Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 93.1%

Time: 16.6s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-263} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-263) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (- t (/ (* (- t x) (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-263) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-263) || !(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(y - a)) / 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, -5e-263], 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[(y - a), $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)))) < -5.00000000000000006e-263 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.4%

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

      1. +-commutative 91.4%

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

      2. remove-double-neg 91.4%

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

      3. unsub-neg 91.4%

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

      4. *-commutative 91.4%

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

      5. associate-*l/ 75.9%

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

      6. associate-/l* 95.9%

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

      7. fma-neg 96.0%

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

      8. remove-double-neg 96.0%

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

   3. Simplified 96.0%

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

   if -5.00000000000000006e-263 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.0%

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

      1. +-commutative 3.0%

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

      2. remove-double-neg 3.0%

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

      3. unsub-neg 3.0%

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

      4. *-commutative 3.0%

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

      5. associate-*l/ 2.9%

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

      6. associate-/l* 3.0%

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

      7. fma-neg 3.0%

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

      8. remove-double-neg 3.0%

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

   3. Simplified 3.0%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. associate--l+ 87.3%

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

      2. associate-*r/ 87.3%

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

      3. associate-*r/ 87.3%

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

      4. mul-1-neg 87.3%

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

      5. div-sub 87.3%

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

      6. mul-1-neg 87.3%

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

      7. distribute-lft-out-- 87.3%

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

      8. associate-*r/ 87.3%

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

      9. mul-1-neg 87.3%

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

      10. unsub-neg 87.3%

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

      11. distribute-rgt-out-- 87.3%

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

   7. Simplified 87.3%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-263} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-263} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-263) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (- t (/ (* (- t x) (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-263) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-263)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t - (((t - x) * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-263) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-263) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-263) || !(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(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-263) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t - (((t - x) * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-263], 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[(y - a), $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)))) < -5.00000000000000006e-263 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. +-commutative 75.0%

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

      2. div-sub 76.8%

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

      3. mul-1-neg 76.8%

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

      4. associate-/l* 87.0%

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

      5. distribute-lft-neg-out 87.0%

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

      6. distribute-rgt-out 91.4%

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

      7. sub-neg 91.4%

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

      8. associate-/r/ 95.9%

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

   5. Simplified 95.9%

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

   if -5.00000000000000006e-263 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.0%

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

      1. +-commutative 3.0%

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

      2. remove-double-neg 3.0%

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

      3. unsub-neg 3.0%

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

      4. *-commutative 3.0%

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

      5. associate-*l/ 2.9%

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

      6. associate-/l* 3.0%

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

      7. fma-neg 3.0%

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

      8. remove-double-neg 3.0%

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

   3. Simplified 3.0%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. associate--l+ 87.3%

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

      2. associate-*r/ 87.3%

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

      3. associate-*r/ 87.3%

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

      4. mul-1-neg 87.3%

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

      5. div-sub 87.3%

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

      6. mul-1-neg 87.3%

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

      7. distribute-lft-out-- 87.3%

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

      8. associate-*r/ 87.3%

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

      9. mul-1-neg 87.3%

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

      10. unsub-neg 87.3%

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

      11. distribute-rgt-out-- 87.3%

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

   7. Simplified 87.3%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-263} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-263} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-308}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-263) (not (<= t_1 2e-308)))
     t_1
     (- t (/ (* (- t x) (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-263) || !(t_1 <= 2e-308)) {
		tmp = t_1;
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-263)) .or. (.not. (t_1 <= 2d-308))) then
        tmp = t_1
    else
        tmp = t - (((t - x) * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-263) || !(t_1 <= 2e-308)) {
		tmp = t_1;
	} else {
		tmp = t - (((t - x) * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-263) or not (t_1 <= 2e-308):
		tmp = t_1
	else:
		tmp = t - (((t - x) * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-263) || !(t_1 <= 2e-308))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-263) || ~((t_1 <= 2e-308)))
		tmp = t_1;
	else
		tmp = t - (((t - x) * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-263], N[Not[LessEqual[t$95$1, 2e-308]], $MachinePrecision]], t$95$1, N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $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)))) < -5.00000000000000006e-263 or 1.9999999999999998e-308 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.7%

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

   if -5.00000000000000006e-263 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9999999999999998e-308

