Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 93.0%

Time: 15.3s

Alternatives: 21

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.3% 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: 93.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-294} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-294) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) 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-294) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), 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-294) || !(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) * Float64(a - y)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-294], 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] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000002e-294 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. remove-double-neg 88.4%

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

      3. unsub-neg 88.4%

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

      4. *-commutative 88.4%

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

      5. associate-*l/ 74.5%

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

      6. associate-/l* 93.4%

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

      7. fma-neg 93.5%

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

      8. remove-double-neg 93.5%

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

   3. Simplified 93.5%

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

   if -1.00000000000000002e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

      1. +-commutative 3.6%

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

      2. remove-double-neg 3.6%

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

      3. unsub-neg 3.6%

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

      4. *-commutative 3.6%

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

      5. associate-*l/ 6.0%

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

      6. associate-/l* 5.9%

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

      7. fma-neg 5.9%

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

      8. remove-double-neg 5.9%

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

   3. Simplified 5.9%

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

   5. Taylor expanded in z around inf 84.6%

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

      1. associate--l+ 84.6%

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

      2. associate-*r/ 84.6%

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

      3. associate-*r/ 84.6%

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

      4. mul-1-neg 84.6%

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

      5. div-sub 84.6%

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

      6. mul-1-neg 84.6%

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

      7. distribute-lft-out-- 84.6%

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

      8. associate-*r/ 84.6%

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

      9. mul-1-neg 84.6%

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

      10. unsub-neg 84.6%

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

      11. distribute-rgt-out-- 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-294} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-294} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-294) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ 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-294) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} 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-294)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    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-294) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} 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-294) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	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-294) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * 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-294) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	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-294], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000002e-294 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 88.4%

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

   3. Taylor expanded in y around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. div-sub 75.5%

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

      3. mul-1-neg 75.5%

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

      4. associate-/l* 86.5%

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

      5. distribute-lft-neg-out 86.5%

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

      6. distribute-rgt-out 88.4%

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

      7. sub-neg 88.4%

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

      8. associate-/r/ 93.4%

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

   5. Simplified 93.4%

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

   if -1.00000000000000002e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

      1. +-commutative 3.6%

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

      2. remove-double-neg 3.6%

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

      3. unsub-neg 3.6%

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

      4. *-commutative 3.6%

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

      5. associate-*l/ 6.0%

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

      6. associate-/l* 5.9%

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

      7. fma-neg 5.9%

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

      8. remove-double-neg 5.9%

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

   3. Simplified 5.9%

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

   5. Taylor expanded in z around inf 84.6%

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

      1. associate--l+ 84.6%

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

      2. associate-*r/ 84.6%

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

      3. associate-*r/ 84.6%

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

      4. mul-1-neg 84.6%

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

      5. div-sub 84.6%

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

      6. mul-1-neg 84.6%

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

      7. distribute-lft-out-- 84.6%

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

      8. associate-*r/ 84.6%

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

      9. mul-1-neg 84.6%

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

      10. unsub-neg 84.6%

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

      11. distribute-rgt-out-- 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-294} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-294} \lor \neg \left(t\_1 \leq 10^{-217}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-294) (not (<= t_1 1e-217)))
     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-294) || !(t_1 <= 1e-217)) {
		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-294)) .or. (.not. (t_1 <= 1d-217))) 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-294) || !(t_1 <= 1e-217)) {
		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-294) or not (t_1 <= 1e-217):
		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-294) || !(t_1 <= 1e-217))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-294) || ~((t_1 <= 1e-217)))
		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-294], N[Not[LessEqual[t$95$1, 1e-217]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000002e-294 or 1.00000000000000008e-217 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.9%

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

   if -1.00000000000000002e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000008e-217

