2.6e-259) {
		tmp = t_1;
	} else if (a <= 2.45e-96) {
		tmp = t_2;
	} else if (a <= 1.05e-67) {
		tmp = x + (t_4 / a);
	} else if (a <= 1.95e+14) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = t - (y * ((t - x) / z))
	t_3 = x + ((t - x) * ((y - z) / a))
	t_4 = y * (t - x)
	tmp = 0
	if a <= -1.35e-8:
		tmp = t_3
	elif a <= -2.7e-74:
		tmp = t_2
	elif a <= -7.5e-204:
		tmp = t_4 / (a - z)
	elif a <= -2.6e-259:
		tmp = t_1
	elif a <= 2.45e-96:
		tmp = t_2
	elif a <= 1.05e-67:
		tmp = x + (t_4 / a)
	elif a <= 1.95e+14:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(t - Float64(y * Float64(Float64(t - x) / z)))
	t_3 = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)))
	t_4 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (a <= -1.35e-8)
		tmp = t_3;
	elseif (a <= -2.7e-74)
		tmp = t_2;
	elseif (a <= -7.5e-204)
		tmp = Float64(t_4 / Float64(a - z));
	elseif (a <= -2.6e-259)
		tmp = t_1;
	elseif (a <= 2.45e-96)
		tmp = t_2;
	elseif (a <= 1.05e-67)
		tmp = Float64(x + Float64(t_4 / a));
	elseif (a <= 1.95e+14)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = t - (y * ((t - x) / z));
	t_3 = x + ((t - x) * ((y - z) / a));
	t_4 = y * (t - x);
	tmp = 0.0;
	if (a <= -1.35e-8)
		tmp = t_3;
	elseif (a <= -2.7e-74)
		tmp = t_2;
	elseif (a <= -7.5e-204)
		tmp = t_4 / (a - z);
	elseif (a <= -2.6e-259)
		tmp = t_1;
	elseif (a <= 2.45e-96)
		tmp = t_2;
	elseif (a <= 1.05e-67)
		tmp = x + (t_4 / a);
	elseif (a <= 1.95e+14)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e-8], t$95$3, If[LessEqual[a, -2.7e-74], t$95$2, If[LessEqual[a, -7.5e-204], N[(t$95$4 / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-259], t$95$1, If[LessEqual[a, 2.45e-96], t$95$2, If[LessEqual[a, 1.05e-67], N[(x + N[(t$95$4 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e+14], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.35000000000000001e-8 or 1.95e14 < a

   1. Initial program 87.5%

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

   3. Taylor expanded in a around inf 62.1%

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

      1. associate-/l* 76.5%

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

   5. Simplified 76.5%

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

   if -1.35000000000000001e-8 < a < -2.70000000000000018e-74 or -2.60000000000000001e-259 < a < 2.45000000000000008e-96

   1. Initial program 72.7%

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

   3. Taylor expanded in z around -inf 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

      3. +-commutative 79.8%

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

      4. associate--l+ 79.8%

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

      5. distribute-rgt-out-- 79.8%

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

      6. associate-*r* 81.0%

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

      7. distribute-rgt-out-- 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in a around 0 80.3%

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

      1. associate-/l* 84.4%

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

   8. Simplified 84.4%

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

   if -2.70000000000000018e-74 < a < -7.5000000000000003e-204

   1. Initial program 78.2%

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

   3. Taylor expanded in y around -inf 81.6%

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

   if -7.5000000000000003e-204 < a < -2.60000000000000001e-259 or 1.0500000000000001e-67 < a < 1.95e14

   1. Initial program 80.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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. associate-/l* 85.2%

