Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.1% → 93.8%

Time: 20.2s

Alternatives: 24

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-275} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{y \cdot \left(x - t\right)}{z}\right) + \frac{a}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-275) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ (+ t (/ (* y (- x t)) z)) (/ a (/ z (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t + ((y * (x - t)) / z)) + (a / (z / (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-275)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = (t + ((y * (x - t)) / z)) + (a / (z / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t + ((y * (x - t)) / z)) + (a / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-275) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = (t + ((y * (x - t)) / z)) + (a / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(Float64(t + Float64(Float64(y * Float64(x - t)) / z)) + Float64(a / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-275) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = (t + ((y * (x - t)) / z)) + (a / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-275], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(a / N[(z / N[(t - x), $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)))) < -4.99999999999999983e-275 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*l/ 76.8%

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

      3. associate-*r/ 94.7%

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

      4. clear-num 94.7%

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

      5. un-div-inv 94.8%

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

   3. Applied egg-rr 94.8%

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

   if -4.99999999999999983e-275 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.1%

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

      1. *-commutative 4.1%

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

      2. associate-*l/ 2.9%

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

      3. associate-*r/ 4.1%

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

      4. clear-num 4.1%

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

      5. un-div-inv 4.1%

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

   3. Applied egg-rr 4.1%

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

   4. Taylor expanded in z around inf 77.8%

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

      1. sub-neg 77.8%

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

      2. +-commutative 77.8%

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

      3. mul-1-neg 77.8%

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

      4. unsub-neg 77.8%

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

      5. mul-1-neg 77.8%

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

      6. remove-double-neg 77.8%

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

      7. associate-/l* 87.2%

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

   6. Simplified 87.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-275} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{y \cdot \left(x - t\right)}{z}\right) + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 2: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-275} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-275) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (+ (* (- t x) a) (* y (- x t))) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-275)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + ((((t - x) * a) + (y * (x - t))) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-275) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(Float64(t - x) * a) + Float64(y * Float64(x - t))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-275) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-275], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] + N[(y * N[(x - t), $MachinePrecision]), $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)))) < -4.99999999999999983e-275 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*l/ 76.8%

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

      3. associate-*r/ 94.7%

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

      4. clear-num 94.7%

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

      5. un-div-inv 94.8%

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

   3. Applied egg-rr 94.8%

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

   if -4.99999999999999983e-275 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.1%

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

   2. Taylor expanded in z around -inf 77.9%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-275} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 3: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-275} \lor \neg \left(t_1 \leq 4 \cdot 10^{-239}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-275) (not (<= t_1 4e-239)))
     t_1
     (+ t (/ (* (- y a) (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 4e-239)) {
		tmp = t_1;
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-275)) .or. (.not. (t_1 <= 4d-239))) then
        tmp = t_1
    else
        tmp = t + (((y - a) * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 4e-239)) {
		tmp = t_1;
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-275) or not (t_1 <= 4e-239):
		tmp = t_1
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-275) || !(t_1 <= 4e-239))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-275) || ~((t_1 <= 4e-239)))
		tmp = t_1;
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-275], N[Not[LessEqual[t$95$1, 4e-239]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $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)))) < -4.99999999999999983e-275 or 4.0000000000000003e-239 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

   if -4.99999999999999983e-275 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.0000000000000003e-239

   1. Initial program 7.1%

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

   2. Taylor expanded in z around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. associate--l+ 77.0%

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

      3. associate-*r/ 77.0%

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

      4. associate-*r/ 77.0%

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

      5. div-sub 77.1%

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

      6. distribute-lft-out-- 77.1%

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

      7. mul-1-neg 77.1%

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

      8. distribute-neg-frac 77.1%

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

      9. unsub-neg 77.1%

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

      10. distribute-rgt-out-- 77.1%

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

   4. Simplified 77.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-275} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 4 \cdot 10^{-239}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 4: 93.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-275} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-275) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (* (- y a) (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-275)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((y - a) * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-275) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-275) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-275) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-275], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $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)))) < -4.99999999999999983e-275 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*l/ 76.8%

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

      3. associate-*r/ 94.7%

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

      4. clear-num 94.7%

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

      5. un-div-inv 94.8%

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

   3. Applied egg-rr 94.8%

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

   if -4.99999999999999983e-275 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 4.1%

