Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.0% → 94.4%

Time: 19.0s

Alternatives: 18

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: 79.0% 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: 94.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-259} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-259) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (/ (- x t) (* z (/ 1.0 (- y a))))))))

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-259) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	}
	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-259) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z * Float64(1.0 / Float64(y - a)))));
	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-259], 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[(x - t), $MachinePrecision] / N[(z * N[(1.0 / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-259 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

      1. +-commutative 90.8%

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

      2. associate-*r/ 79.8%

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

      3. *-commutative 79.8%

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

      4. associate-*r/ 96.1%

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

      5. fma-def 96.1%

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

   3. Simplified 96.1%

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

   if -2.0000000000000001e-259 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. associate--l+ 88.6%

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

      3. associate-*r/ 88.6%

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

      4. associate-*r/ 88.6%

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

      5. div-sub 88.6%

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

      6. distribute-lft-out-- 88.6%

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

      7. mul-1-neg 88.6%

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

      8. distribute-neg-frac 88.6%

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

      9. unsub-neg 88.6%

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

      10. distribute-rgt-out-- 88.8%

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

   4. Simplified 88.8%

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

      1. *-un-lft-identity 88.8%

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

      2. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

      \[\leadsto t - 1 \cdot \frac{t - x}{\color{blue}{z \cdot \frac{1}{y - a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-259} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \]

Alternative 2: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-259} \lor \neg \left(t_1 \leq 5 \cdot 10^{-305}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-259) (not (<= t_1 5e-305)))
     t_1
     (+ t (/ (* x (- y a)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-259) || !(t_1 <= 5e-305)) {
		tmp = t_1;
	} else {
		tmp = t + ((x * (y - a)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-259)) .or. (.not. (t_1 <= 5d-305))) then
        tmp = t_1
    else
        tmp = t + ((x * (y - a)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-259) || !(t_1 <= 5e-305)) {
		tmp = t_1;
	} else {
		tmp = t + ((x * (y - a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-259) or not (t_1 <= 5e-305):
		tmp = t_1
	else:
		tmp = t + ((x * (y - a)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-259) || !(t_1 <= 5e-305))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-259) || ~((t_1 <= 5e-305)))
		tmp = t_1;
	else
		tmp = t + ((x * (y - a)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-259], N[Not[LessEqual[t$95$1, 5e-305]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-259 or 4.99999999999999985e-305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.2%

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

   if -2.0000000000000001e-259 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.99999999999999985e-305

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 89.0%

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

      1. +-commutative 89.0%

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

      2. associate--l+ 89.0%

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

      3. associate-*r/ 89.0%

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

      4. associate-*r/ 89.0%

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

      5. div-sub 89.0%

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

      6. distribute-lft-out-- 89.0%

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

      7. mul-1-neg 89.0%

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

      8. distribute-neg-frac 89.0%

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

      9. unsub-neg 89.0%

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

      10. distribute-rgt-out-- 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in t around 0 89.2%

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

      1. mul-1-neg 89.2%

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

      2. distribute-rgt-neg-in 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in t around 0 89.2%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-259} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-305}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \end{array} \]

Alternative 3: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-259} \lor \neg \left(t_1 \leq 5 \cdot 10^{-305}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-259) (not (<= t_1 5e-305)))
     t_1
     (- t (/ (- t x) (/ z (- y a)))))))

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-259) || !(t_1 <= 5e-305)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-259)) .or. (.not. (t_1 <= 5d-305))) then
        tmp = t_1
    else
        tmp = t - ((t - x) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-259) || !(t_1 <= 5e-305)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	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-259) or not (t_1 <= 5e-305):
		tmp = t_1
	else:
		tmp = t - ((t - x) / (z / (y - a)))
	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-259) || !(t_1 <= 5e-305))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	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-259) || ~((t_1 <= 5e-305)))
		tmp = t_1;
	else
		tmp = t - ((t - x) / (z / (y - a)));
	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-259], N[Not[LessEqual[t$95$1, 5e-305]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-259 or 4.99999999999999985e-305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.2%

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

   if -2.0000000000000001e-259 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.99999999999999985e-305

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 89.0%

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

      1. +-commutative 89.0%

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

      2. associate--l+ 89.0%

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

      3. associate-*r/ 89.0%

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

      4. associate-*r/ 89.0%

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

      5. div-sub 89.0%

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

      6. distribute-lft-out-- 89.0%

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

      7. mul-1-neg 89.0%

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

      8. distribute-neg-frac 89.0%

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

      9. unsub-neg 89.0%

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

      10. distribute-rgt-out-- 89.2%

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

   4. Simplified 89.2%

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

      1. *-un-lft-identity 89.2%

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

      2. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

      \[\leadsto t - \color{blue}{1 \cdot \frac{t - x}{\frac{z}{y - a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-259} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-305}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 4: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-259} \lor \neg \left(t_1 \leq 5 \cdot 10^{-305}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-259) (not (<= t_1 5e-305)))
     t_1
     (+ t (/ (- x t) (* z (/ 1.0 (- y a))))))))

