Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.6% → 95.2%

Time: 12.6s

Alternatives: 17

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-305} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-305) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (* (- y a) (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / 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, -2e-305], 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[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999999e-305 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. remove-double-neg 89.7%

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

      3. unsub-neg 89.7%

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

      4. *-commutative 89.7%

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

      5. associate-*l/ 82.2%

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

      6. associate-/l* 94.0%

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

      7. fma-neg 94.0%

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

      8. remove-double-neg 94.0%

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

   3. Simplified 94.0%

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

   if -1.99999999999999999e-305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 88.5%

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

      1. associate--l+ 88.5%

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

      2. distribute-lft-out-- 88.5%

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

      3. div-sub 88.5%

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

      4. mul-1-neg 88.5%

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

      5. unsub-neg 88.5%

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

      6. div-sub 88.5%

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

      7. associate-/l* 91.5%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac2 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-305} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-305} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-305) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (* (- y a) (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-305)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + ((y - a) * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-305) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + ((y - a) * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-305) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + ((y - a) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-305], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999999e-305 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. remove-double-neg 89.7%

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

      3. unsub-neg 89.7%

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

      4. *-commutative 89.7%

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

      5. associate-*l/ 82.2%

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

      6. associate-/l* 94.0%

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

      7. fma-neg 94.0%

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

      8. remove-double-neg 94.0%

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

   3. Simplified 94.0%

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

      1. fma-undefine 94.0%

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

   6. Applied egg-rr 94.0%

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

   if -1.99999999999999999e-305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 88.5%

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

      1. associate--l+ 88.5%

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

      2. distribute-lft-out-- 88.5%

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

      3. div-sub 88.5%

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

      4. mul-1-neg 88.5%

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

      5. unsub-neg 88.5%

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

      6. div-sub 88.5%

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

      7. associate-/l* 91.5%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac2 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-305} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-305} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-305) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (* (- y a) (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-305)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + ((y - a) * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-305) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + ((y - a) * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-305) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + ((y - a) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-305], 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[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999999e-305 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*l/ 82.2%

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

      3. associate-*r/ 94.0%

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

      4. clear-num 93.9%

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

      5. un-div-inv 93.9%

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

   4. Applied egg-rr 93.9%

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

   if -1.99999999999999999e-305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 88.5%

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

      1. associate--l+ 88.5%

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

      2. distribute-lft-out-- 88.5%

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

      3. div-sub 88.5%

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

      4. mul-1-neg 88.5%

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

      5. unsub-neg 88.5%

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

      6. div-sub 88.5%

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

      7. associate-/l* 91.5%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac2 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-305} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-305} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-305) (not (<= t_1 0.0)))
     t_1
     (+ t (* (- y a) (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-305)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = t + ((y - a) * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((y - a) * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-305) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((y - a) * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-305) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-305) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((y - a) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-305], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999999e-305 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.7%

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

   if -1.99999999999999999e-305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 88.5%