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

   2. Taylor expanded in z around inf 77.8%

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

      1. +-commutative 77.8%

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

      2. associate--l+ 77.8%

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

      3. associate-*r/ 77.8%

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

      4. associate-*r/ 77.8%

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

      5. div-sub 77.9%

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

      6. distribute-lft-out-- 77.9%

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

      7. mul-1-neg 77.9%

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

      8. distribute-neg-frac 77.9%

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

      9. unsub-neg 77.9%

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

      10. distribute-rgt-out-- 77.9%

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

   4. Simplified 77.9%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-275} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 5: 46.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.08 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.08e-20)
     x
     (if (<= a -3.8e-203)
       t_1
       (if (<= a -2.5e-259)
         (* x (/ y z))
         (if (<= a 3.9e+62)
           t_1
           (if (<= a 2.1e+185) (* y (/ (- t x) a)) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.08e-20) {
		tmp = x;
	} else if (a <= -3.8e-203) {
		tmp = t_1;
	} else if (a <= -2.5e-259) {
		tmp = x * (y / z);
	} else if (a <= 3.9e+62) {
		tmp = t_1;
	} else if (a <= 2.1e+185) {
		tmp = y * ((t - x) / a);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-1.08d-20)) then
        tmp = x
    else if (a <= (-3.8d-203)) then
        tmp = t_1
    else if (a <= (-2.5d-259)) then
        tmp = x * (y / z)
    else if (a <= 3.9d+62) then
        tmp = t_1
    else if (a <= 2.1d+185) then
        tmp = y * ((t - x) / a)
    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 t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.08e-20) {
		tmp = x;
	} else if (a <= -3.8e-203) {
		tmp = t_1;
	} else if (a <= -2.5e-259) {
		tmp = x * (y / z);
	} else if (a <= 3.9e+62) {
		tmp = t_1;
	} else if (a <= 2.1e+185) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.08e-20:
		tmp = x
	elif a <= -3.8e-203:
		tmp = t_1
	elif a <= -2.5e-259:
		tmp = x * (y / z)
	elif a <= 3.9e+62:
		tmp = t_1
	elif a <= 2.1e+185:
		tmp = y * ((t - x) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -1.08e-20)
		tmp = x;
	elseif (a <= -3.8e-203)
		tmp = t_1;
	elseif (a <= -2.5e-259)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 3.9e+62)
		tmp = t_1;
	elseif (a <= 2.1e+185)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -1.08e-20)
		tmp = x;
	elseif (a <= -3.8e-203)
		tmp = t_1;
	elseif (a <= -2.5e-259)
		tmp = x * (y / z);
	elseif (a <= 3.9e+62)
		tmp = t_1;
	elseif (a <= 2.1e+185)
		tmp = y * ((t - x) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.08e-20], x, If[LessEqual[a, -3.8e-203], t$95$1, If[LessEqual[a, -2.5e-259], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+62], t$95$1, If[LessEqual[a, 2.1e+185], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.08e-20 or 2.1e185 < a

   1. Initial program 88.1%

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

   2. Taylor expanded in a around inf 50.8%

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

   if -1.08e-20 < a < -3.80000000000000025e-203 or -2.49999999999999989e-259 < a < 3.9e62

   1. Initial program 75.7%

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

   2. Taylor expanded in t around inf 62.0%

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

   3. Taylor expanded in a around 0 58.7%

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

      1. *-commutative 58.7%

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

      2. +-commutative 58.7%

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

      3. mul-1-neg 58.7%

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

      4. unsub-neg 58.7%

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

   5. Simplified 58.7%

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

   if -3.80000000000000025e-203 < a < -2.49999999999999989e-259

   1. Initial program 86.6%

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

   2. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in a around 0 72.1%

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

   if 3.9e62 < a < 2.1e185

   1. Initial program 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l/ 46.9%

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

      3. associate-*r/ 81.7%

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

      4. clear-num 81.7%

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

      5. un-div-inv 81.8%

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

   3. Applied egg-rr 81.8%

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

   4. Taylor expanded in y around inf 53.4%

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

      1. div-sub 53.4%

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

      2. *-commutative 53.4%

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

   6. Simplified 53.4%

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

   7. Taylor expanded in a around inf 43.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-203}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a - z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.45e-162)
     t_2
     (if (<= t 3.6e-240)
       t_1
       (if (<= t 8.2e-175)
         (/ (* x (- y)) (- a z))
         (if (<= t 2.8e-46) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.45e-162) {
		tmp = t_2;
	} else if (t <= 3.6e-240) {
		tmp = t_1;
	} else if (t <= 8.2e-175) {
		tmp = (x * -y) / (a - z);
	} else if (t <= 2.8e-46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-1.45d-162)) then
        tmp = t_2
    else if (t <= 3.6d-240) then
        tmp = t_1
    else if (t <= 8.2d-175) then
        tmp = (x * -y) / (a - z)
    else if (t <= 2.8d-46) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.45e-162) {
		tmp = t_2;
	} else if (t <= 3.6e-240) {
		tmp = t_1;
	} else if (t <= 8.2e-175) {
		tmp = (x * -y) / (a - z);
	} else if (t <= 2.8e-46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.45e-162:
		tmp = t_2
	elif t <= 3.6e-240:
		tmp = t_1
	elif t <= 8.2e-175:
		tmp = (x * -y) / (a - z)
	elif t <= 2.8e-46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.45e-162)
		tmp = t_2;
	elseif (t <= 3.6e-240)
		tmp = t_1;
	elseif (t <= 8.2e-175)
		tmp = Float64(Float64(x * Float64(-y)) / Float64(a - z));
	elseif (t <= 2.8e-46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.45e-162)
		tmp = t_2;
	elseif (t <= 3.6e-240)
		tmp = t_1;
	elseif (t <= 8.2e-175)
		tmp = (x * -y) / (a - z);
	elseif (t <= 2.8e-46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-162], t$95$2, If[LessEqual[t, 3.6e-240], t$95$1, If[LessEqual[t, 8.2e-175], N[(N[(x * (-y)), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-46], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4500000000000001e-162 or 2.7999999999999998e-46 < t

   1. Initial program 86.3%

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

   2. Taylor expanded in t around inf 67.1%

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

      1. div-sub 67.1%

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

   4. Simplified 67.1%

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

   if -1.4500000000000001e-162 < t < 3.5999999999999999e-240 or 8.19999999999999997e-175 < t < 2.7999999999999998e-46