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-259) || !(t_1 <= 5e-305)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-259)) .or. (.not. (t_1 <= 5d-305))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z * (1.0d0 / (y - a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-259) || !(t_1 <= 5e-305)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	}
	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-259) or not (t_1 <= 5e-305):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z * (1.0 / (y - a))))
	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-259) || !(t_1 <= 5e-305))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z * Float64(1.0 / Float64(y - a)))));
	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-259) || ~((t_1 <= 5e-305)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z * (1.0 / (y - a))));
	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-259], N[Not[LessEqual[t$95$1, 5e-305]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z * N[(1.0 / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.0000000000000001e-259 or 4.99999999999999985e-305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.2%

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

   if -2.0000000000000001e-259 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.99999999999999985e-305

   1. Initial program 3.7%

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

   2. Taylor expanded in z around inf 89.0%

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

      1. +-commutative 89.0%

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

      2. associate--l+ 89.0%

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

      3. associate-*r/ 89.0%

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

      4. associate-*r/ 89.0%

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

      5. div-sub 89.0%

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

      6. distribute-lft-out-- 89.0%

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

      7. mul-1-neg 89.0%

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

      8. distribute-neg-frac 89.0%

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

      9. unsub-neg 89.0%

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

      10. distribute-rgt-out-- 89.2%

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

   4. Simplified 89.2%

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

      1. *-un-lft-identity 89.2%

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

      2. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. div-inv 99.7%

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

   8. Applied egg-rr 99.7%

      \[\leadsto t - 1 \cdot \frac{t - x}{\color{blue}{z \cdot \frac{1}{y - a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-259} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-305}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{z \cdot \frac{1}{y - a}}\\ \end{array} \]

Alternative 5: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 9:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z))))))
   (if (<= a -7.5e-102)
     t_1
     (if (<= a -3.8e-130)
       (* x (- 1.0 (/ (- y z) (- a z))))
       (if (<= a -3.8e-168)
         (/ (- t) (/ z (- y z)))
         (if (<= a 9.0) (- t (/ (* (- t x) (- y a)) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (a <= -7.5e-102) {
		tmp = t_1;
	} else if (a <= -3.8e-130) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (a <= -3.8e-168) {
		tmp = -t / (z / (y - z));
	} else if (a <= 9.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / (a - z)))
    if (a <= (-7.5d-102)) then
        tmp = t_1
    else if (a <= (-3.8d-130)) then
        tmp = x * (1.0d0 - ((y - z) / (a - z)))
    else if (a <= (-3.8d-168)) then
        tmp = -t / (z / (y - z))
    else if (a <= 9.0d0) then
        tmp = t - (((t - x) * (y - a)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (a <= -7.5e-102) {
		tmp = t_1;
	} else if (a <= -3.8e-130) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (a <= -3.8e-168) {
		tmp = -t / (z / (y - z));
	} else if (a <= 9.0) {
		tmp = t - (((t - x) * (y - a)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	tmp = 0
	if a <= -7.5e-102:
		tmp = t_1
	elif a <= -3.8e-130:
		tmp = x * (1.0 - ((y - z) / (a - z)))
	elif a <= -3.8e-168:
		tmp = -t / (z / (y - z))
	elif a <= 9.0:
		tmp = t - (((t - x) * (y - a)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (a <= -7.5e-102)
		tmp = t_1;
	elseif (a <= -3.8e-130)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(y - z) / Float64(a - z))));
	elseif (a <= -3.8e-168)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (a <= 9.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) * Float64(y - a)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	tmp = 0.0;
	if (a <= -7.5e-102)
		tmp = t_1;
	elseif (a <= -3.8e-130)
		tmp = x * (1.0 - ((y - z) / (a - z)));
	elseif (a <= -3.8e-168)
		tmp = -t / (z / (y - z));
	elseif (a <= 9.0)
		tmp = t - (((t - x) * (y - a)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e-102], t$95$1, If[LessEqual[a, -3.8e-130], N[(x * N[(1.0 - N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-168], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.0], N[(t - N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.5000000000000008e-102 or 9 < a

   1. Initial program 89.1%

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

   2. Taylor expanded in t around inf 76.7%

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

   if -7.5000000000000008e-102 < a < -3.7999999999999998e-130

   1. Initial program 89.5%

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

   2. Taylor expanded in x around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

   4. Simplified 99.8%

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

   if -3.7999999999999998e-130 < a < -3.8e-168

   1. Initial program 99.7%

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

   2. Taylor expanded in t around inf 80.0%

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

      1. div-sub 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in a around 0 44.0%