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

      1. associate--l+ 88.5%

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

      2. distribute-lft-out-- 88.5%

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

      3. div-sub 88.5%

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

      4. mul-1-neg 88.5%

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

      5. unsub-neg 88.5%

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

      6. div-sub 88.5%

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

      7. associate-/l* 91.5%

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

      8. associate-/l* 99.8%

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

      9. distribute-rgt-out-- 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac2 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-305} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.48 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-204}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= a -1.1e+76)
     t_2
     (if (<= a -4e+31)
       t_1
       (if (<= a -1.48e-21)
         t_2
         (if (<= a -3.6e-137)
           t_1
           (if (<= a -8.2e-204)
             (/ (* x (- y a)) z)
             (if (<= a 1.05e+96) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.1e+76) {
		tmp = t_2;
	} else if (a <= -4e+31) {
		tmp = t_1;
	} else if (a <= -1.48e-21) {
		tmp = t_2;
	} else if (a <= -3.6e-137) {
		tmp = t_1;
	} else if (a <= -8.2e-204) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 1.05e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (a <= (-1.1d+76)) then
        tmp = t_2
    else if (a <= (-4d+31)) then
        tmp = t_1
    else if (a <= (-1.48d-21)) then
        tmp = t_2
    else if (a <= (-3.6d-137)) then
        tmp = t_1
    else if (a <= (-8.2d-204)) then
        tmp = (x * (y - a)) / z
    else if (a <= 1.05d+96) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (a <= -1.1e+76) {
		tmp = t_2;
	} else if (a <= -4e+31) {
		tmp = t_1;
	} else if (a <= -1.48e-21) {
		tmp = t_2;
	} else if (a <= -3.6e-137) {
		tmp = t_1;
	} else if (a <= -8.2e-204) {
		tmp = (x * (y - a)) / z;
	} else if (a <= 1.05e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if a <= -1.1e+76:
		tmp = t_2
	elif a <= -4e+31:
		tmp = t_1
	elif a <= -1.48e-21:
		tmp = t_2
	elif a <= -3.6e-137:
		tmp = t_1
	elif a <= -8.2e-204:
		tmp = (x * (y - a)) / z
	elif a <= 1.05e+96:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (a <= -1.1e+76)
		tmp = t_2;
	elseif (a <= -4e+31)
		tmp = t_1;
	elseif (a <= -1.48e-21)
		tmp = t_2;
	elseif (a <= -3.6e-137)
		tmp = t_1;
	elseif (a <= -8.2e-204)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (a <= 1.05e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (a <= -1.1e+76)
		tmp = t_2;
	elseif (a <= -4e+31)
		tmp = t_1;
	elseif (a <= -1.48e-21)
		tmp = t_2;
	elseif (a <= -3.6e-137)
		tmp = t_1;
	elseif (a <= -8.2e-204)
		tmp = (x * (y - a)) / z;
	elseif (a <= 1.05e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+76], t$95$2, If[LessEqual[a, -4e+31], t$95$1, If[LessEqual[a, -1.48e-21], t$95$2, If[LessEqual[a, -3.6e-137], t$95$1, If[LessEqual[a, -8.2e-204], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.05e+96], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1e76 or -3.9999999999999999e31 < a < -1.48e-21 or 1.0500000000000001e96 < a

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. unsub-neg 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in z around 0 68.8%

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

   if -1.1e76 < a < -3.9999999999999999e31 or -1.48e-21 < a < -3.60000000000000006e-137 or -8.2000000000000002e-204 < a < 1.0500000000000001e96

   1. Initial program 69.9%

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

   3. Taylor expanded in x around 0 60.5%

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

      1. associate-/l* 73.2%

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

   5. Simplified 73.2%

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

   if -3.60000000000000006e-137 < a < -8.2000000000000002e-204

   1. Initial program 51.8%

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

   3. Taylor expanded in z around inf 84.9%

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

      1. associate--l+ 84.9%

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

      2. distribute-lft-out-- 84.9%

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

      3. div-sub 84.9%

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

      4. mul-1-neg 84.9%

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

      5. unsub-neg 84.9%

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

      6. div-sub 84.9%

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

      7. associate-/l* 84.1%

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

      8. associate-/l* 78.5%

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

      9. distribute-rgt-out-- 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in t around 0 63.4%

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

Alternative 6: 48.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+159)
   t
   (if (<= z -2.75e+59)
     (* y (/ (- x t) z))
     (if (<= z -9.5e-19)
       t
       (if (<= z 7.5e+50)
         (* x (- 1.0 (/ y a)))
         (if (<= z 7e+119) (/ (* y (- x t)) z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+159) {
		tmp = t;
	} else if (z <= -2.75e+59) {
		tmp = y * ((x - t) / z);
	} else if (z <= -9.5e-19) {
		tmp = t;
	} else if (z <= 7.5e+50) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 7e+119) {
		tmp = (y * (x - t)) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.9d+159)) then
        tmp = t
    else if (z <= (-2.75d+59)) then
        tmp = y * ((x - t) / z)
    else if (z <= (-9.5d-19)) then
        tmp = t
    else if (z <= 7.5d+50) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 7d+119) then
        tmp = (y * (x - t)) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+159) {
		tmp = t;
	} else if (z <= -2.75e+59) {
		tmp = y * ((x - t) / z);
	} else if (z <= -9.5e-19) {
		tmp = t;
	} else if (z <= 7.5e+50) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 7e+119) {
		tmp = (y * (x - t)) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+159:
		tmp = t
	elif z <= -2.75e+59:
		tmp = y * ((x - t) / z)
	elif z <= -9.5e-19:
		tmp = t
	elif z <= 7.5e+50:
		tmp = x * (1.0 - (y / a))
	elif z <= 7e+119:
		tmp = (y * (x - t)) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+159)
		tmp = t;
	elseif (z <= -2.75e+59)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (z <= -9.5e-19)
		tmp = t;
	elseif (z <= 7.5e+50)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 7e+119)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+159)
		tmp = t;
	elseif (z <= -2.75e+59)
		tmp = y * ((x - t) / z);
	elseif (z <= -9.5e-19)
		tmp = t;
	elseif (z <= 7.5e+50)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 7e+119)
		tmp = (y * (x - t)) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+159], t, If[LessEqual[z, -2.75e+59], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-19], t, If[LessEqual[z, 7.5e+50], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+119], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.90000000000000014e159 or -2.74999999999999995e59 < z < -9.4999999999999995e-19 or 7.0000000000000001e119 < z