   1. Initial program 6.0%

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

      1. +-commutative 6.0%

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

      2. remove-double-neg 6.0%

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

      3. unsub-neg 6.0%

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

      4. *-commutative 6.0%

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

      5. associate-*l/ 16.9%

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

      6. associate-/l* 16.8%

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

      7. fma-neg 16.8%

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

      8. remove-double-neg 16.8%

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

   3. Simplified 16.8%

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

   5. Taylor expanded in z around inf 81.9%

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

      1. associate--l+ 81.9%

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

      2. associate-*r/ 81.9%

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

      3. associate-*r/ 81.9%

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

      4. mul-1-neg 81.9%

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

      5. div-sub 81.9%

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

      6. mul-1-neg 81.9%

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

      7. distribute-lft-out-- 81.9%

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

      8. associate-*r/ 81.9%

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

      9. mul-1-neg 81.9%

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

      10. unsub-neg 81.9%

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

      11. distribute-rgt-out-- 81.9%

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

   7. Simplified 81.9%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-294} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-217}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-178}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a (/ x z)))))
   (if (<= z -8e+63)
     t_1
     (if (<= z -8.2e-178)
       (+ x (/ t (/ (- a z) y)))
       (if (<= z 3.5e+141) (+ x (/ (- t x) (/ a y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -8e+63) {
		tmp = t_1;
	} else if (z <= -8.2e-178) {
		tmp = x + (t / ((a - z) / y));
	} else if (z <= 3.5e+141) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (a * (x / z))
    if (z <= (-8d+63)) then
        tmp = t_1
    else if (z <= (-8.2d-178)) then
        tmp = x + (t / ((a - z) / y))
    else if (z <= 3.5d+141) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -8e+63) {
		tmp = t_1;
	} else if (z <= -8.2e-178) {
		tmp = x + (t / ((a - z) / y));
	} else if (z <= 3.5e+141) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * (x / z))
	tmp = 0
	if z <= -8e+63:
		tmp = t_1
	elif z <= -8.2e-178:
		tmp = x + (t / ((a - z) / y))
	elif z <= 3.5e+141:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * Float64(x / z)))
	tmp = 0.0
	if (z <= -8e+63)
		tmp = t_1;
	elseif (z <= -8.2e-178)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	elseif (z <= 3.5e+141)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * (x / z));
	tmp = 0.0;
	if (z <= -8e+63)
		tmp = t_1;
	elseif (z <= -8.2e-178)
		tmp = x + (t / ((a - z) / y));
	elseif (z <= 3.5e+141)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+63], t$95$1, If[LessEqual[z, -8.2e-178], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+141], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.00000000000000046e63 or 3.5e141 < z

   1. Initial program 55.0%

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

   3. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. distribute-neg-frac 24.1%

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

      3. *-commutative 24.1%

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

      4. distribute-rgt-neg-out 24.1%

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

   5. Simplified 24.1%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-/l* 64.6%

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

   8. Simplified 64.6%

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

   9. Taylor expanded in t around 0 59.7%

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

       1. mul-1-neg 59.7%

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

       2. associate-/l* 64.7%

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

       3. distribute-rgt-neg-in 64.7%

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

       4. distribute-neg-frac 64.7%

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

   11. Simplified 64.7%

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

   if -8.00000000000000046e63 < z < -8.1999999999999998e-178

   1. Initial program 87.7%

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

   3. Taylor expanded in y around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. div-sub 83.8%

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

      3. mul-1-neg 83.8%

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

      4. associate-/l* 84.8%

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

      5. distribute-lft-neg-out 84.8%

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

      6. distribute-rgt-out 87.7%

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

      7. sub-neg 87.7%

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

      8. associate-/r/ 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in t around inf 77.9%

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

   7. Taylor expanded in y around inf 62.8%

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

   if -8.1999999999999998e-178 < z < 3.5e141

   1. Initial program 88.2%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. div-sub 81.2%

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

      3. mul-1-neg 81.2%

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

      4. associate-/l* 86.1%

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

      5. distribute-lft-neg-out 86.1%

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

      6. distribute-rgt-out 88.2%

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

      7. sub-neg 88.2%

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

      8. associate-/r/ 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in z around 0 66.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+63}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-178}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+141}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a (/ x z)))))
   (if (<= z -2.1e+63)
     t_1
     (if (<= z 4.2e-273)
       (+ x (/ t (/ (- a z) y)))
       (if (<= z 2.45e+144) (+ x (* y (/ (- t x) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -2.1e+63) {
		tmp = t_1;
	} else if (z <= 4.2e-273) {
		tmp = x + (t / ((a - z) / y));
	} else if (z <= 2.45e+144) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (a * (x / z))
    if (z <= (-2.1d+63)) then
        tmp = t_1
    else if (z <= 4.2d-273) then
        tmp = x + (t / ((a - z) / y))
    else if (z <= 2.45d+144) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -2.1e+63) {
		tmp = t_1;
	} else if (z <= 4.2e-273) {
		tmp = x + (t / ((a - z) / y));
	} else if (z <= 2.45e+144) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * (x / z))
	tmp = 0
	if z <= -2.1e+63:
		tmp = t_1
	elif z <= 4.2e-273:
		tmp = x + (t / ((a - z) / y))
	elif z <= 2.45e+144:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * Float64(x / z)))
	tmp = 0.0
	if (z <= -2.1e+63)
		tmp = t_1;
	elseif (z <= 4.2e-273)
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	elseif (z <= 2.45e+144)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * (x / z));
	tmp = 0.0;
	if (z <= -2.1e+63)
		tmp = t_1;
	elseif (z <= 4.2e-273)
		tmp = x + (t / ((a - z) / y));
	elseif (z <= 2.45e+144)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+63], t$95$1, If[LessEqual[z, 4.2e-273], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+144], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1000000000000002e63 or 2.45e144 < z