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

      1. mul-1-neg 44.0%

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

      2. associate-/l* 100.0%

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

      3. distribute-neg-frac 100.0%

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

   7. Simplified 100.0%

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

   if -3.8e-168 < a < 9

   1. Initial program 69.5%

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

   2. Taylor expanded in z around inf 81.4%

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

      1. +-commutative 81.4%

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

      2. associate--l+ 81.4%

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

      3. associate-*r/ 81.4%

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

      4. associate-*r/ 81.4%

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

      5. div-sub 81.4%

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

      6. distribute-lft-out-- 81.4%

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

      7. mul-1-neg 81.4%

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

      8. distribute-neg-frac 81.4%

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

      9. unsub-neg 81.4%

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

      10. distribute-rgt-out-- 81.4%

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

   4. Simplified 81.4%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-102}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;a \leq 9:\\ \;\;\;\;t - \frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 6: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-33} \lor \neg \left(z \leq 1.25 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+134)
   (+ t (/ (* x (- y a)) z))
   (if (<= z -4.5e+65)
     (+ x (* (/ t z) (- z y)))
     (if (or (<= z -3.9e-33) (not (<= z 1.25e-22)))
       (+ t (* (/ y z) (- x t)))
       (+ x (/ y (/ a (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+134) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= -4.5e+65) {
		tmp = x + ((t / z) * (z - y));
	} else if ((z <= -3.9e-33) || !(z <= 1.25e-22)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.8d+134)) then
        tmp = t + ((x * (y - a)) / z)
    else if (z <= (-4.5d+65)) then
        tmp = x + ((t / z) * (z - y))
    else if ((z <= (-3.9d-33)) .or. (.not. (z <= 1.25d-22))) then
        tmp = t + ((y / z) * (x - t))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+134) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= -4.5e+65) {
		tmp = x + ((t / z) * (z - y));
	} else if ((z <= -3.9e-33) || !(z <= 1.25e-22)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+134:
		tmp = t + ((x * (y - a)) / z)
	elif z <= -4.5e+65:
		tmp = x + ((t / z) * (z - y))
	elif (z <= -3.9e-33) or not (z <= 1.25e-22):
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+134)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	elseif (z <= -4.5e+65)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(z - y)));
	elseif ((z <= -3.9e-33) || !(z <= 1.25e-22))
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+134)
		tmp = t + ((x * (y - a)) / z);
	elseif (z <= -4.5e+65)
		tmp = x + ((t / z) * (z - y));
	elseif ((z <= -3.9e-33) || ~((z <= 1.25e-22)))
		tmp = t + ((y / z) * (x - t));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+134], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e+65], N[(x + N[(N[(t / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.9e-33], N[Not[LessEqual[z, 1.25e-22]], $MachinePrecision]], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.79999999999999994e134

   1. Initial program 52.6%

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

   2. Taylor expanded in z around inf 72.5%

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

      1. +-commutative 72.5%

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

      2. associate--l+ 72.5%

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

      3. associate-*r/ 72.5%

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

      4. associate-*r/ 72.5%

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

      5. div-sub 72.5%

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

      6. distribute-lft-out-- 72.5%

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

      7. mul-1-neg 72.5%

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

      8. distribute-neg-frac 72.5%

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

      9. unsub-neg 72.5%

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

      10. distribute-rgt-out-- 72.8%

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

   4. Simplified 72.8%

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

   5. Taylor expanded in t around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. distribute-rgt-neg-in 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in t around 0 79.3%