   1. Initial program 71.0%

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

   2. Taylor expanded in x around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

   4. Simplified 70.5%

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

   5. Taylor expanded in z around 0 61.1%

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

   if 3.5999999999999999e-240 < t < 8.19999999999999997e-175

   1. Initial program 71.6%

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

   2. Taylor expanded in y around inf 80.8%

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

      1. div-sub 80.8%

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

      2. *-commutative 80.8%

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

      3. associate-*r/ 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in t around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*r* 80.5%

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

      3. neg-mul-1 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-162}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{a - z}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 7: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e+88)
   (* t (/ (- y z) (- a z)))
   (if (<= z -6e-105)
     (/ y (/ (- a z) (- t x)))
     (if (<= z 1.65e-80)
       (+ x (* (- y z) (/ (- t x) a)))
       (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e+88) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -6e-105) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 1.65e-80) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t / ((a - z) / (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 <= (-2.9d+88)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-6d-105)) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 1.65d-80) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t / ((a - z) / (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 <= -2.9e+88) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -6e-105) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 1.65e-80) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e+88:
		tmp = t * ((y - z) / (a - z))
	elif z <= -6e-105:
		tmp = y / ((a - z) / (t - x))
	elif z <= 1.65e-80:
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e+88)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -6e-105)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 1.65e-80)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e+88)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -6e-105)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 1.65e-80)
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e+88], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e-105], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-80], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9e88

   1. Initial program 60.2%

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

   2. Taylor expanded in t around inf 67.2%

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

      1. div-sub 67.2%

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

   4. Simplified 67.2%

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

   if -2.9e88 < z < -6.0000000000000002e-105

   1. Initial program 84.9%

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

   2. Taylor expanded in y around inf 65.4%

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

      1. div-sub 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*r/ 55.2%

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

      4. associate-/l* 65.4%

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

   4. Simplified 65.4%

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

   if -6.0000000000000002e-105 < z < 1.65e-80

   1. Initial program 95.6%

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

   2. Taylor expanded in a around inf 83.3%

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

   if 1.65e-80 < z

   1. Initial program 76.2%

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

   2. Taylor expanded in x around 0 42.4%

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

      1. associate-/l* 61.7%

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

   4. Simplified 61.7%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 8: 47.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.08 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.08e-20)
     x
     (if (<= a -3.6e-196)
       t_1
       (if (<= a -3.9e-261) (* x (/ y z)) (if (<= a 1.06e+120) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.08e-20) {
		tmp = x;
	} else if (a <= -3.6e-196) {
		tmp = t_1;
	} else if (a <= -3.9e-261) {
		tmp = x * (y / z);
	} else if (a <= 1.06e+120) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-1.08d-20)) then
        tmp = x
    else if (a <= (-3.6d-196)) then
        tmp = t_1
    else if (a <= (-3.9d-261)) then
        tmp = x * (y / z)
    else if (a <= 1.06d+120) then
        tmp = t_1
    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 t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.08e-20) {
		tmp = x;
	} else if (a <= -3.6e-196) {
		tmp = t_1;
	} else if (a <= -3.9e-261) {
		tmp = x * (y / z);
	} else if (a <= 1.06e+120) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.08e-20:
		tmp = x
	elif a <= -3.6e-196:
		tmp = t_1
	elif a <= -3.9e-261:
		tmp = x * (y / z)
	elif a <= 1.06e+120:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -1.08e-20)
		tmp = x;
	elseif (a <= -3.6e-196)
		tmp = t_1;
	elseif (a <= -3.9e-261)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.06e+120)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -1.08e-20)
		tmp = x;
	elseif (a <= -3.6e-196)
		tmp = t_1;
	elseif (a <= -3.9e-261)
		tmp = x * (y / z);
	elseif (a <= 1.06e+120)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.08e-20], x, If[LessEqual[a, -3.6e-196], t$95$1, If[LessEqual[a, -3.9e-261], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e+120], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.08e-20 or 1.05999999999999994e120 < a

   1. Initial program 86.0%

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

   2. Taylor expanded in a around inf 46.8%

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

   if -1.08e-20 < a < -3.6000000000000001e-196 or -3.90000000000000017e-261 < a < 1.05999999999999994e120

   1. Initial program 76.6%

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

   2. Taylor expanded in t around inf 60.7%

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

   3. Taylor expanded in a around 0 56.3%

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

      1. *-commutative 56.3%

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

      2. +-commutative 56.3%

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

      3. mul-1-neg 56.3%

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

      4. unsub-neg 56.3%

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

   5. Simplified 56.3%

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

   if -3.6000000000000001e-196 < a < -3.90000000000000017e-261

   1. Initial program 86.6%

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

   2. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in a around 0 72.1%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 56.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -8e+87)
     t_1
     (if (<= z -1.8e-107)
       (* y (/ (- t x) (- a z)))
       (if (<= z 9e-88) (* x (- 1.0 (/ y a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8e+87) {
		tmp = t_1;
	} else if (z <= -1.8e-107) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 9e-88) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-8d+87)) then
        tmp = t_1
    else if (z <= (-1.8d-107)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 9d-88) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -8e+87) {
		tmp = t_1;
	} else if (z <= -1.8e-107) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 9e-88) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -8e+87:
		tmp = t_1
	elif z <= -1.8e-107:
		tmp = y * ((t - x) / (a - z))
	elif z <= 9e-88:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -8e+87)
		tmp = t_1;
	elseif (z <= -1.8e-107)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 9e-88)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -8e+87)
		tmp = t_1;
	elseif (z <= -1.8e-107)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 9e-88)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+87], t$95$1, If[LessEqual[z, -1.8e-107], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-88], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999997e87 or 8.99999999999999982e-88 < z