   1. Initial program 57.1%

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

   3. Taylor expanded in z around inf 57.3%

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

   if -2.90000000000000014e159 < z < -2.74999999999999995e59

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 44.2%

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

      1. div-sub 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in a around 0 37.8%

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

      1. mul-1-neg 37.8%

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

      2. associate-/l* 42.7%

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

      3. distribute-lft-neg-in 42.7%

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

   8. Simplified 42.7%

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

   if -9.4999999999999995e-19 < z < 7.4999999999999999e50

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. unsub-neg 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in z around 0 59.1%

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

   if 7.4999999999999999e50 < z < 7.0000000000000001e119

   1. Initial program 60.6%

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

   3. Taylor expanded in y around inf 71.5%

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

      1. div-sub 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in a around 0 72.0%

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

      1. associate-*r/ 72.0%

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

      2. mul-1-neg 72.0%

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

      3. distribute-rgt-neg-out 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+159}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) z))))
   (if (<= z -1.05e+161)
     t
     (if (<= z -5.2e+58)
       t_1
       (if (<= z -9.5e-19)
         t
         (if (<= z 1.9e+52)
           (* x (- 1.0 (/ y a)))
           (if (<= z 1.2e+115) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double tmp;
	if (z <= -1.05e+161) {
		tmp = t;
	} else if (z <= -5.2e+58) {
		tmp = t_1;
	} else if (z <= -9.5e-19) {
		tmp = t;
	} else if (z <= 1.9e+52) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.2e+115) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x - t) / z)
    if (z <= (-1.05d+161)) then
        tmp = t
    else if (z <= (-5.2d+58)) then
        tmp = t_1
    else if (z <= (-9.5d-19)) then
        tmp = t
    else if (z <= 1.9d+52) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.2d+115) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / z);
	double tmp;
	if (z <= -1.05e+161) {
		tmp = t;
	} else if (z <= -5.2e+58) {
		tmp = t_1;
	} else if (z <= -9.5e-19) {
		tmp = t;
	} else if (z <= 1.9e+52) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.2e+115) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / z)
	tmp = 0
	if z <= -1.05e+161:
		tmp = t
	elif z <= -5.2e+58:
		tmp = t_1
	elif z <= -9.5e-19:
		tmp = t
	elif z <= 1.9e+52:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.2e+115:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (z <= -1.05e+161)
		tmp = t;
	elseif (z <= -5.2e+58)
		tmp = t_1;
	elseif (z <= -9.5e-19)
		tmp = t;
	elseif (z <= 1.9e+52)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.2e+115)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / z);
	tmp = 0.0;
	if (z <= -1.05e+161)
		tmp = t;
	elseif (z <= -5.2e+58)
		tmp = t_1;
	elseif (z <= -9.5e-19)
		tmp = t;
	elseif (z <= 1.9e+52)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.2e+115)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+161], t, If[LessEqual[z, -5.2e+58], t$95$1, If[LessEqual[z, -9.5e-19], t, If[LessEqual[z, 1.9e+52], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+115], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e161 or -5.19999999999999976e58 < z < -9.4999999999999995e-19 or 1.2e115 < z

   1. Initial program 57.1%

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

   3. Taylor expanded in z around inf 57.3%

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

   if -1.05e161 < z < -5.19999999999999976e58 or 1.9e52 < z < 1.2e115

   1. Initial program 66.2%

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

   3. Taylor expanded in y around inf 53.6%

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

      1. div-sub 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in a around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. associate-/l* 52.6%