   1. Initial program 3.1%

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

      1. +-commutative 3.1%

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

      2. remove-double-neg 3.1%

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

      3. unsub-neg 3.1%

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

      4. *-commutative 3.1%

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

      5. associate-*l/ 6.9%

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

      6. associate-/l* 7.1%

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

      7. fma-neg 7.1%

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

      8. remove-double-neg 7.1%

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

   3. Simplified 7.1%

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

   5. Taylor expanded in z around inf 87.8%

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

      1. associate--l+ 87.8%

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

      2. associate-*r/ 87.8%

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

      3. associate-*r/ 87.8%

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

      4. mul-1-neg 87.8%

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

      5. div-sub 87.8%

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

      6. mul-1-neg 87.8%

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

      7. distribute-lft-out-- 87.8%

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

      8. associate-*r/ 87.8%

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

      9. mul-1-neg 87.8%

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

      10. unsub-neg 87.8%

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

      11. distribute-rgt-out-- 87.8%

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

   7. Simplified 87.8%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-263} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-308}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+156}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-67}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} + \frac{z}{z - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.4e+156)
   (- t (* y (/ (- t x) z)))
   (if (<= z -7.4e-67)
     (+ x (* (- y z) (/ t (- a z))))
     (if (<= z 1.6e+24)
       (+ x (/ y (/ (- a z) (- t x))))
       (* t (+ (/ y (- a z)) (/ z (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.4e+156) {
		tmp = t - (y * ((t - x) / z));
	} else if (z <= -7.4e-67) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 1.6e+24) {
		tmp = x + (y / ((a - z) / (t - x)));
	} else {
		tmp = t * ((y / (a - z)) + (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.4d+156)) then
        tmp = t - (y * ((t - x) / z))
    else if (z <= (-7.4d-67)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (z <= 1.6d+24) then
        tmp = x + (y / ((a - z) / (t - x)))
    else
        tmp = t * ((y / (a - z)) + (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.4e+156) {
		tmp = t - (y * ((t - x) / z));
	} else if (z <= -7.4e-67) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 1.6e+24) {
		tmp = x + (y / ((a - z) / (t - x)));
	} else {
		tmp = t * ((y / (a - z)) + (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.4e+156:
		tmp = t - (y * ((t - x) / z))
	elif z <= -7.4e-67:
		tmp = x + ((y - z) * (t / (a - z)))
	elif z <= 1.6e+24:
		tmp = x + (y / ((a - z) / (t - x)))
	else:
		tmp = t * ((y / (a - z)) + (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.4e+156)
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	elseif (z <= -7.4e-67)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (z <= 1.6e+24)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) + Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.4e+156)
		tmp = t - (y * ((t - x) / z));
	elseif (z <= -7.4e-67)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (z <= 1.6e+24)
		tmp = x + (y / ((a - z) / (t - x)));
	else
		tmp = t * ((y / (a - z)) + (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.4e+156], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.4e-67], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+24], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.40000000000000005e156

   1. Initial program 51.8%

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

      1. +-commutative 51.8%

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

      2. fma-define 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in a around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. distribute-neg-frac2 39.5%