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

   5. Simplified 85.2%

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

   if 2.45000000000000008e-96 < a < 1.0500000000000001e-67

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-8}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-74}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ t_3 := y \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -10600:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-203}:\\ \;\;\;\;\frac{t\_3}{a - z}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{t\_3}{a}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z))))
        (t_2 (+ x (* y (/ (- t x) a))))
        (t_3 (* y (- t x))))
   (if (<= a -10600.0)
     t_2
     (if (<= a -1.15e-72)
       t_1
       (if (<= a -9.4e-203)
         (/ t_3 (- a z))
         (if (<= a -1.5e-257)
           t_1
           (if (<= a 2.45e-96)
             (- t (* y (/ (- t x) z)))
             (if (<= a 1.05e-67)
               (+ x (/ t_3 a))
               (if (<= a 3e+18) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double t_3 = y * (t - x);
	double tmp;
	if (a <= -10600.0) {
		tmp = t_2;
	} else if (a <= -1.15e-72) {
		tmp = t_1;
	} else if (a <= -9.4e-203) {
		tmp = t_3 / (a - z);
	} else if (a <= -1.5e-257) {
		tmp = t_1;
	} else if (a <= 2.45e-96) {
		tmp = t - (y * ((t - x) / z));
	} else if (a <= 1.05e-67) {
		tmp = x + (t_3 / a);
	} else if (a <= 3e+18) {
		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) :: t_3
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y * ((t - x) / a))
    t_3 = y * (t - x)
    if (a <= (-10600.0d0)) then
        tmp = t_2
    else if (a <= (-1.15d-72)) then
        tmp = t_1
    else if (a <= (-9.4d-203)) then
        tmp = t_3 / (a - z)
    else if (a <= (-1.5d-257)) then
        tmp = t_1
    else if (a <= 2.45d-96) then
        tmp = t - (y * ((t - x) / z))
    else if (a <= 1.05d-67) then
        tmp = x + (t_3 / a)
    else if (a <= 3d+18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double t_3 = y * (t - x);
	double tmp;
	if (a <= -10600.0) {
		tmp = t_2;
	} else if (a <= -1.15e-72) {
		tmp = t_1;
	} else if (a <= -9.4e-203) {
		tmp = t_3 / (a - z);
	} else if (a <= -1.5e-257) {
		tmp = t_1;
	} else if (a <= 2.45e-96) {
		tmp = t - (y * ((t - x) / z));
	} else if (a <= 1.05e-67) {
		tmp = x + (t_3 / a);
	} else if (a <= 3e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y * ((t - x) / a))
	t_3 = y * (t - x)
	tmp = 0
	if a <= -10600.0:
		tmp = t_2
	elif a <= -1.15e-72:
		tmp = t_1
	elif a <= -9.4e-203:
		tmp = t_3 / (a - z)
	elif a <= -1.5e-257:
		tmp = t_1
	elif a <= 2.45e-96:
		tmp = t - (y * ((t - x) / z))
	elif a <= 1.05e-67:
		tmp = x + (t_3 / a)
	elif a <= 3e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	t_3 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (a <= -10600.0)
		tmp = t_2;
	elseif (a <= -1.15e-72)
		tmp = t_1;
	elseif (a <= -9.4e-203)
		tmp = Float64(t_3 / Float64(a - z));
	elseif (a <= -1.5e-257)
		tmp = t_1;
	elseif (a <= 2.45e-96)
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	elseif (a <= 1.05e-67)
		tmp = Float64(x + Float64(t_3 / a));
	elseif (a <= 3e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y * ((t - x) / a));
	t_3 = y * (t - x);
	tmp = 0.0;
	if (a <= -10600.0)
		tmp = t_2;
	elseif (a <= -1.15e-72)
		tmp = t_1;
	elseif (a <= -9.4e-203)
		tmp = t_3 / (a - z);
	elseif (a <= -1.5e-257)
		tmp = t_1;
	elseif (a <= 2.45e-96)
		tmp = t - (y * ((t - x) / z));
	elseif (a <= 1.05e-67)
		tmp = x + (t_3 / a);
	elseif (a <= 3e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -10600.0], t$95$2, If[LessEqual[a, -1.15e-72], t$95$1, If[LessEqual[a, -9.4e-203], N[(t$95$3 / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-257], t$95$1, If[LessEqual[a, 2.45e-96], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-67], N[(x + N[(t$95$3 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+18], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -10600 or 3e18 < a

   1. Initial program 87.1%

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

   3. Taylor expanded in z around 0 61.1%

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

      1. associate-/l* 71.4%

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

   5. Simplified 71.4%

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

   if -10600 < a < -1.14999999999999997e-72 or -9.40000000000000012e-203 < a < -1.5e-257 or 1.0500000000000001e-67 < a < 3e18

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 70.0%

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

      1. associate-/l* 82.3%

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

   5. Simplified 82.3%

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

   if -1.14999999999999997e-72 < a < -9.40000000000000012e-203

   1. Initial program 78.2%

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

   3. Taylor expanded in y around -inf 81.6%

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

   if -1.5e-257 < a < 2.45000000000000008e-96

   1. Initial program 72.6%

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

   3. Taylor expanded in z around -inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

      3. +-commutative 80.5%

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

      4. associate--l+ 80.5%

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

      5. distribute-rgt-out-- 80.5%

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

      6. associate-*r* 82.0%

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

      7. distribute-rgt-out-- 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in a around 0 80.9%

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

      1. associate-/l* 86.0%

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

   8. Simplified 86.0%

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

   if 2.45000000000000008e-96 < a < 1.0500000000000001e-67

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -10600:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-96}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -100000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-96}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -100000.0)
     t_2
     (if (<= a -1.05e-140)
       t_1
       (if (<= a 1.1e-96)
         (- t (* y (/ (- t x) z)))
         (if (<= a 1.05e-67)
           (+ x (/ (* y (- t x)) a))
           (if (<= a 4.8e+20) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -100000.0) {
		tmp = t_2;
	} else if (a <= -1.05e-140) {
		tmp = t_1;
	} else if (a <= 1.1e-96) {
		tmp = t - (y * ((t - x) / z));
	} else if (a <= 1.05e-67) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 4.8e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-100000.0d0)) then
        tmp = t_2
    else if (a <= (-1.05d-140)) then
        tmp = t_1
    else if (a <= 1.1d-96) then
        tmp = t - (y * ((t - x) / z))
    else if (a <= 1.05d-67) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 4.8d+20) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -100000.0) {
		tmp = t_2;
	} else if (a <= -1.05e-140) {
		tmp = t_1;
	} else if (a <= 1.1e-96) {
		tmp = t - (y * ((t - x) / z));
	} else if (a <= 1.05e-67) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 4.8e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -100000.0:
		tmp = t_2
	elif a <= -1.05e-140:
		tmp = t_1
	elif a <= 1.1e-96:
		tmp = t - (y * ((t - x) / z))
	elif a <= 1.05e-67:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 4.8e+20:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -100000.0)
		tmp = t_2;
	elseif (a <= -1.05e-140)
		tmp = t_1;
	elseif (a <= 1.1e-96)
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	elseif (a <= 1.05e-67)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 4.8e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -100000.0)
		tmp = t_2;
	elseif (a <= -1.05e-140)
		tmp = t_1;
	elseif (a <= 1.1e-96)
		tmp = t - (y * ((t - x) / z));
	elseif (a <= 1.05e-67)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 4.8e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -100000.0], t$95$2, If[LessEqual[a, -1.05e-140], t$95$1, If[LessEqual[a, 1.1e-96], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-67], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e+20], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1e5 or 4.8e20 < a