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

      3. distribute-lft-neg-in 52.6%

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

   8. Simplified 52.6%

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

   if -9.4999999999999995e-19 < z < 1.9e52

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. unsub-neg 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in z around 0 59.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+161}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{z}\\ t_2 := t + t\_1 \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+17}:\\ \;\;\;\;x - z \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;t - y \cdot t\_1\\ \mathbf{elif}\;z \leq 8.2:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) z)) (t_2 (+ t (* t_1 (- a y)))))
   (if (<= z -1e+111)
     t_2
     (if (<= z -7.8e+17)
       (- x (* z (/ (- t x) (- a z))))
       (if (<= z -9.5e-19)
         (- t (* y t_1))
         (if (<= z 8.2) (+ x (* (- t x) (/ y (- a z)))) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / z;
	double t_2 = t + (t_1 * (a - y));
	double tmp;
	if (z <= -1e+111) {
		tmp = t_2;
	} else if (z <= -7.8e+17) {
		tmp = x - (z * ((t - x) / (a - z)));
	} else if (z <= -9.5e-19) {
		tmp = t - (y * t_1);
	} else if (z <= 8.2) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - x) / z
    t_2 = t + (t_1 * (a - y))
    if (z <= (-1d+111)) then
        tmp = t_2
    else if (z <= (-7.8d+17)) then
        tmp = x - (z * ((t - x) / (a - z)))
    else if (z <= (-9.5d-19)) then
        tmp = t - (y * t_1)
    else if (z <= 8.2d0) then
        tmp = x + ((t - x) * (y / (a - z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / z;
	double t_2 = t + (t_1 * (a - y));
	double tmp;
	if (z <= -1e+111) {
		tmp = t_2;
	} else if (z <= -7.8e+17) {
		tmp = x - (z * ((t - x) / (a - z)));
	} else if (z <= -9.5e-19) {
		tmp = t - (y * t_1);
	} else if (z <= 8.2) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) / z
	t_2 = t + (t_1 * (a - y))
	tmp = 0
	if z <= -1e+111:
		tmp = t_2
	elif z <= -7.8e+17:
		tmp = x - (z * ((t - x) / (a - z)))
	elif z <= -9.5e-19:
		tmp = t - (y * t_1)
	elif z <= 8.2:
		tmp = x + ((t - x) * (y / (a - z)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / z)
	t_2 = Float64(t + Float64(t_1 * Float64(a - y)))
	tmp = 0.0
	if (z <= -1e+111)
		tmp = t_2;
	elseif (z <= -7.8e+17)
		tmp = Float64(x - Float64(z * Float64(Float64(t - x) / Float64(a - z))));
	elseif (z <= -9.5e-19)
		tmp = Float64(t - Float64(y * t_1));
	elseif (z <= 8.2)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / Float64(a - z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) / z;
	t_2 = t + (t_1 * (a - y));
	tmp = 0.0;
	if (z <= -1e+111)
		tmp = t_2;
	elseif (z <= -7.8e+17)
		tmp = x - (z * ((t - x) / (a - z)));
	elseif (z <= -9.5e-19)
		tmp = t - (y * t_1);
	elseif (z <= 8.2)
		tmp = x + ((t - x) * (y / (a - z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(t$95$1 * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+111], t$95$2, If[LessEqual[z, -7.8e+17], N[(x - N[(z * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-19], N[(t - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.99999999999999957e110 or 8.1999999999999993 < z

   1. Initial program 55.6%

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

   3. Taylor expanded in z around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. distribute-lft-out-- 68.8%

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

      3. div-sub 68.8%

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

      4. mul-1-neg 68.8%

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

      5. unsub-neg 68.8%

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

      6. div-sub 68.8%

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

      7. associate-/l* 72.6%

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

      8. associate-/l* 80.5%

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

      9. distribute-rgt-out-- 80.5%

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

   5. Simplified 80.5%

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

   if -9.99999999999999957e110 < z < -7.8e17

   1. Initial program 86.7%

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

   3. Taylor expanded in y around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

      3. associate-/l* 73.5%

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

   5. Simplified 73.5%

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

   if -7.8e17 < z < -9.4999999999999995e-19

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf 81.3%

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

      1. associate--l+ 81.3%

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

      2. distribute-lft-out-- 81.3%

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

      3. div-sub 81.3%

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

      4. mul-1-neg 81.3%

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

      5. unsub-neg 81.3%

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

      6. div-sub 81.3%

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

      7. associate-/l* 81.3%

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

      8. associate-/l* 81.3%

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

      9. distribute-rgt-out-- 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in y around inf 81.3%