   1. Initial program 71.1%

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

   2. Taylor expanded in t around inf 63.4%

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

      1. div-sub 63.4%

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

   4. Simplified 63.4%

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

   if -7.9999999999999997e87 < z < -1.79999999999999988e-107

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l/ 74.6%

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

      3. associate-*r/ 84.8%

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

      4. clear-num 84.8%

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

      5. un-div-inv 85.0%

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

   3. Applied egg-rr 85.0%

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

   4. Taylor expanded in y around inf 65.4%

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

      1. div-sub 65.4%

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

      2. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if -1.79999999999999988e-107 < z < 8.99999999999999982e-88

   1. Initial program 95.4%

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

   2. Taylor expanded in x around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in z around 0 65.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-107}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 10: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.35e+88)
     t_1
     (if (<= z -5.5e-103)
       (* y (/ (- t x) (- a z)))
       (if (<= z 1.3e-79) (+ x (/ y (/ a (- t x)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+88) {
		tmp = t_1;
	} else if (z <= -5.5e-103) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.3e-79) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-1.35d+88)) then
        tmp = t_1
    else if (z <= (-5.5d-103)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.3d-79) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.35e+88) {
		tmp = t_1;
	} else if (z <= -5.5e-103) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.3e-79) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.35e+88:
		tmp = t_1
	elif z <= -5.5e-103:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.3e-79:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.35e+88)
		tmp = t_1;
	elseif (z <= -5.5e-103)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.3e-79)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.35e+88)
		tmp = t_1;
	elseif (z <= -5.5e-103)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.3e-79)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+88], t$95$1, If[LessEqual[z, -5.5e-103], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-79], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000008e88 or 1.29999999999999997e-79 < z

   1. Initial program 70.7%

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

   2. Taylor expanded in t around inf 63.5%

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

      1. div-sub 63.5%

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

   4. Simplified 63.5%

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

   if -1.35000000000000008e88 < z < -5.50000000000000032e-103

   1. Initial program 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*l/ 74.6%

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

      3. associate-*r/ 84.8%

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

      4. clear-num 84.8%

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

      5. un-div-inv 85.0%

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

   3. Applied egg-rr 85.0%

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

   4. Taylor expanded in y around inf 65.4%

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

      1. div-sub 65.4%

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

      2. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if -5.50000000000000032e-103 < z < 1.29999999999999997e-79

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 78.9%

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

      1. +-commutative 78.9%

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

      2. associate-/l* 81.5%

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

   4. Simplified 81.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 11: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.6e+91)
     t_1
     (if (<= z -1.26e-93)
       (* y (/ (- t x) (- a z)))
       (if (<= z 1.75e-79) (+ x (/ (- t x) (/ a y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.6e+91) {
		tmp = t_1;
	} else if (z <= -1.26e-93) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.75e-79) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-1.6d+91)) then
        tmp = t_1
    else if (z <= (-1.26d-93)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.75d-79) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.6e+91) {
		tmp = t_1;
	} else if (z <= -1.26e-93) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.75e-79) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.6e+91:
		tmp = t_1
	elif z <= -1.26e-93:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.75e-79:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.6e+91)
		tmp = t_1;
	elseif (z <= -1.26e-93)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.75e-79)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.6e+91)
		tmp = t_1;
	elseif (z <= -1.26e-93)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.75e-79)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+91], t$95$1, If[LessEqual[z, -1.26e-93], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-79], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999995e91 or 1.75000000000000015e-79 < z

   1. Initial program 70.7%

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

   2. Taylor expanded in t around inf 63.5%

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

      1. div-sub 63.5%

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

   4. Simplified 63.5%

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

   if -1.59999999999999995e91 < z < -1.2600000000000001e-93

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

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

      2. associate-*l/ 72.8%

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

      3. associate-*r/ 83.8%

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

      4. clear-num 83.8%

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

      5. un-div-inv 83.9%

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

   3. Applied egg-rr 83.9%

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

   4. Taylor expanded in y around inf 65.3%

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

      1. div-sub 65.3%

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

      2. *-commutative 65.3%

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

   6. Simplified 65.3%

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

   if -1.2600000000000001e-93 < z < 1.75000000000000015e-79

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-*l/ 96.0%

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

      3. associate-*r/ 98.7%

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

      4. clear-num 98.7%

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

      5. un-div-inv 98.8%

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

   3. Applied egg-rr 98.8%

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

   4. Taylor expanded in z around 0 81.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 12: 65.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+89)
   (* t (/ (- y z) (- a z)))
   (if (<= z -1.85e-95)
     (* y (/ (- t x) (- a z)))
     (if (<= z 1.65e-80)
       (+ x (/ (- t x) (/ a y)))
       (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+89) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -1.85e-95) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.65e-80) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t / ((a - z) / (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+89)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-1.85d-95)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.65d-80) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t / ((a - z) / (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+89) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -1.85e-95) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.65e-80) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+89:
		tmp = t * ((y - z) / (a - z))
	elif z <= -1.85e-95:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.65e-80:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+89)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -1.85e-95)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.65e-80)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+89)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -1.85e-95)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.65e-80)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+89], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.85e-95], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-80], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.2e89