   1. Initial program 87.1%

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

   3. Taylor expanded in z around 0 61.1%

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

      1. associate-/l* 71.4%

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

   5. Simplified 71.4%

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

   if -1e5 < a < -1.05000000000000009e-140 or 1.0500000000000001e-67 < a < 4.8e20

   1. Initial program 76.9%

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

   3. Taylor expanded in x around 0 66.4%

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

      1. associate-/l* 74.8%

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

   5. Simplified 74.8%

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

   if -1.05000000000000009e-140 < a < 1.0999999999999999e-96

   1. Initial program 76.2%

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

   3. Taylor expanded in z around -inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

      3. +-commutative 72.1%

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

      4. associate--l+ 72.1%

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

      5. distribute-rgt-out-- 72.1%

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

      6. associate-*r* 74.3%

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

      7. distribute-rgt-out-- 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in a around 0 80.6%

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

      1. associate-/l* 82.8%

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

   8. Simplified 82.8%

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

   if 1.0999999999999999e-96 < a < 1.0500000000000001e-67

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.8%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -100000:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-96}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-67}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.15e+24)
   t
   (if (<= z -7.5e-77)
     (/ (* x y) z)
     (if (<= z -6.5e-121)
       (* x (/ (- y) a))
       (if (<= z -4.2e-258) x (if (<= z 8.8e-38) (* t (/ y (- a z))) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+24) {
		tmp = t;
	} else if (z <= -7.5e-77) {
		tmp = (x * y) / z;
	} else if (z <= -6.5e-121) {
		tmp = x * (-y / a);
	} else if (z <= -4.2e-258) {
		tmp = x;
	} else if (z <= 8.8e-38) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.15d+24)) then
        tmp = t
    else if (z <= (-7.5d-77)) then
        tmp = (x * y) / z
    else if (z <= (-6.5d-121)) then
        tmp = x * (-y / a)
    else if (z <= (-4.2d-258)) then
        tmp = x
    else if (z <= 8.8d-38) then
        tmp = t * (y / (a - z))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+24) {
		tmp = t;
	} else if (z <= -7.5e-77) {
		tmp = (x * y) / z;
	} else if (z <= -6.5e-121) {
		tmp = x * (-y / a);
	} else if (z <= -4.2e-258) {
		tmp = x;
	} else if (z <= 8.8e-38) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.15e+24:
		tmp = t
	elif z <= -7.5e-77:
		tmp = (x * y) / z
	elif z <= -6.5e-121:
		tmp = x * (-y / a)
	elif z <= -4.2e-258:
		tmp = x
	elif z <= 8.8e-38:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.15e+24)
		tmp = t;
	elseif (z <= -7.5e-77)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= -6.5e-121)
		tmp = Float64(x * Float64(Float64(-y) / a));
	elseif (z <= -4.2e-258)
		tmp = x;
	elseif (z <= 8.8e-38)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.15e+24)
		tmp = t;
	elseif (z <= -7.5e-77)
		tmp = (x * y) / z;
	elseif (z <= -6.5e-121)
		tmp = x * (-y / a);
	elseif (z <= -4.2e-258)
		tmp = x;
	elseif (z <= 8.8e-38)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.15e+24], t, If[LessEqual[z, -7.5e-77], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -6.5e-121], N[(x * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-258], x, If[LessEqual[z, 8.8e-38], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.14999999999999994e24 or 8.80000000000000029e-38 < z

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 46.0%

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

   if -2.14999999999999994e24 < z < -7.5000000000000006e-77

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf 66.8%

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

      1. div-sub 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in t around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. associate-/l* 45.7%

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

      3. distribute-lft-neg-in 45.7%

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

   8. Simplified 45.7%

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

   9. Taylor expanded in a around 0 39.9%

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

   if -7.5000000000000006e-77 < z < -6.5000000000000003e-121

   1. Initial program 82.7%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. div-sub 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in t around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. associate-/l* 40.2%

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

      3. distribute-lft-neg-in 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in a around inf 35.9%

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

   if -6.5000000000000003e-121 < z < -4.1999999999999998e-258

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 46.3%

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

   if -4.1999999999999998e-258 < z < 8.80000000000000029e-38

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf 65.5%

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

      1. div-sub 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in t around inf 43.7%