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

      1. associate-*r/ 81.3%

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

   8. Simplified 81.3%

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

   if -9.4999999999999995e-19 < z < 8.1999999999999993

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. remove-double-neg 94.1%

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

      3. unsub-neg 94.1%

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

      4. *-commutative 94.1%

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

      5. associate-*l/ 93.2%

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

      6. associate-/l* 95.5%

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

      7. fma-neg 95.5%

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

      8. remove-double-neg 95.5%

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

   3. Simplified 95.5%

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

      1. fma-undefine 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in y around inf 89.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+111}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+17}:\\ \;\;\;\;x - z \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 8.2:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 23000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+40}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y)))))
   (if (<= z -3.9e-19)
     t_1
     (if (<= z 23000.0)
       (+ x (* (- t x) (/ y (- a z))))
       (if (<= z 1.46e+40)
         (/ (* (- y z) t) (- a z))
         (if (<= z 2.6e+49) (* x (- 1.0 (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -3.9e-19) {
		tmp = t_1;
	} else if (z <= 23000.0) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else if (z <= 1.46e+40) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 2.6e+49) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (((t - x) / z) * (a - y))
    if (z <= (-3.9d-19)) then
        tmp = t_1
    else if (z <= 23000.0d0) then
        tmp = x + ((t - x) * (y / (a - z)))
    else if (z <= 1.46d+40) then
        tmp = ((y - z) * t) / (a - z)
    else if (z <= 2.6d+49) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -3.9e-19) {
		tmp = t_1;
	} else if (z <= 23000.0) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else if (z <= 1.46e+40) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 2.6e+49) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	tmp = 0
	if z <= -3.9e-19:
		tmp = t_1
	elif z <= 23000.0:
		tmp = x + ((t - x) * (y / (a - z)))
	elif z <= 1.46e+40:
		tmp = ((y - z) * t) / (a - z)
	elif z <= 2.6e+49:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	tmp = 0.0
	if (z <= -3.9e-19)
		tmp = t_1;
	elseif (z <= 23000.0)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / Float64(a - z))));
	elseif (z <= 1.46e+40)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (z <= 2.6e+49)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	tmp = 0.0;
	if (z <= -3.9e-19)
		tmp = t_1;
	elseif (z <= 23000.0)
		tmp = x + ((t - x) * (y / (a - z)));
	elseif (z <= 1.46e+40)
		tmp = ((y - z) * t) / (a - z);
	elseif (z <= 2.6e+49)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e-19], t$95$1, If[LessEqual[z, 23000.0], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.46e+40], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+49], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.89999999999999995e-19 or 2.59999999999999989e49 < z

   1. Initial program 59.5%

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

   3. Taylor expanded in z around inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. distribute-lft-out-- 68.7%

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

      3. div-sub 68.7%

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

      4. mul-1-neg 68.7%

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

      5. unsub-neg 68.7%

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

      6. div-sub 68.7%

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

      7. associate-/l* 72.1%

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

      8. associate-/l* 78.2%

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

      9. distribute-rgt-out-- 78.2%

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

   5. Simplified 78.2%

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

   if -3.89999999999999995e-19 < z < 23000

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. remove-double-neg 94.1%

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

      3. unsub-neg 94.1%

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

      4. *-commutative 94.1%

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

      5. associate-*l/ 93.2%

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

      6. associate-/l* 95.5%

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

      7. fma-neg 95.5%

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

      8. remove-double-neg 95.5%

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

   3. Simplified 95.5%

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

      1. fma-undefine 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in y around inf 89.0%

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

   if 23000 < z < 1.46e40

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 82.7%

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

   if 1.46e40 < z < 2.59999999999999989e49

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in z around 0 77.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-19}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq 23000:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.46 \cdot 10^{+40}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - y \cdot \frac{t - x}{z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 13600:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* y (/ (- t x) z)))))
   (if (<= z -9.5e-19)
     t_1
     (if (<= z 13600.0)
       (+ x (* (- t x) (/ y (- a z))))
       (if (<= z 1.18e+39)
         (/ (* (- y z) t) (- a z))
         (if (<= z 2.2e+49) (* x (- 1.0 (/ y a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y * ((t - x) / z));
	double tmp;
	if (z <= -9.5e-19) {
		tmp = t_1;
	} else if (z <= 13600.0) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else if (z <= 1.18e+39) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 2.2e+49) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (y * ((t - x) / z))
    if (z <= (-9.5d-19)) then
        tmp = t_1
    else if (z <= 13600.0d0) then
        tmp = x + ((t - x) * (y / (a - z)))
    else if (z <= 1.18d+39) then
        tmp = ((y - z) * t) / (a - z)
    else if (z <= 2.2d+49) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y * ((t - x) / z));
	double tmp;
	if (z <= -9.5e-19) {
		tmp = t_1;
	} else if (z <= 13600.0) {
		tmp = x + ((t - x) * (y / (a - z)));
	} else if (z <= 1.18e+39) {
		tmp = ((y - z) * t) / (a - z);
	} else if (z <= 2.2e+49) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (y * ((t - x) / z))
	tmp = 0
	if z <= -9.5e-19:
		tmp = t_1
	elif z <= 13600.0:
		tmp = x + ((t - x) * (y / (a - z)))
	elif z <= 1.18e+39:
		tmp = ((y - z) * t) / (a - z)
	elif z <= 2.2e+49:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(y * Float64(Float64(t - x) / z)))
	tmp = 0.0
	if (z <= -9.5e-19)
		tmp = t_1;
	elseif (z <= 13600.0)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / Float64(a - z))));
	elseif (z <= 1.18e+39)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (z <= 2.2e+49)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (y * ((t - x) / z));
	tmp = 0.0;
	if (z <= -9.5e-19)
		tmp = t_1;
	elseif (z <= 13600.0)
		tmp = x + ((t - x) * (y / (a - z)));
	elseif (z <= 1.18e+39)
		tmp = ((y - z) * t) / (a - z);
	elseif (z <= 2.2e+49)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-19], t$95$1, If[LessEqual[z, 13600.0], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.18e+39], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+49], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.4999999999999995e-19 or 2.2000000000000001e49 < z