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

   7. Simplified 39.5%

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

   8. Taylor expanded in y around 0 71.0%

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

      1. div-sub 71.0%

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

      2. associate-/l* 57.0%

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

      3. mul-1-neg 57.0%

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

      4. unsub-neg 57.0%

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

      5. associate-/l* 71.0%

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

   10. Simplified 71.0%

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

   if -6.40000000000000005e156 < z < -7.3999999999999999e-67

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 80.3%

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

   if -7.3999999999999999e-67 < z < 1.5999999999999999e24

   1. Initial program 91.5%

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

      1. clear-num 91.5%

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

      2. un-div-inv 92.3%

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

   4. Applied egg-rr 92.3%

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

   5. Taylor expanded in y around inf 86.8%

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

   if 1.5999999999999999e24 < z

   1. Initial program 76.2%

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

      1. +-commutative 76.2%

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

      2. remove-double-neg 76.2%

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

      3. unsub-neg 76.2%

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

      4. *-commutative 76.2%

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

      5. associate-*l/ 41.7%

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

      6. associate-/l* 78.6%

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

      7. fma-neg 78.6%

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

      8. remove-double-neg 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in t around inf 70.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+156}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-67}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} + \frac{z}{z - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+156}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-66} \lor \neg \left(z \leq 1.2 \cdot 10^{+20}\right):\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.8e+156)
   (- t (* y (/ (- t x) z)))
   (if (or (<= z -3e-66) (not (<= z 1.2e+20)))
     (- x (* t (/ (- z y) (- a z))))
     (+ x (* y (/ (- t x) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.8e+156) {
		tmp = t - (y * ((t - x) / z));
	} else if ((z <= -3e-66) || !(z <= 1.2e+20)) {
		tmp = x - (t * ((z - y) / (a - z)));
	} else {
		tmp = x + (y * ((t - x) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.8d+156)) then
        tmp = t - (y * ((t - x) / z))
    else if ((z <= (-3d-66)) .or. (.not. (z <= 1.2d+20))) then
        tmp = x - (t * ((z - y) / (a - z)))
    else
        tmp = x + (y * ((t - x) / (a - 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 (z <= -5.8e+156) {
		tmp = t - (y * ((t - x) / z));
	} else if ((z <= -3e-66) || !(z <= 1.2e+20)) {
		tmp = x - (t * ((z - y) / (a - z)));
	} else {
		tmp = x + (y * ((t - x) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.8e+156:
		tmp = t - (y * ((t - x) / z))
	elif (z <= -3e-66) or not (z <= 1.2e+20):
		tmp = x - (t * ((z - y) / (a - z)))
	else:
		tmp = x + (y * ((t - x) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.8e+156)
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	elseif ((z <= -3e-66) || !(z <= 1.2e+20))
		tmp = Float64(x - Float64(t * Float64(Float64(z - y) / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.8e+156)
		tmp = t - (y * ((t - x) / z));
	elseif ((z <= -3e-66) || ~((z <= 1.2e+20)))
		tmp = x - (t * ((z - y) / (a - z)));
	else
		tmp = x + (y * ((t - x) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.8e+156], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3e-66], N[Not[LessEqual[z, 1.2e+20]], $MachinePrecision]], N[(x - N[(t * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.80000000000000021e156

   1. Initial program 51.8%

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

      1. +-commutative 51.8%

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

      2. fma-define 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in a around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. distribute-neg-frac2 39.5%

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

   7. Simplified 39.5%

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

   8. Taylor expanded in y around 0 71.0%

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

      1. div-sub 71.0%

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

      2. associate-/l* 57.0%

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

      3. mul-1-neg 57.0%

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

      4. unsub-neg 57.0%

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

      5. associate-/l* 71.0%

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

   10. Simplified 71.0%

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

   if -5.80000000000000021e156 < z < -3.0000000000000002e-66 or 1.2e20 < z

   1. Initial program 82.8%

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

   3. Taylor expanded in t around inf 55.2%

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

      1. associate-/l* 73.8%

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

   5. Simplified 73.8%

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

   if -3.0000000000000002e-66 < z < 1.2e20

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 85.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+156}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-66} \lor \neg \left(z \leq 1.2 \cdot 10^{+20}\right):\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+156}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-67}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+156)
   (- t (* y (/ (- t x) z)))
   (if (<= z -5.6e-67)
     (+ x (* (- y z) (/ t (- a z))))
     (if (<= z 8.5e+19)
       (+ x (/ y (/ (- a z) (- t x))))
       (- x (* t (/ (- z y) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+156) {
		tmp = t - (y * ((t - x) / z));
	} else if (z <= -5.6e-67) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 8.5e+19) {
		tmp = x + (y / ((a - z) / (t - x)));
	} else {
		tmp = x - (t * ((z - y) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.65d+156)) then
        tmp = t - (y * ((t - x) / z))
    else if (z <= (-5.6d-67)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (z <= 8.5d+19) then
        tmp = x + (y / ((a - z) / (t - x)))
    else
        tmp = x - (t * ((z - y) / (a - 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 (z <= -1.65e+156) {
		tmp = t - (y * ((t - x) / z));
	} else if (z <= -5.6e-67) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 8.5e+19) {
		tmp = x + (y / ((a - z) / (t - x)));
	} else {
		tmp = x - (t * ((z - y) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+156:
		tmp = t - (y * ((t - x) / z))
	elif z <= -5.6e-67:
		tmp = x + ((y - z) * (t / (a - z)))
	elif z <= 8.5e+19:
		tmp = x + (y / ((a - z) / (t - x)))
	else:
		tmp = x - (t * ((z - y) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+156)
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	elseif (z <= -5.6e-67)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (z <= 8.5e+19)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(x - Float64(t * Float64(Float64(z - y) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+156)
		tmp = t - (y * ((t - x) / z));
	elseif (z <= -5.6e-67)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (z <= 8.5e+19)
		tmp = x + (y / ((a - z) / (t - x)));
	else
		tmp = x - (t * ((z - y) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+156], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.6e-67], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+19], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6499999999999999e156

   1. Initial program 51.8%

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

      1. +-commutative 51.8%

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

      2. fma-define 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in a around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. distribute-neg-frac2 39.5%