   1. Initial program 55.0%

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

   3. Taylor expanded in y around 0 24.1%

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

      1. mul-1-neg 24.1%

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

      2. distribute-neg-frac 24.1%

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

      3. *-commutative 24.1%

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

      4. distribute-rgt-neg-out 24.1%

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

   5. Simplified 24.1%

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

   6. Taylor expanded in z around inf 55.5%

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

      1. associate-/l* 64.6%

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

   8. Simplified 64.6%

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

   9. Taylor expanded in t around 0 59.7%

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

       1. mul-1-neg 59.7%

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

       2. associate-/l* 64.7%

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

       3. distribute-rgt-neg-in 64.7%

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

       4. distribute-neg-frac 64.7%

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

   11. Simplified 64.7%

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

   if -2.1000000000000002e63 < z < 4.2000000000000004e-273

   1. Initial program 87.4%

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

   3. Taylor expanded in y around 0 84.4%

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

      1. +-commutative 84.4%

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

      2. div-sub 84.4%

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

      3. mul-1-neg 84.4%

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

      4. associate-/l* 84.0%

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

      5. distribute-lft-neg-out 84.0%

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

      6. distribute-rgt-out 87.4%

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

      7. sub-neg 87.4%

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

      8. associate-/r/ 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in t around inf 79.0%

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

   7. Taylor expanded in y around inf 67.5%

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

   if 4.2000000000000004e-273 < z < 2.45e144

   1. Initial program 88.7%

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

   3. Taylor expanded in z around 0 56.2%

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

      1. associate-/l* 60.0%

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

   5. Simplified 60.0%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+144}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \left(\left(--1\right) - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- t x) a)))))
   (if (<= a -6e+34)
     t_1
     (if (<= a -7.5e-151)
       (* y (/ (- t x) (- a z)))
       (if (<= a 5.8e-23) (* 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 - x) / a));
	double tmp;
	if (a <= -6e+34) {
		tmp = t_1;
	} else if (a <= -7.5e-151) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.8e-23) {
		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 - x) / a))
    if (a <= (-6d+34)) then
        tmp = t_1
    else if (a <= (-7.5d-151)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 5.8d-23) 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 - x) / a));
	double tmp;
	if (a <= -6e+34) {
		tmp = t_1;
	} else if (a <= -7.5e-151) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 5.8e-23) {
		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 - x) / a))
	tmp = 0
	if a <= -6e+34:
		tmp = t_1
	elif a <= -7.5e-151:
		tmp = y * ((t - x) / (a - z))
	elif a <= 5.8e-23:
		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(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -6e+34)
		tmp = t_1;
	elseif (a <= -7.5e-151)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 5.8e-23)
		tmp = Float64(t * Float64(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 - x) / a));
	tmp = 0.0;
	if (a <= -6e+34)
		tmp = t_1;
	elseif (a <= -7.5e-151)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 5.8e-23)
		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[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+34], t$95$1, If[LessEqual[a, -7.5e-151], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-23], N[(t * N[((--1.0) - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.00000000000000037e34 or 5.8000000000000003e-23 < a

   1. Initial program 84.6%

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

   3. Taylor expanded in z around 0 54.2%

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

      1. associate-/l* 64.0%

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

   5. Simplified 64.0%

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

   if -6.00000000000000037e34 < a < -7.5000000000000004e-151

   1. Initial program 75.1%

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

   3. Taylor expanded in y around 0 66.8%

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

      1. +-commutative 66.8%

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

      2. div-sub 66.8%

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

      3. mul-1-neg 66.8%

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

      4. associate-/l* 75.1%

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

      5. distribute-lft-neg-out 75.1%

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

      6. distribute-rgt-out 75.1%

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

      7. sub-neg 75.1%

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

      8. associate-/r/ 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in y around inf 42.5%

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

   7. Taylor expanded in y around inf 57.4%

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

      1. div-sub 57.4%

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

   9. Simplified 57.4%

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

   if -7.5000000000000004e-151 < a < 5.8000000000000003e-23

   1. Initial program 63.9%

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

      1. +-commutative 63.9%

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

      2. fma-define 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in a around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. distribute-neg-frac2 54.4%

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

   7. Simplified 54.4%

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

   8. Taylor expanded in t around -inf 64.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \left(\left(--1\right) - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-103}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a (/ x z)))))
   (if (<= z -1.5e+64)
     t_1
     (if (<= z -1.02e-103)
       (- x (* t (/ y z)))
       (if (<= z 2.8e+21) (+ x (* t (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -1.5e+64) {
		tmp = t_1;
	} else if (z <= -1.02e-103) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.8e+21) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (a * (x / z))
    if (z <= (-1.5d+64)) then
        tmp = t_1
    else if (z <= (-1.02d-103)) then
        tmp = x - (t * (y / z))
    else if (z <= 2.8d+21) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * (x / z));
	double tmp;
	if (z <= -1.5e+64) {
		tmp = t_1;
	} else if (z <= -1.02e-103) {
		tmp = x - (t * (y / z));
	} else if (z <= 2.8e+21) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * (x / z))
	tmp = 0
	if z <= -1.5e+64:
		tmp = t_1
	elif z <= -1.02e-103:
		tmp = x - (t * (y / z))
	elif z <= 2.8e+21:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * Float64(x / z)))
	tmp = 0.0
	if (z <= -1.5e+64)
		tmp = t_1;
	elseif (z <= -1.02e-103)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 2.8e+21)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * (x / z));
	tmp = 0.0;
	if (z <= -1.5e+64)
		tmp = t_1;
	elseif (z <= -1.02e-103)
		tmp = x - (t * (y / z));
	elseif (z <= 2.8e+21)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+64], t$95$1, If[LessEqual[z, -1.02e-103], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+21], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000001e64 or 2.8e21 < z