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

      1. associate-/l* 51.4%

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

   8. Simplified 51.4%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.8e+23)
   t
   (if (<= z -1.4e-77)
     (/ (* x y) z)
     (if (<= z -1.15e-120)
       (* x (/ (- y) a))
       (if (<= z -7.5e-258) x (if (<= z 4.3e-39) (* t (/ y a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+23) {
		tmp = t;
	} else if (z <= -1.4e-77) {
		tmp = (x * y) / z;
	} else if (z <= -1.15e-120) {
		tmp = x * (-y / a);
	} else if (z <= -7.5e-258) {
		tmp = x;
	} else if (z <= 4.3e-39) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.8d+23)) then
        tmp = t
    else if (z <= (-1.4d-77)) then
        tmp = (x * y) / z
    else if (z <= (-1.15d-120)) then
        tmp = x * (-y / a)
    else if (z <= (-7.5d-258)) then
        tmp = x
    else if (z <= 4.3d-39) then
        tmp = t * (y / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.8e+23) {
		tmp = t;
	} else if (z <= -1.4e-77) {
		tmp = (x * y) / z;
	} else if (z <= -1.15e-120) {
		tmp = x * (-y / a);
	} else if (z <= -7.5e-258) {
		tmp = x;
	} else if (z <= 4.3e-39) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.8e+23:
		tmp = t
	elif z <= -1.4e-77:
		tmp = (x * y) / z
	elif z <= -1.15e-120:
		tmp = x * (-y / a)
	elif z <= -7.5e-258:
		tmp = x
	elif z <= 4.3e-39:
		tmp = t * (y / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.8e+23)
		tmp = t;
	elseif (z <= -1.4e-77)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= -1.15e-120)
		tmp = Float64(x * Float64(Float64(-y) / a));
	elseif (z <= -7.5e-258)
		tmp = x;
	elseif (z <= 4.3e-39)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.8e+23)
		tmp = t;
	elseif (z <= -1.4e-77)
		tmp = (x * y) / z;
	elseif (z <= -1.15e-120)
		tmp = x * (-y / a);
	elseif (z <= -7.5e-258)
		tmp = x;
	elseif (z <= 4.3e-39)
		tmp = t * (y / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.8e+23], t, If[LessEqual[z, -1.4e-77], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.15e-120], N[(x * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-258], x, If[LessEqual[z, 4.3e-39], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.8000000000000006e23 or 4.2999999999999999e-39 < z

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 46.0%

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

   if -9.8000000000000006e23 < z < -1.4e-77

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf 66.8%

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

      1. div-sub 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in t around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. associate-/l* 45.7%

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

      3. distribute-lft-neg-in 45.7%

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

   8. Simplified 45.7%

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

   9. Taylor expanded in a around 0 39.9%

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

   if -1.4e-77 < z < -1.14999999999999993e-120

   1. Initial program 82.7%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. div-sub 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in t around 0 34.5%

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

      1. mul-1-neg 34.5%

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

      2. associate-/l* 40.2%

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

      3. distribute-lft-neg-in 40.2%

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

   8. Simplified 40.2%

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

   9. Taylor expanded in a around inf 35.9%

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

   if -1.14999999999999993e-120 < z < -7.4999999999999998e-258

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 46.3%

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

   if -7.4999999999999998e-258 < z < 4.2999999999999999e-39

   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 46.7%

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

      1. associate-/l* 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in z around 0 39.0%

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

      1. associate-*r/ 46.8%

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

   8. Simplified 46.8%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-258}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -340000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+199}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= a -340000.0)
     t_2
     (if (<= a -2e-142)
       t_1
       (if (<= a -3.2e-203)
         (/ (* y (- x t)) z)
         (if (<= a 5.6e+199) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -340000.0) {
		tmp = t_2;
	} else if (a <= -2e-142) {
		tmp = t_1;
	} else if (a <= -3.2e-203) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 5.6e+199) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((y * t) / a)
    if (a <= (-340000.0d0)) then
        tmp = t_2
    else if (a <= (-2d-142)) then
        tmp = t_1
    else if (a <= (-3.2d-203)) then
        tmp = (y * (x - t)) / z
    else if (a <= 5.6d+199) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -340000.0) {
		tmp = t_2;
	} else if (a <= -2e-142) {
		tmp = t_1;
	} else if (a <= -3.2e-203) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 5.6e+199) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if a <= -340000.0:
		tmp = t_2
	elif a <= -2e-142:
		tmp = t_1
	elif a <= -3.2e-203:
		tmp = (y * (x - t)) / z
	elif a <= 5.6e+199:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -340000.0)
		tmp = t_2;
	elseif (a <= -2e-142)
		tmp = t_1;
	elseif (a <= -3.2e-203)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 5.6e+199)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -340000.0)
		tmp = t_2;
	elseif (a <= -2e-142)
		tmp = t_1;
	elseif (a <= -3.2e-203)
		tmp = (y * (x - t)) / z;
	elseif (a <= 5.6e+199)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -340000.0], t$95$2, If[LessEqual[a, -2e-142], t$95$1, If[LessEqual[a, -3.2e-203], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 5.6e+199], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4e5 or 5.6000000000000002e199 < a

   1. Initial program 86.9%

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

   3. Taylor expanded in z around 0 69.0%

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

   4. Taylor expanded in t around inf 64.8%

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

   if -3.4e5 < a < -2.0000000000000001e-142 or -3.2e-203 < a < 5.6000000000000002e199

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 49.9%

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

      1. associate-/l* 64.4%

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

   5. Simplified 64.4%

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

   if -2.0000000000000001e-142 < a < -3.2e-203

   1. Initial program 84.9%

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

   3. Taylor expanded in y around inf 75.3%

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

      1. div-sub 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in a around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. mul-1-neg 75.6%