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

   7. Simplified 39.5%

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

   8. Taylor expanded in y around 0 71.0%

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

      1. div-sub 71.0%

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

      2. associate-/l* 57.0%

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

      3. mul-1-neg 57.0%

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

      4. unsub-neg 57.0%

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

      5. associate-/l* 71.0%

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

   10. Simplified 71.0%

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

   if -1.6499999999999999e156 < z < -5.60000000000000021e-67

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 80.3%

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

   if -5.60000000000000021e-67 < z < 8.5e19

   1. Initial program 91.5%

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

      1. clear-num 91.5%

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

      2. un-div-inv 92.2%

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

   4. Applied egg-rr 92.2%

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

   5. Taylor expanded in y around inf 86.7%

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

   if 8.5e19 < z

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf 37.2%

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

      1. associate-/l* 69.1%

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

   5. Simplified 69.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+156}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-67}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+19}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+162}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-66}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+162)
   (- t (* y (/ (- t x) z)))
   (if (<= z -1.3e-66)
     (+ x (* (- y z) (/ t (- a z))))
     (if (<= z 8.5e+19)
       (+ x (* y (/ (- t x) (- a z))))
       (- x (* t (/ (- z y) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+162) {
		tmp = t - (y * ((t - x) / z));
	} else if (z <= -1.3e-66) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 8.5e+19) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = x - (t * ((z - y) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+162)) then
        tmp = t - (y * ((t - x) / z))
    else if (z <= (-1.3d-66)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (z <= 8.5d+19) then
        tmp = x + (y * ((t - x) / (a - z)))
    else
        tmp = x - (t * ((z - y) / (a - 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 (z <= -1.45e+162) {
		tmp = t - (y * ((t - x) / z));
	} else if (z <= -1.3e-66) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 8.5e+19) {
		tmp = x + (y * ((t - x) / (a - z)));
	} else {
		tmp = x - (t * ((z - y) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+162:
		tmp = t - (y * ((t - x) / z))
	elif z <= -1.3e-66:
		tmp = x + ((y - z) * (t / (a - z)))
	elif z <= 8.5e+19:
		tmp = x + (y * ((t - x) / (a - z)))
	else:
		tmp = x - (t * ((z - y) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+162)
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	elseif (z <= -1.3e-66)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (z <= 8.5e+19)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t * Float64(Float64(z - y) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+162)
		tmp = t - (y * ((t - x) / z));
	elseif (z <= -1.3e-66)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (z <= 8.5e+19)
		tmp = x + (y * ((t - x) / (a - z)));
	else
		tmp = x - (t * ((z - y) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+162], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-66], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+19], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45000000000000003e162

   1. Initial program 51.8%

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

      1. +-commutative 51.8%

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

      2. fma-define 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in a around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. distribute-neg-frac2 39.5%

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

   7. Simplified 39.5%

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

   8. Taylor expanded in y around 0 71.0%

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

      1. div-sub 71.0%

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

      2. associate-/l* 57.0%

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

      3. mul-1-neg 57.0%

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

      4. unsub-neg 57.0%

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

      5. associate-/l* 71.0%

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

   10. Simplified 71.0%

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

   if -1.45000000000000003e162 < z < -1.2999999999999999e-66

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 80.3%

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

   if -1.2999999999999999e-66 < z < 8.5e19

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 85.9%

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

   if 8.5e19 < z

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf 37.2%

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

      1. associate-/l* 69.1%

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

   5. Simplified 69.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+162}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-66}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-230} \lor \neg \left(a \leq 9.5 \cdot 10^{-132}\right):\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.55e-230) (not (<= a 9.5e-132)))
   (- x (* t (/ (- z y) (- a z))))
   (- t (* y (/ (- t x) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.55e-230) || !(a <= 9.5e-132)) {
		tmp = x - (t * ((z - y) / (a - z)));
	} else {
		tmp = t - (y * ((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 ((a <= (-1.55d-230)) .or. (.not. (a <= 9.5d-132))) then
        tmp = x - (t * ((z - y) / (a - z)))
    else
        tmp = t - (y * ((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 ((a <= -1.55e-230) || !(a <= 9.5e-132)) {
		tmp = x - (t * ((z - y) / (a - z)));
	} else {
		tmp = t - (y * ((t - x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.55e-230) or not (a <= 9.5e-132):
		tmp = x - (t * ((z - y) / (a - z)))
	else:
		tmp = t - (y * ((t - x) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.55e-230) || !(a <= 9.5e-132))
		tmp = Float64(x - Float64(t * Float64(Float64(z - y) / Float64(a - z))));
	else
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.55e-230) || ~((a <= 9.5e-132)))
		tmp = x - (t * ((z - y) / (a - z)));
	else
		tmp = t - (y * ((t - x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.55e-230], N[Not[LessEqual[a, 9.5e-132]], $MachinePrecision]], N[(x - N[(t * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e-230 or 9.49999999999999987e-132 < a