   1. Initial program 60.4%

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

   3. Taylor expanded in y around 0 28.6%

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

      1. mul-1-neg 28.6%

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

      2. distribute-neg-frac 28.6%

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

      3. *-commutative 28.6%

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

      4. distribute-rgt-neg-out 28.6%

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

   5. Simplified 28.6%

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

   6. Taylor expanded in z around inf 51.2%

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

      1. associate-/l* 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in t around 0 55.6%

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

       1. mul-1-neg 55.6%

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

       2. associate-/l* 58.7%

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

       3. distribute-rgt-neg-in 58.7%

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

       4. distribute-neg-frac 58.7%

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

   11. Simplified 58.7%

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

   if -1.5000000000000001e64 < z < -1.01999999999999998e-103

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. div-sub 80.4%

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

      3. mul-1-neg 80.4%

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

      4. associate-/l* 83.7%

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

      5. distribute-lft-neg-out 83.7%

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

      6. distribute-rgt-out 85.7%

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

      7. sub-neg 85.7%

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

      8. associate-/r/ 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in t around inf 74.4%

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

   7. Taylor expanded in y around inf 54.1%

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

   8. Taylor expanded in a around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. unsub-neg 42.5%

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

      3. associate-/l* 42.5%

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

   10. Simplified 42.5%

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

   if -1.01999999999999998e-103 < z < 2.8e21

   1. Initial program 91.9%

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

   3. Taylor expanded in t around inf 70.7%

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

      1. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in z around 0 58.6%

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

      1. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+64}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-103}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{x \cdot a}{z}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-103}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* x a) z))))
   (if (<= z -5.2e+60)
     t_1
     (if (<= z -1.02e-103)
       (- x (* t (/ y z)))
       (if (<= z 4.8e+21) (+ x (* t (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((x * a) / z);
	double tmp;
	if (z <= -5.2e+60) {
		tmp = t_1;
	} else if (z <= -1.02e-103) {
		tmp = x - (t * (y / z));
	} else if (z <= 4.8e+21) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((x * a) / z)
    if (z <= (-5.2d+60)) then
        tmp = t_1
    else if (z <= (-1.02d-103)) then
        tmp = x - (t * (y / z))
    else if (z <= 4.8d+21) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((x * a) / z);
	double tmp;
	if (z <= -5.2e+60) {
		tmp = t_1;
	} else if (z <= -1.02e-103) {
		tmp = x - (t * (y / z));
	} else if (z <= 4.8e+21) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((x * a) / z)
	tmp = 0
	if z <= -5.2e+60:
		tmp = t_1
	elif z <= -1.02e-103:
		tmp = x - (t * (y / z))
	elif z <= 4.8e+21:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(x * a) / z))
	tmp = 0.0
	if (z <= -5.2e+60)
		tmp = t_1;
	elseif (z <= -1.02e-103)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 4.8e+21)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((x * a) / z);
	tmp = 0.0;
	if (z <= -5.2e+60)
		tmp = t_1;
	elseif (z <= -1.02e-103)
		tmp = x - (t * (y / z));
	elseif (z <= 4.8e+21)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(x * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+60], t$95$1, If[LessEqual[z, -1.02e-103], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+21], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000016e60 or 4.8e21 < z

   1. Initial program 60.4%

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

   3. Taylor expanded in y around 0 28.6%

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

      1. mul-1-neg 28.6%

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

      2. distribute-neg-frac 28.6%

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

      3. *-commutative 28.6%

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

      4. distribute-rgt-neg-out 28.6%

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

   5. Simplified 28.6%

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

   6. Taylor expanded in z around inf 51.2%

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

      1. associate-/l* 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in t around 0 55.6%

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

       1. mul-1-neg 55.6%

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

   11. Simplified 55.6%

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

   if -5.20000000000000016e60 < z < -1.01999999999999998e-103

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. div-sub 80.4%

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

      3. mul-1-neg 80.4%

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

      4. associate-/l* 83.7%

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

      5. distribute-lft-neg-out 83.7%

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

      6. distribute-rgt-out 85.7%

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

      7. sub-neg 85.7%

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

      8. associate-/r/ 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in t around inf 74.4%