   1. Initial program 59.5%

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

   3. Taylor expanded in z around inf 68.7%

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

      1. associate--l+ 68.7%

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

      2. distribute-lft-out-- 68.7%

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

      3. div-sub 68.7%

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

      4. mul-1-neg 68.7%

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

      5. unsub-neg 68.7%

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

      6. div-sub 68.7%

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

      7. associate-/l* 72.1%

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

      8. associate-/l* 78.2%

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

      9. distribute-rgt-out-- 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in y around inf 66.9%

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

      1. associate-*r/ 72.1%

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

   8. Simplified 72.1%

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

   if -9.4999999999999995e-19 < z < 13600

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. remove-double-neg 94.1%

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

      3. unsub-neg 94.1%

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

      4. *-commutative 94.1%

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

      5. associate-*l/ 93.2%

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

      6. associate-/l* 95.5%

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

      7. fma-neg 95.5%

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

      8. remove-double-neg 95.5%

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

   3. Simplified 95.5%

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

      1. fma-undefine 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in y around inf 89.0%

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

   if 13600 < z < 1.17999999999999996e39

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0 82.7%

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

   if 1.17999999999999996e39 < z < 2.2000000000000001e49

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in z around 0 77.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{elif}\;z \leq 13600:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-135}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-21)
   x
   (if (<= a -7e-135)
     t
     (if (<= a -2.3e-221)
       (* x (/ y z))
       (if (<= a 1.45e+95) t (* x (+ 1.0 (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-21) {
		tmp = x;
	} else if (a <= -7e-135) {
		tmp = t;
	} else if (a <= -2.3e-221) {
		tmp = x * (y / z);
	} else if (a <= 1.45e+95) {
		tmp = t;
	} else {
		tmp = x * (1.0 + (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 (a <= (-1.6d-21)) then
        tmp = x
    else if (a <= (-7d-135)) then
        tmp = t
    else if (a <= (-2.3d-221)) then
        tmp = x * (y / z)
    else if (a <= 1.45d+95) then
        tmp = t
    else
        tmp = x * (1.0d0 + (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 (a <= -1.6e-21) {
		tmp = x;
	} else if (a <= -7e-135) {
		tmp = t;
	} else if (a <= -2.3e-221) {
		tmp = x * (y / z);
	} else if (a <= 1.45e+95) {
		tmp = t;
	} else {
		tmp = x * (1.0 + (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-21:
		tmp = x
	elif a <= -7e-135:
		tmp = t
	elif a <= -2.3e-221:
		tmp = x * (y / z)
	elif a <= 1.45e+95:
		tmp = t
	else:
		tmp = x * (1.0 + (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-21)
		tmp = x;
	elseif (a <= -7e-135)
		tmp = t;
	elseif (a <= -2.3e-221)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.45e+95)
		tmp = t;
	else
		tmp = Float64(x * Float64(1.0 + Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-21)
		tmp = x;
	elseif (a <= -7e-135)
		tmp = t;
	elseif (a <= -2.3e-221)
		tmp = x * (y / z);
	elseif (a <= 1.45e+95)
		tmp = t;
	else
		tmp = x * (1.0 + (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-21], x, If[LessEqual[a, -7e-135], t, If[LessEqual[a, -2.3e-221], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+95], t, N[(x * N[(1.0 + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.6000000000000001e-21

   1. Initial program 91.9%

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

   3. Taylor expanded in a around inf 52.5%

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

   if -1.6000000000000001e-21 < a < -6.9999999999999997e-135 or -2.3e-221 < a < 1.45000000000000007e95