   1. Initial program 85.2%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   if -1.55e-230 < a < 9.49999999999999987e-132

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. fma-define 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in a around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. distribute-neg-frac2 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in y around 0 77.2%

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

      1. div-sub 85.5%

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

      2. associate-/l* 86.3%

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

      3. mul-1-neg 86.3%

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

      4. unsub-neg 86.3%

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

      5. associate-/l* 85.5%

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

   10. Simplified 85.5%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-230} \lor \neg \left(a \leq 9.5 \cdot 10^{-132}\right):\\ \;\;\;\;x - t \cdot \frac{z - y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-48} \lor \neg \left(y \leq 1.22 \cdot 10^{+117}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.2e+112)
   (* x (/ (- y) a))
   (if (or (<= y -2.6e-48) (not (<= y 1.22e+117))) (* t (/ y a)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.2e+112) {
		tmp = x * (-y / a);
	} else if ((y <= -2.6e-48) || !(y <= 1.22e+117)) {
		tmp = t * (y / a);
	} 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 (y <= (-6.2d+112)) then
        tmp = x * (-y / a)
    else if ((y <= (-2.6d-48)) .or. (.not. (y <= 1.22d+117))) then
        tmp = t * (y / a)
    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 (y <= -6.2e+112) {
		tmp = x * (-y / a);
	} else if ((y <= -2.6e-48) || !(y <= 1.22e+117)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.2e+112:
		tmp = x * (-y / a)
	elif (y <= -2.6e-48) or not (y <= 1.22e+117):
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.2e+112)
		tmp = Float64(x * Float64(Float64(-y) / a));
	elseif ((y <= -2.6e-48) || !(y <= 1.22e+117))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.2e+112)
		tmp = x * (-y / a);
	elseif ((y <= -2.6e-48) || ~((y <= 1.22e+117)))
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.2e+112], N[(x * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.6e-48], N[Not[LessEqual[y, 1.22e+117]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999965e112

   1. Initial program 91.0%

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

   3. Taylor expanded in z around 0 50.9%

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

      1. associate-/l* 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in x around inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. unsub-neg 50.8%

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

   8. Simplified 50.8%

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

   9. Taylor expanded in y around inf 50.1%

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

       1. neg-mul-1 50.1%

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

       2. distribute-neg-frac 50.1%

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

   11. Simplified 50.1%

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

   if -6.19999999999999965e112 < y < -2.59999999999999987e-48 or 1.22000000000000004e117 < y

   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/ 66.5%

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

      6. associate-/l* 90.7%

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

      7. fma-neg 90.7%

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

      8. remove-double-neg 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in t around inf 71.1%

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

   6. Taylor expanded in z around 0 53.2%

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

   if -2.59999999999999987e-48 < y < 1.22000000000000004e117

   1. Initial program 79.5%

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

   3. Taylor expanded in t around inf 64.1%

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

      1. associate-/l* 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around inf 46.7%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-48} \lor \neg \left(y \leq 1.22 \cdot 10^{+117}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-20} \lor \neg \left(z \leq 20000000\right):\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e-20) (not (<= z 20000000.0)))
   (- t (* y (/ (- t x) z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e-20) || !(z <= 20000000.0)) {
		tmp = t - (y * ((t - x) / 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 ((z <= (-4.5d-20)) .or. (.not. (z <= 20000000.0d0))) then
        tmp = t - (y * ((t - x) / 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 ((z <= -4.5e-20) || !(z <= 20000000.0)) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e-20) or not (z <= 20000000.0):
		tmp = t - (y * ((t - x) / z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e-20) || !(z <= 20000000.0))
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / 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 ((z <= -4.5e-20) || ~((z <= 20000000.0)))
		tmp = t - (y * ((t - x) / z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e-20], N[Not[LessEqual[z, 20000000.0]], $MachinePrecision]], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000001e-20 or 2e7 < z

   1. Initial program 72.8%

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

      1. +-commutative 72.8%

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

      2. fma-define 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in a around 0 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 68.4%