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

   7. Taylor expanded in y around inf 54.1%

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

   8. Taylor expanded in a around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. unsub-neg 42.5%

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

      3. associate-/l* 42.5%

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

   10. Simplified 42.5%

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

   if -1.01999999999999998e-103 < z < 4.8e21

   1. Initial program 91.9%

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

   3. Taylor expanded in t around inf 70.7%

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

      1. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in z around 0 58.6%

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

      1. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-103}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+156}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-103}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+100}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+156)
   t
   (if (<= z -1.02e-103)
     (- x (* t (/ y z)))
     (if (<= z 4.5e+100) (+ x (* t (/ y a))) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+156) {
		tmp = t;
	} else if (z <= -1.02e-103) {
		tmp = x - (t * (y / z));
	} else if (z <= 4.5e+100) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+156)) then
        tmp = t
    else if (z <= (-1.02d-103)) then
        tmp = x - (t * (y / z))
    else if (z <= 4.5d+100) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+156) {
		tmp = t;
	} else if (z <= -1.02e-103) {
		tmp = x - (t * (y / z));
	} else if (z <= 4.5e+100) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+156:
		tmp = t
	elif z <= -1.02e-103:
		tmp = x - (t * (y / z))
	elif z <= 4.5e+100:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+156)
		tmp = t;
	elseif (z <= -1.02e-103)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 4.5e+100)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+156)
		tmp = t;
	elseif (z <= -1.02e-103)
		tmp = x - (t * (y / z));
	elseif (z <= 4.5e+100)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+156], t, If[LessEqual[z, -1.02e-103], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+100], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000001e156 or 4.50000000000000036e100 < z

   1. Initial program 55.1%

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

   3. Taylor expanded in z around inf 43.3%

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

   4. Taylor expanded in x around 0 60.0%

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

   if -5.4000000000000001e156 < z < -1.01999999999999998e-103

   1. Initial program 77.4%

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

   3. Taylor expanded in y around 0 67.1%

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

      1. +-commutative 67.1%

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

      2. div-sub 67.2%

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

      3. mul-1-neg 67.2%

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

      4. associate-/l* 76.1%

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

      5. distribute-lft-neg-out 76.1%

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

      6. distribute-rgt-out 77.4%

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

      7. sub-neg 77.4%

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

      8. associate-/r/ 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around inf 64.4%

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

   7. Taylor expanded in y around inf 46.7%

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

   8. Taylor expanded in a around 0 38.3%

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

      1. mul-1-neg 38.3%

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

      2. unsub-neg 38.3%

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

      3. associate-/l* 37.1%

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

   10. Simplified 37.1%

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

   if -1.01999999999999998e-103 < z < 4.50000000000000036e100

   1. Initial program 88.8%

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

   3. Taylor expanded in t around inf 66.3%

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

      1. associate-/l* 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in z around 0 53.3%

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

      1. associate-/l* 57.2%

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

   8. Simplified 57.2%

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

Alternative 10: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-96} \lor \neg \left(a \leq 1.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.7e-96) (not (<= a 1.8e-11)))
   (+ x (* t (/ (- y z) (- a z))))
   (+ t (/ (* (- t x) (- a y)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.7e-96) || !(a <= 1.8e-11)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.7d-96)) .or. (.not. (a <= 1.8d-11))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.7e-96) || !(a <= 1.8e-11)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.7e-96) or not (a <= 1.8e-11):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.7e-96) || !(a <= 1.8e-11))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.7e-96) || ~((a <= 1.8e-11)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.7e-96], N[Not[LessEqual[a, 1.8e-11]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7e-96 or 1.79999999999999992e-11 < a

   1. Initial program 85.1%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 77.2%

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

   5. Simplified 77.2%

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

   if -2.7e-96 < a < 1.79999999999999992e-11

   1. Initial program 63.8%

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

      1. +-commutative 63.8%

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

      2. remove-double-neg 63.8%

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

      3. unsub-neg 63.8%

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

      4. *-commutative 63.8%

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

      5. associate-*l/ 60.7%

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

      6. associate-/l* 69.5%

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

      7. fma-neg 69.6%

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

      8. remove-double-neg 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in z around inf 83.7%

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

      1. associate--l+ 83.7%

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

      2. associate-*r/ 83.7%

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

      3. associate-*r/ 83.7%

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

      4. mul-1-neg 83.7%

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

      5. div-sub 83.7%

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

      6. mul-1-neg 83.7%

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

      7. distribute-lft-out-- 83.7%

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

      8. associate-*r/ 83.7%

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

      9. mul-1-neg 83.7%

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

      10. unsub-neg 83.7%

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

      11. distribute-rgt-out-- 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-96} \lor \neg \left(a \leq 1.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-96} \lor \neg \left(a \leq 5 \cdot 10^{-16}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.1e-96) (not (<= a 5e-16)))
   (+ x (* t (/ (- y z) (- a z))))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1e-96) || !(a <= 5e-16)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.1d-96)) .or. (.not. (a <= 5d-16))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.1e-96) || !(a <= 5e-16)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.1e-96) or not (a <= 5e-16):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.1e-96) || !(a <= 5e-16))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.1e-96) || ~((a <= 5e-16)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.1e-96], N[Not[LessEqual[a, 5e-16]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0999999999999999e-96 or 5.0000000000000004e-16 < a

   1. Initial program 84.6%

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

   3. Taylor expanded in t around inf 61.0%

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

      1. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   if -1.0999999999999999e-96 < a < 5.0000000000000004e-16

   1. Initial program 64.3%

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

      1. +-commutative 64.3%

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

      2. fma-define 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in a around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. distribute-neg-frac2 54.8%