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

   if -1.79999999999999994e134 < z < -4.5e65

   1. Initial program 88.8%

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

   2. Taylor expanded in t around inf 83.0%

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

   3. Taylor expanded in a around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. mul-1-neg 77.1%

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

   5. Simplified 77.1%

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

   if -4.5e65 < z < -3.89999999999999974e-33 or 1.24999999999999988e-22 < z

   1. Initial program 80.8%

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

   2. Taylor expanded in z around inf 66.6%

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

      1. +-commutative 66.6%

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

      2. associate--l+ 66.6%

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

      3. associate-*r/ 66.6%

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

      4. associate-*r/ 66.6%

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

      5. div-sub 66.6%

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

      6. distribute-lft-out-- 66.6%

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

      7. mul-1-neg 66.6%

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

      8. distribute-neg-frac 66.6%

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

      9. unsub-neg 66.6%

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

      10. distribute-rgt-out-- 66.8%

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

   4. Simplified 66.8%

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

      1. *-un-lft-identity 66.8%

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

      2. associate-/l* 75.2%

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

   6. Applied egg-rr 75.2%

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

   7. Taylor expanded in a around 0 67.1%

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

      1. associate-/l* 68.8%

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

      2. associate-/r/ 72.6%

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

   9. Simplified 72.6%

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

   if -3.89999999999999974e-33 < z < 1.24999999999999988e-22

   1. Initial program 90.8%

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

   2. Taylor expanded in z around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-/l* 77.2%

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

   4. Simplified 77.2%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+65}:\\ \;\;\;\;x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-33} \lor \neg \left(z \leq 1.25 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 7: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;a \leq 15.5:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z))))))
   (if (<= a -2.1e-109)
     t_1
     (if (<= a -3.8e-130)
       (* x (- 1.0 (/ (- y z) (- a z))))
       (if (<= a 15.5) (+ t (* (/ y z) (- x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (a <= -2.1e-109) {
		tmp = t_1;
	} else if (a <= -3.8e-130) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (a <= 15.5) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / (a - z)))
    if (a <= (-2.1d-109)) then
        tmp = t_1
    else if (a <= (-3.8d-130)) then
        tmp = x * (1.0d0 - ((y - z) / (a - z)))
    else if (a <= 15.5d0) then
        tmp = t + ((y / z) * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (a <= -2.1e-109) {
		tmp = t_1;
	} else if (a <= -3.8e-130) {
		tmp = x * (1.0 - ((y - z) / (a - z)));
	} else if (a <= 15.5) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	tmp = 0
	if a <= -2.1e-109:
		tmp = t_1
	elif a <= -3.8e-130:
		tmp = x * (1.0 - ((y - z) / (a - z)))
	elif a <= 15.5:
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (a <= -2.1e-109)
		tmp = t_1;
	elseif (a <= -3.8e-130)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(y - z) / Float64(a - z))));
	elseif (a <= 15.5)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	tmp = 0.0;
	if (a <= -2.1e-109)
		tmp = t_1;
	elseif (a <= -3.8e-130)
		tmp = x * (1.0 - ((y - z) / (a - z)));
	elseif (a <= 15.5)
		tmp = t + ((y / z) * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e-109], t$95$1, If[LessEqual[a, -3.8e-130], N[(x * N[(1.0 - N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 15.5], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.09999999999999996e-109 or 15.5 < a

   1. Initial program 89.1%

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

   2. Taylor expanded in t around inf 76.7%

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

   if -2.09999999999999996e-109 < a < -3.7999999999999998e-130

   1. Initial program 89.5%

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

   2. Taylor expanded in x around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

   4. Simplified 99.8%

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

   if -3.7999999999999998e-130 < a < 15.5

   1. Initial program 71.0%

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

   2. Taylor expanded in z around inf 80.4%

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

      1. +-commutative 80.4%

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

      2. associate--l+ 80.4%

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

      3. associate-*r/ 80.4%

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

      4. associate-*r/ 80.4%

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

      5. div-sub 80.4%

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

      6. distribute-lft-out-- 80.4%

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

      7. mul-1-neg 80.4%

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

      8. distribute-neg-frac 80.4%

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

      9. unsub-neg 80.4%

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

      10. distribute-rgt-out-- 80.4%

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

   4. Simplified 80.4%

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

      1. *-un-lft-identity 80.4%

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

      2. associate-/l* 83.0%

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

   6. Applied egg-rr 83.0%

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

   7. Taylor expanded in a around 0 76.3%

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

      1. associate-/l* 72.4%

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

      2. associate-/r/ 79.0%

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

   9. Simplified 79.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-109}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(1 - \frac{y - z}{a - z}\right)\\ \mathbf{elif}\;a \leq 15.5:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]

Alternative 8: 38.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-187}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+125)
   t
   (if (<= z -3.6e+65)
     x
     (if (<= z -1.45e+20)
       (* x (/ y z))
       (if (<= z -6.2e-187) (* t (/ y (- a z))) (if (<= z 1.7e-37) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+125) {
		tmp = t;
	} else if (z <= -3.6e+65) {
		tmp = x;
	} else if (z <= -1.45e+20) {
		tmp = x * (y / z);
	} else if (z <= -6.2e-187) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.7e-37) {
		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 <= (-1.25d+125)) then
        tmp = t
    else if (z <= (-3.6d+65)) then
        tmp = x
    else if (z <= (-1.45d+20)) then
        tmp = x * (y / z)
    else if (z <= (-6.2d-187)) then
        tmp = t * (y / (a - z))
    else if (z <= 1.7d-37) 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 <= -1.25e+125) {
		tmp = t;
	} else if (z <= -3.6e+65) {
		tmp = x;
	} else if (z <= -1.45e+20) {
		tmp = x * (y / z);
	} else if (z <= -6.2e-187) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.7e-37) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+125:
		tmp = t
	elif z <= -3.6e+65:
		tmp = x
	elif z <= -1.45e+20:
		tmp = x * (y / z)
	elif z <= -6.2e-187:
		tmp = t * (y / (a - z))
	elif z <= 1.7e-37:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+125)
		tmp = t;
	elseif (z <= -3.6e+65)
		tmp = x;
	elseif (z <= -1.45e+20)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -6.2e-187)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.7e-37)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e+125)
		tmp = t;
	elseif (z <= -3.6e+65)
		tmp = x;
	elseif (z <= -1.45e+20)
		tmp = x * (y / z);
	elseif (z <= -6.2e-187)
		tmp = t * (y / (a - z));
	elseif (z <= 1.7e-37)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+125], t, If[LessEqual[z, -3.6e+65], x, If[LessEqual[z, -1.45e+20], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-187], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-37], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.24999999999999991e125 or 1.70000000000000009e-37 < z

   1. Initial program 71.2%

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

   2. Taylor expanded in z around inf 46.1%

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

   if -1.24999999999999991e125 < z < -3.59999999999999978e65 or -6.20000000000000039e-187 < z < 1.70000000000000009e-37