   1. Initial program 60.2%

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

   2. Taylor expanded in t around inf 67.2%

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

      1. div-sub 67.2%

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

   4. Simplified 67.2%

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

   if -7.2e89 < z < -1.84999999999999997e-95

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

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

      2. associate-*l/ 72.8%

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

      3. associate-*r/ 83.8%

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

      4. clear-num 83.8%

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

      5. un-div-inv 83.9%

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

   3. Applied egg-rr 83.9%

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

   4. Taylor expanded in y around inf 65.3%

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

      1. div-sub 65.3%

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

      2. *-commutative 65.3%

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

   6. Simplified 65.3%

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

   if -1.84999999999999997e-95 < z < 1.65e-80

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-*l/ 96.0%

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

      3. associate-*r/ 98.7%

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

      4. clear-num 98.7%

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

      5. un-div-inv 98.8%

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

   3. Applied egg-rr 98.8%

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

   4. Taylor expanded in z around 0 81.3%

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

   if 1.65e-80 < z

   1. Initial program 76.2%

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

   2. Taylor expanded in x around 0 42.4%

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

      1. associate-/l* 61.7%

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

   4. Simplified 61.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 13: 65.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+90)
   (* t (/ (- y z) (- a z)))
   (if (<= z -1.4e-93)
     (/ y (/ (- a z) (- t x)))
     (if (<= z 1.7e-79) (+ x (/ (- t x) (/ a y))) (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+90) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -1.4e-93) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 1.7e-79) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t / ((a - z) / (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 <= (-1.8d+90)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= (-1.4d-93)) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 1.7d-79) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t / ((a - z) / (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 <= -1.8e+90) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= -1.4e-93) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 1.7e-79) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+90:
		tmp = t * ((y - z) / (a - z))
	elif z <= -1.4e-93:
		tmp = y / ((a - z) / (t - x))
	elif z <= 1.7e-79:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+90)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= -1.4e-93)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 1.7e-79)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+90)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= -1.4e-93)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 1.7e-79)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+90], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4e-93], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-79], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e90

   1. Initial program 60.2%

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

   2. Taylor expanded in t around inf 67.2%

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

      1. div-sub 67.2%

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

   4. Simplified 67.2%

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

   if -1.8e90 < z < -1.39999999999999999e-93

   1. Initial program 86.2%

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

   2. Taylor expanded in y around inf 65.3%

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

      1. div-sub 65.3%

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

      2. *-commutative 65.3%

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

      3. associate-*r/ 52.0%

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

      4. associate-/l* 65.3%

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

   4. Simplified 65.3%

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

   if -1.39999999999999999e-93 < z < 1.69999999999999988e-79

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-*l/ 96.0%

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

      3. associate-*r/ 98.7%

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

      4. clear-num 98.7%

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

      5. un-div-inv 98.8%

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

   3. Applied egg-rr 98.8%

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

   4. Taylor expanded in z around 0 81.3%

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

   if 1.69999999999999988e-79 < z

   1. Initial program 76.2%

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

   2. Taylor expanded in x around 0 42.4%

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

      1. associate-/l* 61.7%

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

   4. Simplified 61.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 14: 63.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-50} \lor \neg \left(x \leq 1.9 \cdot 10^{-60}\right):\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -6.2e-50) (not (<= x 1.9e-60)))
   (* x (+ (/ (- z y) (- a z)) 1.0))
   (/ t (/ (- a z) (- y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.2e-50) || !(x <= 1.9e-60)) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = t / ((a - z) / (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 ((x <= (-6.2d-50)) .or. (.not. (x <= 1.9d-60))) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    else
        tmp = t / ((a - z) / (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 ((x <= -6.2e-50) || !(x <= 1.9e-60)) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -6.2e-50) or not (x <= 1.9e-60):
		tmp = x * (((z - y) / (a - z)) + 1.0)
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -6.2e-50) || !(x <= 1.9e-60))
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -6.2e-50) || ~((x <= 1.9e-60)))
		tmp = x * (((z - y) / (a - z)) + 1.0);
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -6.2e-50], N[Not[LessEqual[x, 1.9e-60]], $MachinePrecision]], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000004e-50 or 1.89999999999999997e-60 < x

   1. Initial program 79.0%

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

   2. Taylor expanded in x around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. unsub-neg 61.0%

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

   4. Simplified 61.0%

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

   if -6.2000000000000004e-50 < x < 1.89999999999999997e-60

   1. Initial program 84.2%

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

   2. Taylor expanded in x around 0 62.3%

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

      1. associate-/l* 80.5%

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

   4. Simplified 80.5%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-50} \lor \neg \left(x \leq 1.9 \cdot 10^{-60}\right):\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 15: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 10^{+78}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.65e+124)
   (* t (/ (- y z) (- a z)))
   (if (<= z 1e+78)
     (+ x (/ (- t x) (/ (- a z) y)))
     (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.65e+124) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1e+78) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t / ((a - z) / (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 <= (-3.65d+124)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 1d+78) then
        tmp = x + ((t - x) / ((a - z) / y))
    else
        tmp = t / ((a - z) / (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 <= -3.65e+124) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1e+78) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.65e+124:
		tmp = t * ((y - z) / (a - z))
	elif z <= 1e+78:
		tmp = x + ((t - x) / ((a - z) / y))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.65e+124)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 1e+78)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.65e+124)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 1e+78)
		tmp = x + ((t - x) / ((a - z) / y));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.65e+124], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+78], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.64999999999999997e124