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

   7. Simplified 54.8%

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

   8. Taylor expanded in y around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. div-sub 77.4%

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

      3. associate-/l* 75.0%

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

      4. unsub-neg 75.0%

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

      5. associate-/l* 77.4%

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

   10. Simplified 77.4%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-96} \lor \neg \left(a \leq 5 \cdot 10^{-16}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-10} \lor \neg \left(y \leq 2.8 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.06e-10) (not (<= y 2.8e+43)))
   (* y (/ (- t x) (- a z)))
   (+ t (* a (/ (- t x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.06e-10) || !(y <= 2.8e+43)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.06d-10)) .or. (.not. (y <= 2.8d+43))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t + (a * ((t - x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.06e-10) || !(y <= 2.8e+43)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t + (a * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.06e-10) or not (y <= 2.8e+43):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t + (a * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.06e-10) || !(y <= 2.8e+43))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(t + Float64(a * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.06e-10) || ~((y <= 2.8e+43)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t + (a * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.06e-10], N[Not[LessEqual[y, 2.8e+43]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e-10 or 2.80000000000000019e43 < y

   1. Initial program 84.7%

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

   3. Taylor expanded in y around 0 72.6%

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

      1. +-commutative 72.6%

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

      2. div-sub 73.4%

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

      3. mul-1-neg 73.4%

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

      4. associate-/l* 82.2%

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

      5. distribute-lft-neg-out 82.2%

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

      6. distribute-rgt-out 84.7%

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

      7. sub-neg 84.7%

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

      8. associate-/r/ 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in y around inf 63.0%

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

   7. Taylor expanded in y around inf 66.8%

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

      1. div-sub 67.6%

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

   9. Simplified 67.6%

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

   if -1.06e-10 < y < 2.80000000000000019e43

   1. Initial program 67.9%

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

   3. Taylor expanded in y around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. distribute-neg-frac 46.6%

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

      3. *-commutative 46.6%

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

      4. distribute-rgt-neg-out 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in z around inf 48.0%

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

      1. associate-/l* 54.1%

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

   8. Simplified 54.1%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-10} \lor \neg \left(y \leq 2.8 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-14} \lor \neg \left(y \leq 6.2 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.4e-14) (not (<= y 6.2e+47)))
   (* y (/ (- t x) (- a z)))
   (- t (* a (/ x z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e-14) || !(y <= 6.2e+47)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t - (a * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.4d-14)) .or. (.not. (y <= 6.2d+47))) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t - (a * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e-14) || !(y <= 6.2e+47)) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t - (a * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.4e-14) or not (y <= 6.2e+47):
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t - (a * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.4e-14) || !(y <= 6.2e+47))
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = Float64(t - Float64(a * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.4e-14) || ~((y <= 6.2e+47)))
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t - (a * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.4e-14], N[Not[LessEqual[y, 6.2e+47]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-14 or 6.2000000000000001e47 < y

   1. Initial program 84.6%

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

   3. Taylor expanded in y around 0 73.1%

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

      1. +-commutative 73.1%

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

      2. div-sub 74.0%

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

      3. mul-1-neg 74.0%

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

      4. associate-/l* 82.1%

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

      5. distribute-lft-neg-out 82.1%

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

      6. distribute-rgt-out 84.6%

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

      7. sub-neg 84.6%

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

      8. associate-/r/ 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around inf 63.5%

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

   7. Taylor expanded in y around inf 67.3%

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

      1. div-sub 68.2%

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

   9. Simplified 68.2%

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

   if -1.4e-14 < y < 6.2000000000000001e47

   1. Initial program 68.1%

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

   3. Taylor expanded in y around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. distribute-neg-frac 46.3%

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

      3. *-commutative 46.3%

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

      4. distribute-rgt-neg-out 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in z around inf 47.6%

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

      1. associate-/l* 53.7%

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

   8. Simplified 53.7%

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

   9. Taylor expanded in t around 0 50.0%

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

       1. mul-1-neg 50.0%

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

       2. associate-/l* 53.3%

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

       3. distribute-rgt-neg-in 53.3%

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

       4. distribute-neg-frac 53.3%

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

   11. Simplified 53.3%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-14} \lor \neg \left(y \leq 6.2 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - a \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-23}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e+50)
   (+ x (* y (/ (- t x) a)))
   (if (<= a 9.5e-23) (+ t (* y (/ (- x t) z))) (+ x (/ (- t x) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+50) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 9.5e-23) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.8d+50)) then
        tmp = x + (y * ((t - x) / a))
    else if (a <= 9.5d-23) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+50) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 9.5e-23) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e+50:
		tmp = x + (y * ((t - x) / a))
	elif a <= 9.5e-23:
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e+50)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= 9.5e-23)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.8e+50)
		tmp = x + (y * ((t - x) / a));
	elseif (a <= 9.5e-23)
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e+50], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-23], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.79999999999999987e50

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 0 56.9%

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

      1. associate-/l* 68.1%

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

   5. Simplified 68.1%

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

   if -3.79999999999999987e50 < a < 9.50000000000000058e-23

   1. Initial program 67.7%

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

      1. +-commutative 67.7%

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

      2. fma-define 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in a around 0 53.2%

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

      1. mul-1-neg 53.2%

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

      2. distribute-neg-frac2 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in y around 0 72.7%