   1. Initial program 91.4%

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

   2. Taylor expanded in a around inf 46.0%

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

   if -3.59999999999999978e65 < z < -1.45e20

   1. Initial program 91.0%

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

   2. Taylor expanded in y around inf 48.4%

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

      1. div-sub 48.4%

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

      2. *-commutative 48.4%

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

      3. associate-*r/ 48.4%

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

      4. associate-/l* 48.4%

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

   4. Simplified 48.4%

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

   5. Taylor expanded in t around 0 40.8%

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

      1. associate-*r/ 40.8%

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

      2. mul-1-neg 40.8%

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

   7. Simplified 40.8%

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

   8. Taylor expanded in a around 0 40.8%

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

      1. associate-/l* 40.8%

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

   10. Simplified 40.8%

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

       1. associate-/r/ 40.8%

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

   12. Applied egg-rr 40.8%

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

   if -1.45e20 < z < -6.20000000000000039e-187

   1. Initial program 88.9%

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

   2. Taylor expanded in t around inf 43.3%

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

      1. div-sub 43.3%

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

   4. Simplified 43.3%

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

   5. Taylor expanded in y around inf 29.5%

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

      1. associate-/l* 31.8%

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

      2. associate-/r/ 34.0%

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

   7. Simplified 34.0%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-187}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 33.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z - a}\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y (- z a)))))
   (if (<= x -4.7e+81)
     t_1
     (if (<= x -3.5e-161)
       x
       (if (<= x -8.5e-289) (* t (/ y (- a z))) (if (<= x 5e+91) t t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / (z - a));
	double tmp;
	if (x <= -4.7e+81) {
		tmp = t_1;
	} else if (x <= -3.5e-161) {
		tmp = x;
	} else if (x <= -8.5e-289) {
		tmp = t * (y / (a - z));
	} else if (x <= 5e+91) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (z - a))
    if (x <= (-4.7d+81)) then
        tmp = t_1
    else if (x <= (-3.5d-161)) then
        tmp = x
    else if (x <= (-8.5d-289)) then
        tmp = t * (y / (a - z))
    else if (x <= 5d+91) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / (z - a));
	double tmp;
	if (x <= -4.7e+81) {
		tmp = t_1;
	} else if (x <= -3.5e-161) {
		tmp = x;
	} else if (x <= -8.5e-289) {
		tmp = t * (y / (a - z));
	} else if (x <= 5e+91) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / (z - a))
	tmp = 0
	if x <= -4.7e+81:
		tmp = t_1
	elif x <= -3.5e-161:
		tmp = x
	elif x <= -8.5e-289:
		tmp = t * (y / (a - z))
	elif x <= 5e+91:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / Float64(z - a)))
	tmp = 0.0
	if (x <= -4.7e+81)
		tmp = t_1;
	elseif (x <= -3.5e-161)
		tmp = x;
	elseif (x <= -8.5e-289)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (x <= 5e+91)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / (z - a));
	tmp = 0.0;
	if (x <= -4.7e+81)
		tmp = t_1;
	elseif (x <= -3.5e-161)
		tmp = x;
	elseif (x <= -8.5e-289)
		tmp = t * (y / (a - z));
	elseif (x <= 5e+91)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.7e+81], t$95$1, If[LessEqual[x, -3.5e-161], x, If[LessEqual[x, -8.5e-289], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+91], t, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.7000000000000002e81 or 5.0000000000000002e91 < x