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

      3. distribute-rgt-neg-out 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -340000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+199}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -66000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -66000.0)
     (+ x (/ (* y t) a))
     (if (<= a -2.05e-142)
       t_1
       (if (<= a -7.5e-203)
         (/ (* y (- x t)) z)
         (if (<= a 1.65e+149) t_1 (* x (+ (/ (- z y) a) 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -66000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -2.05e-142) {
		tmp = t_1;
	} else if (a <= -7.5e-203) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.65e+149) {
		tmp = t_1;
	} else {
		tmp = x * (((z - y) / a) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-66000.0d0)) then
        tmp = x + ((y * t) / a)
    else if (a <= (-2.05d-142)) then
        tmp = t_1
    else if (a <= (-7.5d-203)) then
        tmp = (y * (x - t)) / z
    else if (a <= 1.65d+149) then
        tmp = t_1
    else
        tmp = x * (((z - y) / a) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -66000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -2.05e-142) {
		tmp = t_1;
	} else if (a <= -7.5e-203) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.65e+149) {
		tmp = t_1;
	} else {
		tmp = x * (((z - y) / a) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -66000.0:
		tmp = x + ((y * t) / a)
	elif a <= -2.05e-142:
		tmp = t_1
	elif a <= -7.5e-203:
		tmp = (y * (x - t)) / z
	elif a <= 1.65e+149:
		tmp = t_1
	else:
		tmp = x * (((z - y) / a) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -66000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= -2.05e-142)
		tmp = t_1;
	elseif (a <= -7.5e-203)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 1.65e+149)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -66000.0)
		tmp = x + ((y * t) / a);
	elseif (a <= -2.05e-142)
		tmp = t_1;
	elseif (a <= -7.5e-203)
		tmp = (y * (x - t)) / z;
	elseif (a <= 1.65e+149)
		tmp = t_1;
	else
		tmp = x * (((z - y) / a) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -66000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e-142], t$95$1, If[LessEqual[a, -7.5e-203], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.65e+149], t$95$1, N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -66000

   1. Initial program 86.9%

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

   3. Taylor expanded in z around 0 68.7%

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

   4. Taylor expanded in t around inf 63.2%

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

   if -66000 < a < -2.05e-142 or -7.50000000000000027e-203 < a < 1.65e149

   1. Initial program 78.6%

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

   3. Taylor expanded in x around 0 53.9%

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

      1. associate-/l* 66.7%

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

   5. Simplified 66.7%

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

   if -2.05e-142 < a < -7.50000000000000027e-203

   1. Initial program 84.9%

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

   3. Taylor expanded in y around inf 75.3%

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

      1. div-sub 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in a around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. mul-1-neg 75.6%

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

      3. distribute-rgt-neg-out 75.6%

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

   8. Simplified 75.6%

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

   if 1.65e149 < a

   1. Initial program 88.6%

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

   3. Taylor expanded in a around inf 56.0%

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

      1. associate-/l* 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in x around inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

   8. Simplified 58.3%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -66000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+149}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -380000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-203}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -380000.0)
     (+ x (/ (* y t) a))
     (if (<= a -3.5e-75)
       t_1
       (if (<= a -1.02e-203)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.3e+149) t_1 (* x (+ (/ (- z y) a) 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -380000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -3.5e-75) {
		tmp = t_1;
	} else if (a <= -1.02e-203) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.3e+149) {
		tmp = t_1;
	} else {
		tmp = x * (((z - y) / a) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-380000.0d0)) then
        tmp = x + ((y * t) / a)
    else if (a <= (-3.5d-75)) then
        tmp = t_1
    else if (a <= (-1.02d-203)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.3d+149) then
        tmp = t_1
    else
        tmp = x * (((z - y) / a) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -380000.0) {
		tmp = x + ((y * t) / a);
	} else if (a <= -3.5e-75) {
		tmp = t_1;
	} else if (a <= -1.02e-203) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.3e+149) {
		tmp = t_1;
	} else {
		tmp = x * (((z - y) / a) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -380000.0:
		tmp = x + ((y * t) / a)
	elif a <= -3.5e-75:
		tmp = t_1
	elif a <= -1.02e-203:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.3e+149:
		tmp = t_1
	else:
		tmp = x * (((z - y) / a) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -380000.0)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= -3.5e-75)
		tmp = t_1;
	elseif (a <= -1.02e-203)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.3e+149)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(Float64(z - y) / a) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -380000.0)
		tmp = x + ((y * t) / a);
	elseif (a <= -3.5e-75)
		tmp = t_1;
	elseif (a <= -1.02e-203)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.3e+149)
		tmp = t_1;
	else
		tmp = x * (((z - y) / a) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -380000.0], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.5e-75], t$95$1, If[LessEqual[a, -1.02e-203], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+149], t$95$1, N[(x * N[(N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.8e5

   1. Initial program 86.9%

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

   3. Taylor expanded in z around 0 68.7%

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

   4. Taylor expanded in t around inf 63.2%

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

   if -3.8e5 < a < -3.49999999999999985e-75 or -1.02000000000000005e-203 < a < 1.29999999999999989e149

   1. Initial program 79.2%

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

   3. Taylor expanded in x around 0 54.1%

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

      1. associate-/l* 66.9%

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

   5. Simplified 66.9%

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

   if -3.49999999999999985e-75 < a < -1.02000000000000005e-203

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. div-sub 74.4%

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

   5. Simplified 74.4%

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

   if 1.29999999999999989e149 < a

   1. Initial program 88.6%

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

   3. Taylor expanded in a around inf 56.0%

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

      1. associate-/l* 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in x around inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