   1. Initial program 59.0%

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

   2. Taylor expanded in t around inf 74.3%

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

      1. div-sub 74.3%

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

   4. Simplified 74.3%

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

   if -3.64999999999999997e124 < z < 1.00000000000000001e78

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 85.1%

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

      3. associate-*r/ 92.8%

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

      4. clear-num 92.9%

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

      5. un-div-inv 92.9%

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

   3. Applied egg-rr 92.9%

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

   4. Taylor expanded in y around inf 80.9%

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

   if 1.00000000000000001e78 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in x around 0 42.4%

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

      1. associate-/l* 72.6%

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

   4. Simplified 72.6%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.65 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 10^{+78}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 16: 49.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+72}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{-x}{\frac{z}{a - y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+72)
   (- t (/ y (/ z t)))
   (if (<= z -2.8e-90)
     (/ (- x) (/ z (- a y)))
     (if (<= z 6.2e+75) (* x (- 1.0 (/ y a))) (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+72) {
		tmp = t - (y / (z / t));
	} else if (z <= -2.8e-90) {
		tmp = -x / (z / (a - y));
	} else if (z <= 6.2e+75) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d+72)) then
        tmp = t - (y / (z / t))
    else if (z <= (-2.8d-90)) then
        tmp = -x / (z / (a - y))
    else if (z <= 6.2d+75) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+72) {
		tmp = t - (y / (z / t));
	} else if (z <= -2.8e-90) {
		tmp = -x / (z / (a - y));
	} else if (z <= 6.2e+75) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+72:
		tmp = t - (y / (z / t))
	elif z <= -2.8e-90:
		tmp = -x / (z / (a - y))
	elif z <= 6.2e+75:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+72)
		tmp = Float64(t - Float64(y / Float64(z / t)));
	elseif (z <= -2.8e-90)
		tmp = Float64(Float64(-x) / Float64(z / Float64(a - y)));
	elseif (z <= 6.2e+75)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+72)
		tmp = t - (y / (z / t));
	elseif (z <= -2.8e-90)
		tmp = -x / (z / (a - y));
	elseif (z <= 6.2e+75)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+72], N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-90], N[((-x) / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+75], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.7999999999999997e72

   1. Initial program 64.4%

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

   2. Taylor expanded in t around inf 64.8%

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

   3. Taylor expanded in z around -inf 41.5%

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

      1. +-commutative 41.5%

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

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

      4. associate-/l* 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in y around inf 47.5%

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

      1. associate-/l* 56.6%

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

   8. Simplified 56.6%

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

   if -6.7999999999999997e72 < z < -2.7999999999999999e-90

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in z around inf 42.1%

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

      1. mul-1-neg 42.1%

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

      2. neg-mul-1 42.1%

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

      3. sub-neg 42.1%

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

      4. *-commutative 42.1%

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

      5. associate-/l* 45.0%

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

   7. Simplified 45.0%

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

   if -2.7999999999999999e-90 < z < 6.2000000000000002e75

   1. Initial program 92.1%

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

   2. Taylor expanded in x around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   4. Simplified 63.2%

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

   5. Taylor expanded in z around 0 55.2%

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

   if 6.2000000000000002e75 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in t around inf 72.5%

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

   3. Taylor expanded in a around 0 58.8%

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

      1. *-commutative 58.8%

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

      2. +-commutative 58.8%

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

      3. mul-1-neg 58.8%

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

      4. unsub-neg 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+72}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{-x}{\frac{z}{a - y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 17: 49.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+73}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-90}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+73)
   (- t (/ y (/ z t)))
   (if (<= z -2.9e-90)
     (/ (- y) (/ (- a z) x))
     (if (<= z 1.65e+76) (* x (- 1.0 (/ y a))) (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+73) {
		tmp = t - (y / (z / t));
	} else if (z <= -2.9e-90) {
		tmp = -y / ((a - z) / x);
	} else if (z <= 1.65e+76) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d+73)) then
        tmp = t - (y / (z / t))
    else if (z <= (-2.9d-90)) then
        tmp = -y / ((a - z) / x)
    else if (z <= 1.65d+76) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+73) {
		tmp = t - (y / (z / t));
	} else if (z <= -2.9e-90) {
		tmp = -y / ((a - z) / x);
	} else if (z <= 1.65e+76) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+73:
		tmp = t - (y / (z / t))
	elif z <= -2.9e-90:
		tmp = -y / ((a - z) / x)
	elif z <= 1.65e+76:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+73)
		tmp = Float64(t - Float64(y / Float64(z / t)));
	elseif (z <= -2.9e-90)
		tmp = Float64(Float64(-y) / Float64(Float64(a - z) / x));
	elseif (z <= 1.65e+76)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+73)
		tmp = t - (y / (z / t));
	elseif (z <= -2.9e-90)
		tmp = -y / ((a - z) / x);
	elseif (z <= 1.65e+76)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+73], N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-90], N[((-y) / N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+76], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6000000000000001e73

   1. Initial program 64.4%

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

   2. Taylor expanded in t around inf 64.8%

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

   3. Taylor expanded in z around -inf 41.5%

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

      1. +-commutative 41.5%

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

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

      4. associate-/l* 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in y around inf 47.5%