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

      1. div-sub 68.4%

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

      2. associate-/l* 62.8%

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

      3. mul-1-neg 62.8%

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

      4. unsub-neg 62.8%

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

      5. associate-/l* 68.4%

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

   10. Simplified 68.4%

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

   if -4.5000000000000001e-20 < z < 2e7

   1. Initial program 91.8%

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

   3. Taylor expanded in y around 0 89.0%

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

      1. +-commutative 89.0%

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

      2. div-sub 91.9%

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

      3. mul-1-neg 91.9%

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

      4. associate-/l* 84.7%

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

      5. distribute-lft-neg-out 84.7%

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

      6. distribute-rgt-out 91.8%

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

      7. sub-neg 91.8%

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

      8. associate-/r/ 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in z around 0 80.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-20} \lor \neg \left(z \leq 20000000\right):\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-13} \lor \neg \left(z \leq 2.55 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e-13) (not (<= z 2.55e+26)))
   (* t (- 1.0 (/ y z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e-13) || !(z <= 2.55e+26)) {
		tmp = t * (1.0 - (y / 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 ((z <= (-2.6d-13)) .or. (.not. (z <= 2.55d+26))) then
        tmp = t * (1.0d0 - (y / 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 ((z <= -2.6e-13) || !(z <= 2.55e+26)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e-13) or not (z <= 2.55e+26):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e-13) || !(z <= 2.55e+26))
		tmp = Float64(t * Float64(1.0 - Float64(y / 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 ((z <= -2.6e-13) || ~((z <= 2.55e+26)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e-13], N[Not[LessEqual[z, 2.55e+26]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e-13 or 2.5499999999999999e26 < z

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. remove-double-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. *-commutative 72.5%

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

      5. associate-*l/ 45.0%

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

      6. associate-/l* 76.2%

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

      7. fma-neg 76.2%

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

      8. remove-double-neg 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in t around inf 66.9%

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

   6. Taylor expanded in a around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   8. Simplified 58.5%

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

   if -2.6e-13 < z < 2.5499999999999999e26

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0 88.7%

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

      1. +-commutative 88.7%

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

      2. div-sub 91.5%

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

      3. mul-1-neg 91.5%

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

      4. associate-/l* 84.5%

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

      5. distribute-lft-neg-out 84.5%

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

      6. distribute-rgt-out 91.4%

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

      7. sub-neg 91.4%

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

      8. associate-/r/ 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in z around 0 79.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-13} \lor \neg \left(z \leq 2.55 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-13} \lor \neg \left(z \leq 1.7 \cdot 10^{+29}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.45e-13) (not (<= z 1.7e+29)))
   (* t (- 1.0 (/ y z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.45e-13) || !(z <= 1.7e+29)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y / (a / (t - 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 ((z <= (-2.45d-13)) .or. (.not. (z <= 1.7d+29))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (y / (a / (t - 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 ((z <= -2.45e-13) || !(z <= 1.7e+29)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.45e-13) or not (z <= 1.7e+29):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.45e-13) || !(z <= 1.7e+29))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.45e-13) || ~((z <= 1.7e+29)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.45e-13], N[Not[LessEqual[z, 1.7e+29]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45000000000000016e-13 or 1.69999999999999991e29 < z

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. remove-double-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. *-commutative 72.5%

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

      5. associate-*l/ 45.0%

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

      6. associate-/l* 76.2%

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

      7. fma-neg 76.2%

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

      8. remove-double-neg 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in t around inf 66.9%

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

   6. Taylor expanded in a around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   8. Simplified 58.5%

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

   if -2.45000000000000016e-13 < z < 1.69999999999999991e29

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 70.2%

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

      1. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

      1. clear-num 75.9%

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

      2. un-div-inv 76.7%

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

   7. Applied egg-rr 76.7%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-13} \lor \neg \left(z \leq 1.7 \cdot 10^{+29}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-13} \lor \neg \left(z \leq 2.9 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.45e-13) (not (<= z 2.9e+23)))
   (* t (- 1.0 (/ y z)))
   (+ x (* y (/ (- t x) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.45e-13) || !(z <= 2.9e+23)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.45d-13)) .or. (.not. (z <= 2.9d+23))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (y * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.45e-13) || !(z <= 2.9e+23)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.45e-13) or not (z <= 2.9e+23):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.45e-13) || !(z <= 2.9e+23))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.45e-13) || ~((z <= 2.9e+23)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.45e-13], N[Not[LessEqual[z, 2.9e+23]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45000000000000016e-13 or 2.90000000000000013e23 < z

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. remove-double-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. *-commutative 72.5%

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

      5. associate-*l/ 45.0%

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

      6. associate-/l* 76.2%

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

      7. fma-neg 76.2%

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

      8. remove-double-neg 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in t around inf 66.9%