   8. Simplified 58.3%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -380000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-203}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+149}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -160000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -160000.0)
     t_2
     (if (<= a -1e-74)
       t_1
       (if (<= a -4.2e-204)
         (* y (/ (- t x) (- a z)))
         (if (<= a 1.15e+16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -160000.0) {
		tmp = t_2;
	} else if (a <= -1e-74) {
		tmp = t_1;
	} else if (a <= -4.2e-204) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.15e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-160000.0d0)) then
        tmp = t_2
    else if (a <= (-1d-74)) then
        tmp = t_1
    else if (a <= (-4.2d-204)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.15d+16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -160000.0) {
		tmp = t_2;
	} else if (a <= -1e-74) {
		tmp = t_1;
	} else if (a <= -4.2e-204) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.15e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -160000.0:
		tmp = t_2
	elif a <= -1e-74:
		tmp = t_1
	elif a <= -4.2e-204:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.15e+16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -160000.0)
		tmp = t_2;
	elseif (a <= -1e-74)
		tmp = t_1;
	elseif (a <= -4.2e-204)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.15e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -160000.0)
		tmp = t_2;
	elseif (a <= -1e-74)
		tmp = t_1;
	elseif (a <= -4.2e-204)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.15e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -160000.0], t$95$2, If[LessEqual[a, -1e-74], t$95$1, If[LessEqual[a, -4.2e-204], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6e5 or 1.15e16 < a

   1. Initial program 87.1%

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

   3. Taylor expanded in z around 0 61.1%

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

      1. associate-/l* 71.4%

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

   5. Simplified 71.4%

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

   if -1.6e5 < a < -9.99999999999999958e-75 or -4.20000000000000018e-204 < a < 1.15e16

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0 58.6%

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

      1. associate-/l* 69.9%

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

   5. Simplified 69.9%

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

   if -9.99999999999999958e-75 < a < -4.20000000000000018e-204

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. div-sub 74.4%

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

   5. Simplified 74.4%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -160000:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= z -4.4e+24)
     t
     (if (<= z -6.5e-192)
       t_1
       (if (<= z -4.1e-241) x (if (<= z 7.5e-38) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -4.4e+24) {
		tmp = t;
	} else if (z <= -6.5e-192) {
		tmp = t_1;
	} else if (z <= -4.1e-241) {
		tmp = x;
	} else if (z <= 7.5e-38) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (z <= (-4.4d+24)) then
        tmp = t
    else if (z <= (-6.5d-192)) then
        tmp = t_1
    else if (z <= (-4.1d-241)) then
        tmp = x
    else if (z <= 7.5d-38) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (z <= -4.4e+24) {
		tmp = t;
	} else if (z <= -6.5e-192) {
		tmp = t_1;
	} else if (z <= -4.1e-241) {
		tmp = x;
	} else if (z <= 7.5e-38) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if z <= -4.4e+24:
		tmp = t
	elif z <= -6.5e-192:
		tmp = t_1
	elif z <= -4.1e-241:
		tmp = x
	elif z <= 7.5e-38:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -4.4e+24)
		tmp = t;
	elseif (z <= -6.5e-192)
		tmp = t_1;
	elseif (z <= -4.1e-241)
		tmp = x;
	elseif (z <= 7.5e-38)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -4.4e+24)
		tmp = t;
	elseif (z <= -6.5e-192)
		tmp = t_1;
	elseif (z <= -4.1e-241)
		tmp = x;
	elseif (z <= 7.5e-38)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+24], t, If[LessEqual[z, -6.5e-192], t$95$1, If[LessEqual[z, -4.1e-241], x, If[LessEqual[z, 7.5e-38], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000003e24 or 7.5e-38 < z

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 46.0%

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

   if -4.40000000000000003e24 < z < -6.49999999999999966e-192 or -4.0999999999999999e-241 < z < 7.5e-38

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 60.7%

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

      1. div-sub 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in a around inf 48.5%

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

   if -6.49999999999999966e-192 < z < -4.0999999999999999e-241

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 77.3%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-241}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-38}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+59}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -1.35e+59)
     t
     (if (<= z -2.1e-241)
       t_1
       (if (<= z -5.2e-306) (* y (/ (- t x) a)) (if (<= z 4.4e+163) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.35e+59) {
		tmp = t;
	} else if (z <= -2.1e-241) {
		tmp = t_1;
	} else if (z <= -5.2e-306) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.4e+163) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-1.35d+59)) then
        tmp = t
    else if (z <= (-2.1d-241)) then
        tmp = t_1
    else if (z <= (-5.2d-306)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.4d+163) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.35e+59) {
		tmp = t;
	} else if (z <= -2.1e-241) {
		tmp = t_1;
	} else if (z <= -5.2e-306) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.4e+163) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.35e+59:
		tmp = t
	elif z <= -2.1e-241:
		tmp = t_1
	elif z <= -5.2e-306:
		tmp = y * ((t - x) / a)
	elif z <= 4.4e+163:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.35e+59)
		tmp = t;
	elseif (z <= -2.1e-241)
		tmp = t_1;
	elseif (z <= -5.2e-306)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.4e+163)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.35e+59)
		tmp = t;
	elseif (z <= -2.1e-241)
		tmp = t_1;
	elseif (z <= -5.2e-306)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.4e+163)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+59], t, If[LessEqual[z, -2.1e-241], t$95$1, If[LessEqual[z, -5.2e-306], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+163], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3500000000000001e59 or 4.39999999999999973e163 < z

   1. Initial program 62.2%

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

   3. Taylor expanded in z around inf 59.2%

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

   if -1.3500000000000001e59 < z < -2.0999999999999999e-241 or -5.2000000000000001e-306 < z < 4.39999999999999973e163