   1. Initial program 71.0%

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

   3. Taylor expanded in z around inf 40.2%

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

   if -6.9999999999999997e-135 < a < -2.3e-221

   1. Initial program 45.4%

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

   3. Taylor expanded in x around inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. unsub-neg 33.0%

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

   5. Simplified 33.0%

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

   6. Taylor expanded in a around 0 58.3%

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

   if 1.45000000000000007e95 < a

   1. Initial program 91.5%

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

   3. Taylor expanded in x around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in y around 0 65.4%

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

      1. +-commutative 65.4%

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

   8. Simplified 65.4%

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

   9. Taylor expanded in z around 0 64.1%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-135}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+158}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+110}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+158)
   t
   (if (<= z 2e+52)
     (* x (- 1.0 (/ y a)))
     (if (<= z 3.2e+110) (* t (/ y (- z))) (if (<= z 2.15e+111) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+158) {
		tmp = t;
	} else if (z <= 2e+52) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.2e+110) {
		tmp = t * (y / -z);
	} else if (z <= 2.15e+111) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4d+158)) then
        tmp = t
    else if (z <= 2d+52) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 3.2d+110) then
        tmp = t * (y / -z)
    else if (z <= 2.15d+111) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+158) {
		tmp = t;
	} else if (z <= 2e+52) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 3.2e+110) {
		tmp = t * (y / -z);
	} else if (z <= 2.15e+111) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+158:
		tmp = t
	elif z <= 2e+52:
		tmp = x * (1.0 - (y / a))
	elif z <= 3.2e+110:
		tmp = t * (y / -z)
	elif z <= 2.15e+111:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+158)
		tmp = t;
	elseif (z <= 2e+52)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 3.2e+110)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (z <= 2.15e+111)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e+158)
		tmp = t;
	elseif (z <= 2e+52)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 3.2e+110)
		tmp = t * (y / -z);
	elseif (z <= 2.15e+111)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+158], t, If[LessEqual[z, 2e+52], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+110], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+111], x, t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.99999999999999981e158 or 2.14999999999999997e111 < z

   1. Initial program 48.9%

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

   3. Taylor expanded in z around inf 60.0%

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

   if -3.99999999999999981e158 < z < 2e52

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. unsub-neg 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in z around 0 53.4%

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

   if 2e52 < z < 3.19999999999999994e110

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in a around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. associate-/l* 85.5%

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

      3. distribute-lft-neg-in 85.5%

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

   8. Simplified 85.5%

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

   9. Taylor expanded in t around inf 52.4%

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

       1. mul-1-neg 52.4%

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

       2. distribute-neg-frac2 52.4%

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

       3. *-commutative 52.4%

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

   11. Simplified 52.4%

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

   12. Taylor expanded in y around 0 52.4%

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

       1. mul-1-neg 52.4%

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

       2. associate-*r/ 65.4%

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

       3. distribute-rgt-neg-in 65.4%

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

   14. Simplified 65.4%

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

   if 3.19999999999999994e110 < z < 2.14999999999999997e111

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 100.0%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+158}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+110}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-136}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-222}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-21)
   x
   (if (<= a -1.2e-136)
     t
     (if (<= a -1.08e-222) (* x (/ y z)) (if (<= a 1.02e+95) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-21) {
		tmp = x;
	} else if (a <= -1.2e-136) {
		tmp = t;
	} else if (a <= -1.08e-222) {
		tmp = x * (y / z);
	} else if (a <= 1.02e+95) {
		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 <= (-1.6d-21)) then
        tmp = x
    else if (a <= (-1.2d-136)) then
        tmp = t
    else if (a <= (-1.08d-222)) then
        tmp = x * (y / z)
    else if (a <= 1.02d+95) 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 <= -1.6e-21) {
		tmp = x;
	} else if (a <= -1.2e-136) {
		tmp = t;
	} else if (a <= -1.08e-222) {
		tmp = x * (y / z);
	} else if (a <= 1.02e+95) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-21:
		tmp = x
	elif a <= -1.2e-136:
		tmp = t
	elif a <= -1.08e-222:
		tmp = x * (y / z)
	elif a <= 1.02e+95:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-21)
		tmp = x;
	elseif (a <= -1.2e-136)
		tmp = t;
	elseif (a <= -1.08e-222)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.02e+95)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-21)
		tmp = x;
	elseif (a <= -1.2e-136)
		tmp = t;
	elseif (a <= -1.08e-222)
		tmp = x * (y / z);
	elseif (a <= 1.02e+95)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-21], x, If[LessEqual[a, -1.2e-136], t, If[LessEqual[a, -1.08e-222], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+95], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6000000000000001e-21 or 1.0200000000000001e95 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in a around inf 57.4%

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

   if -1.6000000000000001e-21 < a < -1.1999999999999999e-136 or -1.07999999999999995e-222 < a < 1.0200000000000001e95