   1. Initial program 75.6%

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

   2. Taylor expanded in y around inf 47.8%

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

      1. div-sub 47.8%

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

      2. *-commutative 47.8%

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

      3. associate-*r/ 43.8%

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

      4. associate-/l* 47.7%

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

   4. Simplified 47.7%

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

   5. Taylor expanded in t around 0 45.5%

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

      1. associate-*r/ 45.5%

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

      2. mul-1-neg 45.5%

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

   7. Simplified 45.5%

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

   8. Taylor expanded in y around 0 42.7%

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

      1. associate-/l* 45.5%

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

   10. Simplified 45.5%

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

       1. associate-/r/ 49.8%

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

   12. Applied egg-rr 49.8%

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

   if -4.7000000000000002e81 < x < -3.5000000000000002e-161

   1. Initial program 85.9%

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

   2. Taylor expanded in a around inf 35.8%

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

   if -3.5000000000000002e-161 < x < -8.49999999999999931e-289

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 92.7%

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

      1. div-sub 92.7%

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

   4. Simplified 92.7%

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

   5. Taylor expanded in y around inf 51.8%

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

      1. associate-/l* 49.0%

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

      2. associate-/r/ 51.8%

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

   7. Simplified 51.8%

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

   if -8.49999999999999931e-289 < x < 5.0000000000000002e91

   1. Initial program 81.6%

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

   2. Taylor expanded in z around inf 41.2%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 10: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+15} \lor \neg \left(z \leq 3.4 \cdot 10^{-16}\right):\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+15) (not (<= z 3.4e-16)))
   (+ t (/ y (/ z x)))
   (+ x (/ t (/ a (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+15) || !(z <= 3.4e-16)) {
		tmp = t + (y / (z / x));
	} else {
		tmp = x + (t / (a / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.2d+15)) .or. (.not. (z <= 3.4d-16))) then
        tmp = t + (y / (z / x))
    else
        tmp = x + (t / (a / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+15) || !(z <= 3.4e-16)) {
		tmp = t + (y / (z / x));
	} else {
		tmp = x + (t / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e+15) or not (z <= 3.4e-16):
		tmp = t + (y / (z / x))
	else:
		tmp = x + (t / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e+15) || !(z <= 3.4e-16))
		tmp = Float64(t + Float64(y / Float64(z / x)));
	else
		tmp = Float64(x + Float64(t / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e+15) || ~((z <= 3.4e-16)))
		tmp = t + (y / (z / x));
	else
		tmp = x + (t / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e+15], N[Not[LessEqual[z, 3.4e-16]], $MachinePrecision]], N[(t + N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e15 or 3.4e-16 < z

   1. Initial program 74.3%

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

   2. Taylor expanded in z around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. associate--l+ 67.7%

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

      3. associate-*r/ 67.7%

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

      4. associate-*r/ 67.7%

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

      5. div-sub 67.7%

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

      6. distribute-lft-out-- 67.7%

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

      7. mul-1-neg 67.7%

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

      8. distribute-neg-frac 67.7%

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

      9. unsub-neg 67.7%

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

      10. distribute-rgt-out-- 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in t around 0 64.4%

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

      1. mul-1-neg 64.4%

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

      2. distribute-rgt-neg-in 64.4%

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

   7. Simplified 64.4%

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

   8. Taylor expanded in a around 0 60.7%

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

      1. sub-neg 60.7%

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

      2. mul-1-neg 60.7%

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

      3. associate-*l/ 63.3%

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

      4. remove-double-neg 63.3%

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

      5. associate-/r/ 62.0%

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

   10. Simplified 62.0%

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

   if -7.2e15 < z < 3.4e-16

   1. Initial program 90.3%

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

   2. Taylor expanded in t around inf 73.0%

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

   3. Taylor expanded in a around inf 63.2%

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

      1. associate-/l* 64.6%

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

   5. Simplified 64.6%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+15} \lor \neg \left(z \leq 3.4 \cdot 10^{-16}\right):\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 11: 65.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+14} \lor \neg \left(z \leq 2.3 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e+14) (not (<= z 2.3e-22)))
   (+ t (/ y (/ z x)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+14) || !(z <= 2.3e-22)) {
		tmp = t + (y / (z / x));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.4d+14)) .or. (.not. (z <= 2.3d-22))) then
        tmp = t + (y / (z / x))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+14) || !(z <= 2.3e-22)) {
		tmp = t + (y / (z / x));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e+14) or not (z <= 2.3e-22):
		tmp = t + (y / (z / x))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e+14) || !(z <= 2.3e-22))
		tmp = Float64(t + Float64(y / Float64(z / x)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.4e+14) || ~((z <= 2.3e-22)))
		tmp = t + (y / (z / x));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e+14], N[Not[LessEqual[z, 2.3e-22]], $MachinePrecision]], N[(t + N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e14 or 2.2999999999999998e-22 < z

   1. Initial program 74.7%

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

   2. Taylor expanded in z around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. associate--l+ 67.5%

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

      3. associate-*r/ 67.5%

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

      4. associate-*r/ 67.5%

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

      5. div-sub 67.5%

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

      6. distribute-lft-out-- 67.5%

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

      7. mul-1-neg 67.5%

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

      8. distribute-neg-frac 67.5%

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

      9. unsub-neg 67.5%

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

      10. distribute-rgt-out-- 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in t around 0 64.2%

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

      1. mul-1-neg 64.2%

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

      2. distribute-rgt-neg-in 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in a around 0 60.6%

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

      1. sub-neg 60.6%

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

      2. mul-1-neg 60.6%

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

      3. associate-*l/ 63.2%

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

      4. remove-double-neg 63.2%

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

      5. associate-/r/ 61.9%

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

   10. Simplified 61.9%

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

   if -2.4e14 < z < 2.2999999999999998e-22

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-/l* 72.5%

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

   4. Simplified 72.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+14} \lor \neg \left(z \leq 2.3 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 12: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-34} \lor \neg \left(z \leq 2.8 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e-34) (not (<= z 2.8e-22)))
   (+ t (* (/ y z) (- x t)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-34) || !(z <= 2.8e-22)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d-34)) .or. (.not. (z <= 2.8d-22))) then
        tmp = t + ((y / z) * (x - t))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e-34) || !(z <= 2.8e-22)) {
		tmp = t + ((y / z) * (x - t));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e-34) or not (z <= 2.8e-22):
		tmp = t + ((y / z) * (x - t))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e-34) || !(z <= 2.8e-22))
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e-34) || ~((z <= 2.8e-22)))
		tmp = t + ((y / z) * (x - t));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e-34], N[Not[LessEqual[z, 2.8e-22]], $MachinePrecision]], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000017e-34 or 2.79999999999999995e-22 < z