   1. Initial program 90.2%

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

   3. Taylor expanded in z around 0 57.9%

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

   4. Taylor expanded in t around inf 48.7%

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

   if -2.0999999999999999e-241 < z < -5.2000000000000001e-306

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf 78.8%

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

      1. div-sub 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in a around inf 79.2%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+59}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-241}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+163}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 360000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= a -2.9e-8)
     t_2
     (if (<= a -1.1e-75)
       t_1
       (if (<= a -8.2e-208)
         (* y (/ (- t x) a))
         (if (<= a 360000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -2.9e-8) {
		tmp = t_2;
	} else if (a <= -1.1e-75) {
		tmp = t_1;
	} else if (a <= -8.2e-208) {
		tmp = y * ((t - x) / a);
	} else if (a <= 360000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + ((y * t) / a)
    if (a <= (-2.9d-8)) then
        tmp = t_2
    else if (a <= (-1.1d-75)) then
        tmp = t_1
    else if (a <= (-8.2d-208)) then
        tmp = y * ((t - x) / a)
    else if (a <= 360000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (a <= -2.9e-8) {
		tmp = t_2;
	} else if (a <= -1.1e-75) {
		tmp = t_1;
	} else if (a <= -8.2e-208) {
		tmp = y * ((t - x) / a);
	} else if (a <= 360000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if a <= -2.9e-8:
		tmp = t_2
	elif a <= -1.1e-75:
		tmp = t_1
	elif a <= -8.2e-208:
		tmp = y * ((t - x) / a)
	elif a <= 360000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -2.9e-8)
		tmp = t_2;
	elseif (a <= -1.1e-75)
		tmp = t_1;
	elseif (a <= -8.2e-208)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= 360000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -2.9e-8)
		tmp = t_2;
	elseif (a <= -1.1e-75)
		tmp = t_1;
	elseif (a <= -8.2e-208)
		tmp = y * ((t - x) / a);
	elseif (a <= 360000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e-8], t$95$2, If[LessEqual[a, -1.1e-75], t$95$1, If[LessEqual[a, -8.2e-208], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 360000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.9000000000000002e-8 or 3.6e8 < a

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0 60.0%

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

   4. Taylor expanded in t around inf 54.7%

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

   if -2.9000000000000002e-8 < a < -1.10000000000000003e-75 or -8.1999999999999998e-208 < a < 3.6e8

   1. Initial program 77.1%

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

   3. Taylor expanded in x around 0 58.0%

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

      1. associate-/l* 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in a around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. div-sub 60.9%

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

      3. sub-neg 60.9%

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

      4. *-inverses 60.9%

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

      5. metadata-eval 60.9%

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

   8. Simplified 60.9%

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

   if -1.10000000000000003e-75 < a < -8.1999999999999998e-208

   1. Initial program 76.4%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. div-sub 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in a around inf 57.3%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 360000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -2600:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1660000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= a -2600.0)
     t_1
     (if (<= a -3.1e-75)
       (* t (/ z (- z a)))
       (if (<= a -8.2e-208)
         (* y (/ (- t x) a))
         (if (<= a 1660000000.0) (* t (- 1.0 (/ y z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (a <= -2600.0) {
		tmp = t_1;
	} else if (a <= -3.1e-75) {
		tmp = t * (z / (z - a));
	} else if (a <= -8.2e-208) {
		tmp = y * ((t - x) / a);
	} else if (a <= 1660000000.0) {
		tmp = t * (1.0 - (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 * t) / a)
    if (a <= (-2600.0d0)) then
        tmp = t_1
    else if (a <= (-3.1d-75)) then
        tmp = t * (z / (z - a))
    else if (a <= (-8.2d-208)) then
        tmp = y * ((t - x) / a)
    else if (a <= 1660000000.0d0) then
        tmp = t * (1.0d0 - (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 * t) / a);
	double tmp;
	if (a <= -2600.0) {
		tmp = t_1;
	} else if (a <= -3.1e-75) {
		tmp = t * (z / (z - a));
	} else if (a <= -8.2e-208) {
		tmp = y * ((t - x) / a);
	} else if (a <= 1660000000.0) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if a <= -2600.0:
		tmp = t_1
	elif a <= -3.1e-75:
		tmp = t * (z / (z - a))
	elif a <= -8.2e-208:
		tmp = y * ((t - x) / a)
	elif a <= 1660000000.0:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (a <= -2600.0)
		tmp = t_1;
	elseif (a <= -3.1e-75)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (a <= -8.2e-208)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= 1660000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (a <= -2600.0)
		tmp = t_1;
	elseif (a <= -3.1e-75)
		tmp = t * (z / (z - a));
	elseif (a <= -8.2e-208)
		tmp = y * ((t - x) / a);
	elseif (a <= 1660000000.0)
		tmp = t * (1.0 - (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 * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2600.0], t$95$1, If[LessEqual[a, -3.1e-75], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.2e-208], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1660000000.0], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2600 or 1.66e9 < a

   1. Initial program 87.2%

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

   3. Taylor expanded in z around 0 60.6%

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

   4. Taylor expanded in t around inf 55.1%

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

   if -2600 < a < -3.10000000000000007e-75

   1. Initial program 78.3%

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

   3. Taylor expanded in x around 0 75.6%

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

      1. associate-/l* 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in y around 0 58.2%

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

      1. neg-mul-1 58.2%

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

      2. distribute-neg-frac2 58.2%

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

      3. neg-sub0 58.2%

         \[\leadsto t \cdot \frac{z}{\color{blue}{0 - \left(a - z\right)}} \]

      4. associate--r- 58.2%

         \[\leadsto t \cdot \frac{z}{\color{blue}{\left(0 - a\right) + z}} \]