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

      1. mul-1-neg 72.7%

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

      2. div-sub 73.5%

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

      3. associate-/l* 69.6%

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

      4. unsub-neg 69.6%

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

      5. associate-/l* 73.5%

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

   10. Simplified 73.5%

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

   if 9.50000000000000058e-23 < a

   1. Initial program 84.3%

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

   3. Taylor expanded in y around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. div-sub 71.1%

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

      3. mul-1-neg 71.1%

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

      4. associate-/l* 82.8%

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

      5. distribute-lft-neg-out 82.8%

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

      6. distribute-rgt-out 84.3%

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

      7. sub-neg 84.3%

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

      8. associate-/r/ 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in z around 0 62.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-23}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+49} \lor \neg \left(a \leq 4.9 \cdot 10^{-24}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(--1\right) - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.8e+49) (not (<= a 4.9e-24)))
   (+ x (* t (/ y a)))
   (* t (- (- -1.0) (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.8e+49) || !(a <= 4.9e-24)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * (-(-1.0) - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.8d+49)) .or. (.not. (a <= 4.9d-24))) then
        tmp = x + (t * (y / a))
    else
        tmp = t * (-(-1.0d0) - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.8e+49) || !(a <= 4.9e-24)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * (-(-1.0) - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.8e+49) or not (a <= 4.9e-24):
		tmp = x + (t * (y / a))
	else:
		tmp = t * (-(-1.0) - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.8e+49) || !(a <= 4.9e-24))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(-(-1.0)) - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.8e+49) || ~((a <= 4.9e-24)))
		tmp = x + (t * (y / a));
	else
		tmp = t * (-(-1.0) - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.8e+49], N[Not[LessEqual[a, 4.9e-24]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[((--1.0) - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7999999999999999e49 or 4.9000000000000001e-24 < a

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. associate-/l* 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around 0 49.6%

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

      1. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

   if -3.7999999999999999e49 < a < 4.9000000000000001e-24

   1. Initial program 67.4%

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

      1. +-commutative 67.4%

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

      2. fma-define 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in a around 0 52.8%

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

      1. mul-1-neg 52.8%

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

      2. distribute-neg-frac2 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in t around -inf 57.3%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+49} \lor \neg \left(a \leq 4.9 \cdot 10^{-24}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(--1\right) - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -160000000000 \lor \neg \left(a \leq 3.9 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -160000000000.0) (not (<= a 3.9e-20)))
   (* x (- 1.0 (/ y a)))
   (+ t (* a (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -160000000000.0) || !(a <= 3.9e-20)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t + (a * (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-160000000000.0d0)) .or. (.not. (a <= 3.9d-20))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t + (a * (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -160000000000.0) || !(a <= 3.9e-20)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t + (a * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -160000000000.0) or not (a <= 3.9e-20):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t + (a * (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -160000000000.0) || !(a <= 3.9e-20))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t + Float64(a * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -160000000000.0) || ~((a <= 3.9e-20)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = t + (a * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -160000000000.0], N[Not[LessEqual[a, 3.9e-20]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6e11 or 3.90000000000000007e-20 < a

   1. Initial program 84.8%

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

   3. Taylor expanded in y around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. div-sub 71.6%

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

      3. mul-1-neg 71.6%

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

      4. associate-/l* 84.8%

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

      5. distribute-lft-neg-out 84.8%

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

      6. distribute-rgt-out 84.8%

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

      7. sub-neg 84.8%

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

      8. associate-/r/ 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in z around 0 62.9%

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

   7. Taylor expanded in x around inf 47.7%

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

      1. mul-1-neg 47.7%

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

      2. unsub-neg 47.7%

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

   9. Simplified 47.7%

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

   if -1.6e11 < a < 3.90000000000000007e-20

   1. Initial program 66.7%

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

   3. Taylor expanded in y around 0 22.0%

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

      1. mul-1-neg 22.0%

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

      2. distribute-neg-frac 22.0%

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

      3. *-commutative 22.0%

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

      4. distribute-rgt-neg-out 22.0%

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

   5. Simplified 22.0%

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

   6. Taylor expanded in z around inf 48.8%

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

      1. associate-/l* 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in t around inf 41.8%

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

       1. associate-/l* 44.8%

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

   11. Simplified 44.8%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -160000000000 \lor \neg \left(a \leq 3.9 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+156}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+99}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+156) t (if (<= z 3.5e+99) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+156) {
		tmp = t;
	} else if (z <= 3.5e+99) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+156)) then
        tmp = t
    else if (z <= 3.5d+99) then
        tmp = x + (t * (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+156) {
		tmp = t;
	} else if (z <= 3.5e+99) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+156:
		tmp = t
	elif z <= 3.5e+99:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+156)
		tmp = t;
	elseif (z <= 3.5e+99)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+156)
		tmp = t;
	elseif (z <= 3.5e+99)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+156], t, If[LessEqual[z, 3.5e+99], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000027e156 or 3.4999999999999998e99 < z