   1. Initial program 75.5%

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

   2. Taylor expanded in z around inf 67.0%

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

      1. +-commutative 67.0%

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

      2. associate--l+ 67.0%

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

      3. associate-*r/ 67.0%

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

      4. associate-*r/ 67.0%

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

      5. div-sub 67.0%

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

      6. distribute-lft-out-- 67.0%

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

      7. mul-1-neg 67.0%

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

      8. distribute-neg-frac 67.0%

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

      9. unsub-neg 67.0%

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

      10. distribute-rgt-out-- 67.2%

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

   4. Simplified 67.2%

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

      1. *-un-lft-identity 67.2%

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

      2. associate-/l* 76.2%

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

   6. Applied egg-rr 76.2%

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

   7. Taylor expanded in a around 0 64.0%

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

      1. associate-/l* 67.2%

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

      2. associate-/r/ 70.4%

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

   9. Simplified 70.4%

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

   if -2.70000000000000017e-34 < z < 2.79999999999999995e-22

   1. Initial program 90.8%

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

   2. Taylor expanded in z around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-/l* 77.2%

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

   4. Simplified 77.2%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-34} \lor \neg \left(z \leq 2.8 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 13: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-33}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e-33)
   (+ t (/ (* x (- y a)) z))
   (if (<= z 2.2e-22) (+ x (/ y (/ a (- t x)))) (+ t (/ y (/ z x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e-33) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= 2.2e-22) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (y / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.5d-33)) then
        tmp = t + ((x * (y - a)) / z)
    else if (z <= 2.2d-22) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + (y / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e-33) {
		tmp = t + ((x * (y - a)) / z);
	} else if (z <= 2.2e-22) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (y / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e-33:
		tmp = t + ((x * (y - a)) / z)
	elif z <= 2.2e-22:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + (y / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e-33)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	elseif (z <= 2.2e-22)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(y / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e-33)
		tmp = t + ((x * (y - a)) / z);
	elseif (z <= 2.2e-22)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + (y / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e-33], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-22], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999991e-33

   1. Initial program 72.9%

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

   2. Taylor expanded in z around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. associate--l+ 66.3%

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

      3. associate-*r/ 66.3%

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

      4. associate-*r/ 66.3%

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

      5. div-sub 66.3%

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

      6. distribute-lft-out-- 66.3%

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

      7. mul-1-neg 66.3%

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

      8. distribute-neg-frac 66.3%

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

      9. unsub-neg 66.3%

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

      10. distribute-rgt-out-- 66.4%

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

   4. Simplified 66.4%

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

   5. Taylor expanded in t around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. distribute-rgt-neg-in 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in t around 0 60.5%

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

   if -4.49999999999999991e-33 < z < 2.2000000000000001e-22

   1. Initial program 90.8%

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

   2. Taylor expanded in z around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-/l* 77.2%

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

   4. Simplified 77.2%

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

   if 2.2000000000000001e-22 < z

   1. Initial program 78.3%

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

   2. Taylor expanded in z around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. associate--l+ 67.8%

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

      3. associate-*r/ 67.8%

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

      4. associate-*r/ 67.8%

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

      5. div-sub 67.8%

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

      6. distribute-lft-out-- 67.8%

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

      7. mul-1-neg 67.8%

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

      8. distribute-neg-frac 67.8%

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

      9. unsub-neg 67.8%

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

      10. distribute-rgt-out-- 68.0%

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

   4. Simplified 68.0%

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

   5. Taylor expanded in t around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-rgt-neg-in 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in a around 0 64.2%

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

      1. sub-neg 64.2%

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

      2. mul-1-neg 64.2%

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

      3. associate-*l/ 66.5%

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

      4. remove-double-neg 66.5%

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

      5. associate-/r/ 64.0%

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

   10. Simplified 64.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-33}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 14: 47.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-98} \lor \neg \left(z \leq 3.5 \cdot 10^{-36}\right):\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.3e-98) (not (<= z 3.5e-36))) (+ t (/ y (/ z x))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e-98) || !(z <= 3.5e-36)) {
		tmp = t + (y / (z / x));
	} 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 ((z <= (-4.3d-98)) .or. (.not. (z <= 3.5d-36))) then
        tmp = t + (y / (z / x))
    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 ((z <= -4.3e-98) || !(z <= 3.5e-36)) {
		tmp = t + (y / (z / x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.3e-98) or not (z <= 3.5e-36):
		tmp = t + (y / (z / x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.3e-98) || !(z <= 3.5e-36))
		tmp = Float64(t + Float64(y / Float64(z / x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.3e-98) || ~((z <= 3.5e-36)))
		tmp = t + (y / (z / x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.3e-98], N[Not[LessEqual[z, 3.5e-36]], $MachinePrecision]], N[(t + N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.29999999999999988e-98 or 3.5e-36 < z