   1. Initial program 71.0%

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

   3. Taylor expanded in z around inf 40.2%

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

   if -1.1999999999999999e-136 < a < -1.07999999999999995e-222

   1. Initial program 45.4%

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

   3. Taylor expanded in x around inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. unsub-neg 33.0%

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

   5. Simplified 33.0%

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

   6. Taylor expanded in a around 0 58.3%

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

Alternative 14: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-69} \lor \neg \left(z \leq 4.2 \cdot 10^{-53}\right):\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e-69) (not (<= z 4.2e-53)))
   (- t (* y (/ (- t x) z)))
   (+ x (/ (* y (- t x)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e-69) || !(z <= 4.2e-53)) {
		tmp = t - (y * ((t - x) / 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 <= (-1.9d-69)) .or. (.not. (z <= 4.2d-53))) then
        tmp = t - (y * ((t - x) / 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 <= -1.9e-69) || !(z <= 4.2e-53)) {
		tmp = t - (y * ((t - x) / z));
	} else {
		tmp = x + ((y * (t - x)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e-69) or not (z <= 4.2e-53):
		tmp = t - (y * ((t - x) / z))
	else:
		tmp = x + ((y * (t - x)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e-69) || !(z <= 4.2e-53))
		tmp = Float64(t - Float64(y * Float64(Float64(t - x) / z)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e-69) || ~((z <= 4.2e-53)))
		tmp = t - (y * ((t - x) / z));
	else
		tmp = x + ((y * (t - x)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e-69], N[Not[LessEqual[z, 4.2e-53]], $MachinePrecision]], N[(t - N[(y * N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e-69 or 4.19999999999999955e-53 < z

   1. Initial program 64.4%

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

   3. Taylor expanded in z around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. distribute-lft-out-- 65.8%

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

      3. div-sub 65.8%

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

      4. mul-1-neg 65.8%

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

      5. unsub-neg 65.8%

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

      6. div-sub 65.8%

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

      7. associate-/l* 68.5%

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

      8. associate-/l* 74.1%

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

      9. distribute-rgt-out-- 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in y around inf 64.6%

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

      1. associate-*r/ 68.7%

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

   8. Simplified 68.7%

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

   if -1.8999999999999999e-69 < z < 4.19999999999999955e-53

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 82.7%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-69} \lor \neg \left(z \leq 4.2 \cdot 10^{-53}\right):\\ \;\;\;\;t - y \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-71} \lor \neg \left(z \leq 4.8 \cdot 10^{-17}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.6e-71) (not (<= z 4.8e-17)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ (* y (- t x)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e-71) || !(z <= 4.8e-17)) {
		tmp = t * ((y - z) / (a - 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 <= (-3.6d-71)) .or. (.not. (z <= 4.8d-17))) then
        tmp = t * ((y - z) / (a - 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 <= -3.6e-71) || !(z <= 4.8e-17)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((y * (t - x)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.6e-71) or not (z <= 4.8e-17):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((y * (t - x)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.6e-71) || !(z <= 4.8e-17))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.6e-71) || ~((z <= 4.8e-17)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((y * (t - x)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.6e-71], N[Not[LessEqual[z, 4.8e-17]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e-71 or 4.79999999999999973e-17 < z

   1. Initial program 64.1%

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

   3. Taylor expanded in x around 0 47.6%

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

      1. associate-/l* 62.0%

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

   5. Simplified 62.0%

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

   if -3.6e-71 < z < 4.79999999999999973e-17

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 80.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-71} \lor \neg \left(z \leq 4.8 \cdot 10^{-17}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+95}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-21) x (if (<= a 1.12e+95) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-21) {
		tmp = x;
	} else if (a <= 1.12e+95) {
		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 <= (-1.6d-21)) then
        tmp = x
    else if (a <= 1.12d+95) 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 <= -1.6e-21) {
		tmp = x;
	} else if (a <= 1.12e+95) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-21:
		tmp = x
	elif a <= 1.12e+95:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-21)
		tmp = x;
	elseif (a <= 1.12e+95)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-21)
		tmp = x;
	elseif (a <= 1.12e+95)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-21], x, If[LessEqual[a, 1.12e+95], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6000000000000001e-21 or 1.11999999999999999e95 < a

   1. Initial program 91.7%

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

   3. Taylor expanded in a around inf 57.4%

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

   if -1.6000000000000001e-21 < a < 1.11999999999999999e95

   1. Initial program 66.8%

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

   3. Taylor expanded in z around inf 38.9%

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

Alternative 17: 25.0% 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 78.3%

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

3. Taylor expanded in z around inf 25.0%

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

Reproduce

herbie shell --seed 2024091 
(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)))))