   1. Initial program 55.1%

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

   3. Taylor expanded in z around inf 43.3%

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

   4. Taylor expanded in x around 0 60.0%

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

   if -6.50000000000000027e156 < z < 3.4999999999999998e99

   1. Initial program 84.2%

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

   3. Taylor expanded in t around inf 63.5%

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

      1. associate-/l* 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in z around 0 42.8%

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

      1. associate-/l* 46.7%

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

   8. Simplified 46.7%

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

Alternative 18: 48.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+161) t (if (<= z 1.35e+22) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+161) {
		tmp = t;
	} else if (z <= 1.35e+22) {
		tmp = x * (1.0 - (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 <= (-1.95d+161)) then
        tmp = t
    else if (z <= 1.35d+22) then
        tmp = x * (1.0d0 - (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 <= -1.95e+161) {
		tmp = t;
	} else if (z <= 1.35e+22) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+161:
		tmp = t
	elif z <= 1.35e+22:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+161)
		tmp = t;
	elseif (z <= 1.35e+22)
		tmp = Float64(x * Float64(1.0 - 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 <= -1.95e+161)
		tmp = t;
	elseif (z <= 1.35e+22)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+161], t, If[LessEqual[z, 1.35e+22], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e161 or 1.3500000000000001e22 < z

   1. Initial program 60.4%

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

   3. Taylor expanded in z around inf 38.7%

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

   4. Taylor expanded in x around 0 53.5%

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

   if -1.9500000000000001e161 < z < 1.3500000000000001e22

   1. Initial program 85.2%

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

   3. Taylor expanded in y around 0 79.7%

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

      1. +-commutative 79.7%

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

      2. div-sub 80.4%

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

      3. mul-1-neg 80.4%

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

      4. associate-/l* 82.6%

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

      5. distribute-lft-neg-out 82.6%

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

      6. distribute-rgt-out 85.2%

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

      7. sub-neg 85.2%

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

      8. associate-/r/ 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in z around 0 60.3%

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

   7. Taylor expanded in x around inf 41.0%

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

      1. mul-1-neg 41.0%

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

      2. unsub-neg 41.0%

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

   9. Simplified 41.0%

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

Alternative 19: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e+49) x (if (<= a 2.35e+80) t (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+49) {
		tmp = x;
	} else if (a <= 2.35e+80) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.5d+49)) then
        tmp = x
    else if (a <= 2.35d+80) then
        tmp = t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+49) {
		tmp = x;
	} else if (a <= 2.35e+80) {
		tmp = t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e+49:
		tmp = x
	elif a <= 2.35e+80:
		tmp = t
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e+49)
		tmp = x;
	elseif (a <= 2.35e+80)
		tmp = t;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e+49)
		tmp = x;
	elseif (a <= 2.35e+80)
		tmp = t;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e+49], x, If[LessEqual[a, 2.35e+80], t, N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.49999999999999982e49

   1. Initial program 86.9%

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

      1. +-commutative 86.9%

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

      2. remove-double-neg 86.9%

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

      3. unsub-neg 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-*l/ 66.3%

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

      6. associate-/l* 90.4%

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

      7. fma-neg 90.5%

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

      8. remove-double-neg 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in a around inf 41.3%

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

   if -4.49999999999999982e49 < a < 2.35000000000000005e80

   1. Initial program 68.8%

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

   3. Taylor expanded in z around inf 25.7%

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

   4. Taylor expanded in x around 0 37.4%

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

   if 2.35000000000000005e80 < a

   1. Initial program 87.5%

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

   3. Taylor expanded in t around inf 59.9%

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

      1. associate-/l* 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in z around inf 48.5%

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

Alternative 20: 39.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e+49) x (if (<= a 2.5e+80) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e+49) {
		tmp = x;
	} else if (a <= 2.5e+80) {
		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 <= (-4.5d+49)) then
        tmp = x
    else if (a <= 2.5d+80) 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 <= -4.5e+49) {
		tmp = x;
	} else if (a <= 2.5e+80) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e+49:
		tmp = x
	elif a <= 2.5e+80:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e+49)
		tmp = x;
	elseif (a <= 2.5e+80)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e+49)
		tmp = x;
	elseif (a <= 2.5e+80)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e+49], x, If[LessEqual[a, 2.5e+80], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.49999999999999982e49 or 2.4999999999999998e80 < a

   1. Initial program 87.2%

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

      1. +-commutative 87.2%

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

      2. remove-double-neg 87.2%

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

      3. unsub-neg 87.2%

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

      4. *-commutative 87.2%

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

      5. associate-*l/ 63.2%

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

      6. associate-/l* 90.8%

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

      7. fma-neg 90.8%

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

      8. remove-double-neg 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in a around inf 43.6%

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

   if -4.49999999999999982e49 < a < 2.4999999999999998e80

   1. Initial program 68.8%

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

   3. Taylor expanded in z around inf 25.7%

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

   4. Taylor expanded in x around 0 37.4%

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

Alternative 21: 25.3% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 75.8%

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

3. Taylor expanded in z around inf 20.9%

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

4. Taylor expanded in x around 0 28.3%

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

Reproduce

herbie shell --seed 2024139 
(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)))))