   1. Initial program 76.0%

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

   2. Taylor expanded in z around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. associate--l+ 65.5%

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

      3. associate-*r/ 65.5%

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

      4. associate-*r/ 65.5%

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

      5. div-sub 65.5%

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

      6. distribute-lft-out-- 65.5%

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

      7. mul-1-neg 65.5%

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

      8. distribute-neg-frac 65.5%

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

      9. unsub-neg 65.5%

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

      10. distribute-rgt-out-- 65.7%

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

   4. Simplified 65.7%

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

   5. Taylor expanded in t around 0 60.6%

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

      1. mul-1-neg 60.6%

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

      2. distribute-rgt-neg-in 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in a around 0 55.4%

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

      1. sub-neg 55.4%

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

      2. mul-1-neg 55.4%

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

      3. associate-*l/ 57.6%

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

      4. remove-double-neg 57.6%

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

      5. associate-/r/ 55.9%

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

   10. Simplified 55.9%

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

   if -4.29999999999999988e-98 < z < 3.5e-36

   1. Initial program 93.1%

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

   2. Taylor expanded in a around inf 43.3%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-98} \lor \neg \left(z \leq 3.5 \cdot 10^{-36}\right):\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 59.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+18} \lor \neg \left(z \leq 2.8 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+18) (not (<= z 2.8e-22)))
   (+ t (/ y (/ z x)))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+18) || !(z <= 2.8e-22)) {
		tmp = t + (y / (z / x));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.6d+18)) .or. (.not. (z <= 2.8d-22))) then
        tmp = t + (y / (z / x))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+18) || !(z <= 2.8e-22)) {
		tmp = t + (y / (z / x));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e+18) or not (z <= 2.8e-22):
		tmp = t + (y / (z / x))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+18) || !(z <= 2.8e-22))
		tmp = Float64(t + Float64(y / Float64(z / x)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e+18) || ~((z <= 2.8e-22)))
		tmp = t + (y / (z / x));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+18], N[Not[LessEqual[z, 2.8e-22]], $MachinePrecision]], N[(t + N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e18 or 2.79999999999999995e-22 < z

   1. Initial program 74.7%

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

   2. Taylor expanded in z around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. associate--l+ 67.5%

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

      3. associate-*r/ 67.5%

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

      4. associate-*r/ 67.5%

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

      5. div-sub 67.5%

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

      6. distribute-lft-out-- 67.5%

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

      7. mul-1-neg 67.5%

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

      8. distribute-neg-frac 67.5%

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

      9. unsub-neg 67.5%

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

      10. distribute-rgt-out-- 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in t around 0 64.2%

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

      1. mul-1-neg 64.2%

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

      2. distribute-rgt-neg-in 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in a around 0 60.6%

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

      1. sub-neg 60.6%

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

      2. mul-1-neg 60.6%

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

      3. associate-*l/ 63.2%

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

      4. remove-double-neg 63.2%

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

      5. associate-/r/ 61.9%

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

   10. Simplified 61.9%

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

   if -1.6e18 < z < 2.79999999999999995e-22

   1. Initial program 90.1%

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

   2. Taylor expanded in t around inf 73.4%

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

   3. Taylor expanded in z around 0 57.8%

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

      1. associate-/l* 59.4%

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

   5. Simplified 59.4%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+18} \lor \neg \left(z \leq 2.8 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 16: 37.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+125) t (if (<= z 2.45e-37) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+125) {
		tmp = t;
	} else if (z <= 2.45e-37) {
		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 <= (-1.35d+125)) then
        tmp = t
    else if (z <= 2.45d-37) 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 <= -1.35e+125) {
		tmp = t;
	} else if (z <= 2.45e-37) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+125:
		tmp = t
	elif z <= 2.45e-37:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+125)
		tmp = t;
	elseif (z <= 2.45e-37)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+125)
		tmp = t;
	elseif (z <= 2.45e-37)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+125], t, If[LessEqual[z, 2.45e-37], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e125 or 2.45000000000000009e-37 < z

   1. Initial program 71.2%

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

   2. Taylor expanded in z around inf 46.1%

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

   if -1.3499999999999999e125 < z < 2.45000000000000009e-37

   1. Initial program 90.6%

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

   2. Taylor expanded in a around inf 38.5%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 82.0%

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

2. Taylor expanded in t around 0 43.0%

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

   1. neg-mul-1 43.0%

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

   2. distribute-neg-frac 43.0%

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

4. Simplified 43.0%

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

5. Taylor expanded in z around inf 2.8%

   \[\leadsto \color{blue}{-1 \cdot x + x} \]
6. Step-by-step derivation

   1. distribute-lft1-in 2.8%

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

   2. metadata-eval 2.8%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.8%

      \[\leadsto \color{blue}{0} \]

7. Simplified 2.8%

   \[\leadsto \color{blue}{0} \]

8. Final simplification 2.8%

   \[\leadsto 0 \]

Alternative 18: 24.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.0%

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

2. Taylor expanded in z around inf 25.7%

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

3. Final simplification 25.7%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023230 
(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)))))