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

   6. Taylor expanded in a around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   8. Simplified 58.5%

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

   if -2.45000000000000016e-13 < z < 2.90000000000000013e23

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 70.2%

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

      1. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-13} \lor \neg \left(z \leq 2.9 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-13} \lor \neg \left(z \leq 4.1 \cdot 10^{+33}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.2e-13) (not (<= z 4.1e+33)))
   (* t (- 1.0 (/ y z)))
   (+ x (* t (/ (- y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e-13) || !(z <= 4.1e+33)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (t * ((y - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.2d-13)) .or. (.not. (z <= 4.1d+33))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (t * ((y - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.2e-13) || !(z <= 4.1e+33)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (t * ((y - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.2e-13) or not (z <= 4.1e+33):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (t * ((y - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.2e-13) || !(z <= 4.1e+33))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.2e-13) || ~((z <= 4.1e+33)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (t * ((y - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.2e-13], N[Not[LessEqual[z, 4.1e+33]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.19999999999999997e-13 or 4.09999999999999995e33 < z

   1. Initial program 72.3%

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

      1. +-commutative 72.3%

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

      2. remove-double-neg 72.3%

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

      3. unsub-neg 72.3%

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

      4. *-commutative 72.3%

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

      5. associate-*l/ 44.5%

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

      6. associate-/l* 76.0%

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

      7. fma-neg 76.0%

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

      8. remove-double-neg 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in t around inf 66.6%

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

   6. Taylor expanded in a around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. unsub-neg 59.0%

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

   8. Simplified 59.0%

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

   if -2.19999999999999997e-13 < z < 4.09999999999999995e33

   1. Initial program 91.5%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. associate-/l* 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in a around inf 67.8%

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

      1. associate-/l* 72.9%

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

   8. Simplified 72.9%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-13} \lor \neg \left(z \leq 4.1 \cdot 10^{+33}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-15} \lor \neg \left(z \leq 2.8 \cdot 10^{+21}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e-15) (not (<= z 2.8e+21)))
   (* t (- 1.0 (/ y z)))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e-15) || !(z <= 2.8e+21)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8d-15)) .or. (.not. (z <= 2.8d+21))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e-15) || !(z <= 2.8e+21)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e-15) or not (z <= 2.8e+21):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e-15) || !(z <= 2.8e+21))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e-15) || ~((z <= 2.8e+21)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e-15], N[Not[LessEqual[z, 2.8e+21]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000006e-15 or 2.8e21 < z

   1. Initial program 72.5%

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

      1. +-commutative 72.5%

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

      2. remove-double-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. *-commutative 72.5%

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

      5. associate-*l/ 45.0%

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

      6. associate-/l* 76.2%

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

      7. fma-neg 76.2%

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

      8. remove-double-neg 76.2%

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

   3. Simplified 76.2%

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

   5. Taylor expanded in t around inf 66.9%

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

   6. Taylor expanded in a around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   8. Simplified 58.5%

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

   if -8.0000000000000006e-15 < z < 2.8e21

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 70.2%

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

      1. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in t around inf 66.7%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-15} \lor \neg \left(z \leq 2.8 \cdot 10^{+21}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-87} \lor \neg \left(z \leq 10^{+30}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e-87) (not (<= z 1e+30)))
   (* t (- 1.0 (/ y z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-87) || !(z <= 1e+30)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.5d-87)) .or. (.not. (z <= 1d+30))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.5e-87) || !(z <= 1e+30)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.5e-87) or not (z <= 1e+30):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.5e-87) || !(z <= 1e+30))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e-87) || ~((z <= 1e+30)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.5e-87], N[Not[LessEqual[z, 1e+30]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000021e-87 or 1e30 < z

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

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

      2. remove-double-neg 75.2%

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

      3. unsub-neg 75.2%

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

      4. *-commutative 75.2%

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

      5. associate-*l/ 52.0%

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

      6. associate-/l* 79.2%

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

      7. fma-neg 79.3%

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

      8. remove-double-neg 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around inf 66.4%

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

   6. Taylor expanded in a around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. unsub-neg 56.9%

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

   8. Simplified 56.9%

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

   if -2.50000000000000021e-87 < z < 1e30

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 70.9%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