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

      1. associate-/l* 56.6%

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

   8. Simplified 56.6%

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

   if -2.6000000000000001e73 < z < -2.89999999999999983e-90

   1. Initial program 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-*l/ 74.6%

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

      3. associate-*r/ 82.7%

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

      4. clear-num 82.6%

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

      5. un-div-inv 82.9%

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

   3. Applied egg-rr 82.9%

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

   4. Taylor expanded in y around inf 68.3%

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

      1. div-sub 68.3%

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

      2. *-commutative 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in t around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. associate-/l* 48.5%

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

   9. Simplified 48.5%

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

   if -2.89999999999999983e-90 < z < 1.65e76

   1. Initial program 92.1%

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

   2. Taylor expanded in x around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   4. Simplified 63.2%

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

   5. Taylor expanded in z around 0 55.2%

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

   if 1.65e76 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in t around inf 72.5%

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

   3. Taylor expanded in a around 0 58.8%

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

      1. *-commutative 58.8%

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

      2. +-commutative 58.8%

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

      3. mul-1-neg 58.8%

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

      4. unsub-neg 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+73}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-90}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 18: 37.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-115}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.2e-21)
   x
   (if (<= a -1.05e-115)
     t
     (if (<= a -1.15e-260) (* x (/ y z)) (if (<= a 1.55e+112) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.2e-21) {
		tmp = x;
	} else if (a <= -1.05e-115) {
		tmp = t;
	} else if (a <= -1.15e-260) {
		tmp = x * (y / z);
	} else if (a <= 1.55e+112) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.2d-21)) then
        tmp = x
    else if (a <= (-1.05d-115)) then
        tmp = t
    else if (a <= (-1.15d-260)) then
        tmp = x * (y / z)
    else if (a <= 1.55d+112) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.2e-21) {
		tmp = x;
	} else if (a <= -1.05e-115) {
		tmp = t;
	} else if (a <= -1.15e-260) {
		tmp = x * (y / z);
	} else if (a <= 1.55e+112) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.2e-21:
		tmp = x
	elif a <= -1.05e-115:
		tmp = t
	elif a <= -1.15e-260:
		tmp = x * (y / z)
	elif a <= 1.55e+112:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.2e-21)
		tmp = x;
	elseif (a <= -1.05e-115)
		tmp = t;
	elseif (a <= -1.15e-260)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.55e+112)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.2e-21)
		tmp = x;
	elseif (a <= -1.05e-115)
		tmp = t;
	elseif (a <= -1.15e-260)
		tmp = x * (y / z);
	elseif (a <= 1.55e+112)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.2e-21], x, If[LessEqual[a, -1.05e-115], t, If[LessEqual[a, -1.15e-260], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+112], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.19999999999999988e-21 or 1.54999999999999991e112 < a

   1. Initial program 86.1%

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

   2. Taylor expanded in a around inf 46.3%

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

   if -8.19999999999999988e-21 < a < -1.05000000000000001e-115 or -1.15e-260 < a < 1.54999999999999991e112

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf 37.9%

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

   if -1.05000000000000001e-115 < a < -1.15e-260

   1. Initial program 78.7%

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

   2. Taylor expanded in x around inf 52.9%

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

      1. mul-1-neg 52.9%

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

      2. unsub-neg 52.9%

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

   4. Simplified 52.9%

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

   5. Taylor expanded in a around 0 56.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-115}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-116}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.08e-20)
   x
   (if (<= a -8.2e-116)
     t
     (if (<= a -8e-261) (/ (* x y) z) (if (<= a 2.3e+111) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e-20) {
		tmp = x;
	} else if (a <= -8.2e-116) {
		tmp = t;
	} else if (a <= -8e-261) {
		tmp = (x * y) / z;
	} else if (a <= 2.3e+111) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.08d-20)) then
        tmp = x
    else if (a <= (-8.2d-116)) then
        tmp = t
    else if (a <= (-8d-261)) then
        tmp = (x * y) / z
    else if (a <= 2.3d+111) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.08e-20) {
		tmp = x;
	} else if (a <= -8.2e-116) {
		tmp = t;
	} else if (a <= -8e-261) {
		tmp = (x * y) / z;
	} else if (a <= 2.3e+111) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.08e-20:
		tmp = x
	elif a <= -8.2e-116:
		tmp = t
	elif a <= -8e-261:
		tmp = (x * y) / z
	elif a <= 2.3e+111:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.08e-20)
		tmp = x;
	elseif (a <= -8.2e-116)
		tmp = t;
	elseif (a <= -8e-261)
		tmp = Float64(Float64(x * y) / z);
	elseif (a <= 2.3e+111)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.08e-20)
		tmp = x;
	elseif (a <= -8.2e-116)
		tmp = t;
	elseif (a <= -8e-261)
		tmp = (x * y) / z;
	elseif (a <= 2.3e+111)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.08e-20], x, If[LessEqual[a, -8.2e-116], t, If[LessEqual[a, -8e-261], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 2.3e+111], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.08e-20 or 2.30000000000000002e111 < a

   1. Initial program 86.1%

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

   2. Taylor expanded in a around inf 46.3%

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

   if -1.08e-20 < a < -8.1999999999999998e-116 or -7.99999999999999987e-261 < a < 2.30000000000000002e111