      5. neg-sub0 58.2%

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

   8. Simplified 58.2%

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

   if -3.10000000000000007e-75 < a < -8.1999999999999998e-208

   1. Initial program 76.4%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. div-sub 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in a around inf 57.3%

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

   if -8.1999999999999998e-208 < a < 1.66e9

   1. Initial program 77.7%

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

   3. Taylor expanded in x around 0 56.3%

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

      1. associate-/l* 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in a around 0 60.6%

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

      1. mul-1-neg 60.6%

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

      2. div-sub 60.6%

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

      3. sub-neg 60.6%

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

      4. *-inverses 60.6%

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

      5. metadata-eval 60.6%

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

   8. Simplified 60.6%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2600:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1660000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-55} \lor \neg \left(z \leq 2.9 \cdot 10^{+19}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e-55) (not (<= z 2.9e+19)))
   (+ t (* (- t x) (/ (- a y) z)))
   (+ x (* (- t x) (/ (- y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e-55) || !(z <= 2.9e+19)) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9d-55)) .or. (.not. (z <= 2.9d+19))) then
        tmp = t + ((t - x) * ((a - y) / z))
    else
        tmp = x + ((t - x) * ((y - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e-55) || !(z <= 2.9e+19)) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else {
		tmp = x + ((t - x) * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e-55) or not (z <= 2.9e+19):
		tmp = t + ((t - x) * ((a - y) / z))
	else:
		tmp = x + ((t - x) * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e-55) || !(z <= 2.9e+19))
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e-55) || ~((z <= 2.9e+19)))
		tmp = t + ((t - x) * ((a - y) / z));
	else
		tmp = x + ((t - x) * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e-55], N[Not[LessEqual[z, 2.9e+19]], $MachinePrecision]], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999941e-55 or 2.9e19 < z

   1. Initial program 70.6%

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

      1. clear-num 70.6%

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

      2. un-div-inv 70.7%

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

   4. Applied egg-rr 70.7%

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

   5. Taylor expanded in z around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. associate-*r/ 62.3%

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

      3. associate-*r/ 62.3%

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

      4. div-sub 62.3%

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

      5. distribute-lft-out-- 62.3%

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

      6. distribute-rgt-out-- 64.0%

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

      7. associate-*r/ 64.0%

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

      8. distribute-rgt-out-- 62.3%

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

      9. mul-1-neg 62.3%

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

      10. distribute-rgt-out-- 64.0%

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

      11. unsub-neg 64.0%

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

      12. associate-/l* 76.8%

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

   7. Simplified 76.8%

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

   if -8.99999999999999941e-55 < z < 2.9e19

   1. Initial program 93.4%

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

   3. Taylor expanded in a around inf 74.3%

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

      1. associate-/l* 81.5%

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

   5. Simplified 81.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-55} \lor \neg \left(z \leq 2.9 \cdot 10^{+19}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+54)
   t
   (if (<= z -6.1e-257) x (if (<= z 1.05e-38) (* t (/ y a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+54) {
		tmp = t;
	} else if (z <= -6.1e-257) {
		tmp = x;
	} else if (z <= 1.05e-38) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+54)) then
        tmp = t
    else if (z <= (-6.1d-257)) then
        tmp = x
    else if (z <= 1.05d-38) then
        tmp = t * (y / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+54) {
		tmp = t;
	} else if (z <= -6.1e-257) {
		tmp = x;
	} else if (z <= 1.05e-38) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+54:
		tmp = t
	elif z <= -6.1e-257:
		tmp = x
	elif z <= 1.05e-38:
		tmp = t * (y / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+54)
		tmp = t;
	elseif (z <= -6.1e-257)
		tmp = x;
	elseif (z <= 1.05e-38)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+54)
		tmp = t;
	elseif (z <= -6.1e-257)
		tmp = x;
	elseif (z <= 1.05e-38)
		tmp = t * (y / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+54], t, If[LessEqual[z, -6.1e-257], x, If[LessEqual[z, 1.05e-38], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e54 or 1.05000000000000006e-38 < z

   1. Initial program 72.2%

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

   3. Taylor expanded in z around inf 47.0%

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

   if -6.5e54 < z < -6.0999999999999996e-257

   1. Initial program 90.6%

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

   3. Taylor expanded in a around inf 33.0%

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

   if -6.0999999999999996e-257 < z < 1.05000000000000006e-38

   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 46.7%

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

      1. associate-/l* 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in z around 0 39.0%

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

      1. associate-*r/ 46.8%

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

   8. Simplified 46.8%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -390:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+143}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -390.0) x (if (<= a 1.05e+143) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -390.0) {
		tmp = x;
	} else if (a <= 1.05e+143) {
		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 <= (-390.0d0)) then
        tmp = x
    else if (a <= 1.05d+143) 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 <= -390.0) {
		tmp = x;
	} else if (a <= 1.05e+143) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -390.0:
		tmp = x
	elif a <= 1.05e+143:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -390.0)
		tmp = x;
	elseif (a <= 1.05e+143)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -390.0)
		tmp = x;
	elseif (a <= 1.05e+143)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -390.0], x, If[LessEqual[a, 1.05e+143], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -390 or 1.04999999999999994e143 < a

   1. Initial program 87.6%

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

   3. Taylor expanded in a around inf 50.0%

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

   if -390 < a < 1.04999999999999994e143

   1. Initial program 79.0%

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

   3. Taylor expanded in z around inf 33.3%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -390:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+143}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 24.5% 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 82.2%

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

3. Taylor expanded in z around inf 25.5%

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

4. Final simplification 25.5%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024082 
(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)))))