   8. Simplified 56.8%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-87} \lor \neg \left(z \leq 10^{+30}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e+66) x (if (<= a 2.65e+70) (* t (- 1.0 (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+66) {
		tmp = x;
	} else if (a <= 2.65e+70) {
		tmp = t * (1.0 - (y / z));
	} 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 <= (-5.5d+66)) then
        tmp = x
    else if (a <= 2.65d+70) then
        tmp = t * (1.0d0 - (y / z))
    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 <= -5.5e+66) {
		tmp = x;
	} else if (a <= 2.65e+70) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e+66:
		tmp = x
	elif a <= 2.65e+70:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e+66)
		tmp = x;
	elseif (a <= 2.65e+70)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e+66)
		tmp = x;
	elseif (a <= 2.65e+70)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e+66], x, If[LessEqual[a, 2.65e+70], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5e66 or 2.65e70 < a

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. remove-double-neg 91.8%

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

      3. unsub-neg 91.8%

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

      4. *-commutative 91.8%

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

      5. associate-*l/ 66.6%

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

      6. associate-/l* 92.7%

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

      7. fma-neg 92.7%

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

      8. remove-double-neg 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in a around inf 52.3%

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

   if -5.5e66 < a < 2.65e70

   1. Initial program 78.0%

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

      1. +-commutative 78.0%

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

      2. remove-double-neg 78.0%

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

      3. unsub-neg 78.0%

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

      4. *-commutative 78.0%

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

      5. associate-*l/ 71.1%

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

      6. associate-/l* 84.3%

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

      7. fma-neg 84.3%

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

      8. remove-double-neg 84.3%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in t around inf 65.7%

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

   6. Taylor expanded in a around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. unsub-neg 50.0%

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

   8. Simplified 50.0%

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

Alternative 18: 38.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-48} \lor \neg \left(y \leq 1.05 \cdot 10^{+117}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.6e-48) (not (<= y 1.05e+117))) (* t (/ y a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.6e-48) || !(y <= 1.05e+117)) {
		tmp = t * (y / a);
	} 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 ((y <= (-2.6d-48)) .or. (.not. (y <= 1.05d+117))) then
        tmp = t * (y / a)
    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 ((y <= -2.6e-48) || !(y <= 1.05e+117)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.6e-48) or not (y <= 1.05e+117):
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.6e-48) || !(y <= 1.05e+117))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.6e-48) || ~((y <= 1.05e+117)))
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.6e-48], N[Not[LessEqual[y, 1.05e+117]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999987e-48 or 1.0500000000000001e117 < y

   1. Initial program 88.3%

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

      1. +-commutative 88.3%

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

      2. remove-double-neg 88.3%

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

      3. unsub-neg 88.3%

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

      4. *-commutative 88.3%

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

      5. associate-*l/ 69.4%

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

      6. associate-/l* 91.8%

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

      7. fma-neg 91.9%

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

      8. remove-double-neg 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in t around inf 63.9%

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

   6. Taylor expanded in z around 0 47.4%

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

   if -2.59999999999999987e-48 < y < 1.0500000000000001e117

   1. Initial program 79.5%

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

   3. Taylor expanded in t around inf 64.1%

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

      1. associate-/l* 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around inf 46.7%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-48} \lor \neg \left(y \leq 1.05 \cdot 10^{+117}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 39.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+70}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.5e+62) x (if (<= a 2e+70) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.5e+62) {
		tmp = x;
	} else if (a <= 2e+70) {
		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 <= (-6.5d+62)) then
        tmp = x
    else if (a <= 2d+70) 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 <= -6.5e+62) {
		tmp = x;
	} else if (a <= 2e+70) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.5e+62:
		tmp = x
	elif a <= 2e+70:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.5e+62)
		tmp = x;
	elseif (a <= 2e+70)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.5e+62)
		tmp = x;
	elseif (a <= 2e+70)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.5e+62], x, If[LessEqual[a, 2e+70], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5000000000000003e62 or 2.00000000000000015e70 < a

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. remove-double-neg 91.8%

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

      3. unsub-neg 91.8%

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

      4. *-commutative 91.8%

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

      5. associate-*l/ 66.6%

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

      6. associate-/l* 92.7%

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

      7. fma-neg 92.7%

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

      8. remove-double-neg 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in a around inf 52.3%

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

   if -6.5000000000000003e62 < a < 2.00000000000000015e70

   1. Initial program 78.0%

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

   3. Taylor expanded in t around inf 49.4%

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

      1. associate-/l* 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in z around inf 28.0%

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

   7. Taylor expanded in x around 0 33.3%

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

Alternative 20: 25.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.4%

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

3. Taylor expanded in t around inf 57.6%

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

   1. associate-/l* 70.8%

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

5. Simplified 70.8%

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

6. Taylor expanded in z around inf 32.3%

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

7. Taylor expanded in x around 0 22.6%

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

Reproduce

herbie shell --seed 2024136 
(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)))))