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf 37.9%

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

   if -8.1999999999999998e-116 < a < -7.99999999999999987e-261

   1. Initial program 78.7%

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

   2. Taylor expanded in x around inf 52.9%

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

      1. mul-1-neg 52.9%

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

      2. unsub-neg 52.9%

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

   4. Simplified 52.9%

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

   5. Taylor expanded in a around 0 56.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-116}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+122} \lor \neg \left(z \leq 3.1 \cdot 10^{+78}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.4e+122) (not (<= z 3.1e+78)))
   (* t (- 1.0 (/ y z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e+122) || !(z <= 3.1e+78)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.4d+122)) .or. (.not. (z <= 3.1d+78))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e+122) || !(z <= 3.1e+78)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.4e+122) or not (z <= 3.1e+78):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.4e+122) || !(z <= 3.1e+78))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.4e+122) || ~((z <= 3.1e+78)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.4e+122], N[Not[LessEqual[z, 3.1e+78]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.40000000000000024e122 or 3.1e78 < z

   1. Initial program 63.2%

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

   2. Taylor expanded in t around inf 73.3%

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

   3. Taylor expanded in a around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. +-commutative 61.9%

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

      3. mul-1-neg 61.9%

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

      4. unsub-neg 61.9%

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

   5. Simplified 61.9%

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

   if -6.40000000000000024e122 < z < 3.1e78

   1. Initial program 89.8%

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

   2. Taylor expanded in x around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. unsub-neg 60.6%

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

   4. Simplified 60.6%

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

   5. Taylor expanded in z around 0 48.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+122} \lor \neg \left(z \leq 3.1 \cdot 10^{+78}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 21: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+122}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+122)
   (- t (/ t (/ z y)))
   (if (<= z 1.6e+78) (* x (- 1.0 (/ y a))) (* t (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+122) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.6e+78) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d+122)) then
        tmp = t - (t / (z / y))
    else if (z <= 1.6d+78) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+122) {
		tmp = t - (t / (z / y));
	} else if (z <= 1.6e+78) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+122:
		tmp = t - (t / (z / y))
	elif z <= 1.6e+78:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+122)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	elseif (z <= 1.6e+78)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+122)
		tmp = t - (t / (z / y));
	elseif (z <= 1.6e+78)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+122], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+78], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999998e122

   1. Initial program 59.0%

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

   2. Taylor expanded in t around inf 74.3%

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

   3. Taylor expanded in z around -inf 45.7%

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

      1. +-commutative 45.7%

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

      2. mul-1-neg 45.7%

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

      3. unsub-neg 45.7%

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

      4. associate-/l* 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in y around inf 65.5%

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

   if -5.4999999999999998e122 < z < 1.59999999999999997e78

   1. Initial program 89.8%

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

   2. Taylor expanded in x around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. unsub-neg 60.6%

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

   4. Simplified 60.6%

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

   5. Taylor expanded in z around 0 48.5%

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

   if 1.59999999999999997e78 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in t around inf 72.5%

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

   3. Taylor expanded in a around 0 58.8%

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

      1. *-commutative 58.8%

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

      2. +-commutative 58.8%

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

      3. mul-1-neg 58.8%

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

      4. unsub-neg 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+122}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 22: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+122}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.6e+122)
   (- t (/ y (/ z t)))
   (if (<= z 9e+75) (* x (- 1.0 (/ y a))) (* t (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.6e+122) {
		tmp = t - (y / (z / t));
	} else if (z <= 9e+75) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.6d+122)) then
        tmp = t - (y / (z / t))
    else if (z <= 9d+75) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.6e+122) {
		tmp = t - (y / (z / t));
	} else if (z <= 9e+75) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.6e+122:
		tmp = t - (y / (z / t))
	elif z <= 9e+75:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.6e+122)
		tmp = Float64(t - Float64(y / Float64(z / t)));
	elseif (z <= 9e+75)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.6e+122)
		tmp = t - (y / (z / t));
	elseif (z <= 9e+75)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.6e+122], N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+75], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.6000000000000007e122

   1. Initial program 59.0%

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

   2. Taylor expanded in t around inf 74.3%

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

   3. Taylor expanded in z around -inf 45.7%

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

      1. +-commutative 45.7%

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

      2. mul-1-neg 45.7%

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

      3. unsub-neg 45.7%

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

      4. associate-/l* 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in y around inf 53.3%

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

      1. associate-/l* 65.6%

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

   8. Simplified 65.6%

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

   if -9.6000000000000007e122 < z < 9.0000000000000007e75

   1. Initial program 89.8%

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

   2. Taylor expanded in x around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. unsub-neg 60.6%

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

   4. Simplified 60.6%

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

   5. Taylor expanded in z around 0 48.5%

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

   if 9.0000000000000007e75 < z

   1. Initial program 66.8%

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

   2. Taylor expanded in t around inf 72.5%

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

   3. Taylor expanded in a around 0 58.8%

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

      1. *-commutative 58.8%

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

      2. +-commutative 58.8%

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

      3. mul-1-neg 58.8%

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

      4. unsub-neg 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+122}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 23: 38.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.02e-20) x (if (<= a 2.3e+111) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.02e-20) {
		tmp = x;
	} else if (a <= 2.3e+111) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.02d-20)) then
        tmp = x
    else if (a <= 2.3d+111) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.02e-20) {
		tmp = x;
	} else if (a <= 2.3e+111) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.02e-20:
		tmp = x
	elif a <= 2.3e+111:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.02e-20)
		tmp = x;
	elseif (a <= 2.3e+111)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.02e-20)
		tmp = x;
	elseif (a <= 2.3e+111)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.02e-20], x, If[LessEqual[a, 2.3e+111], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.02000000000000001e-20 or 2.30000000000000002e111 < a

   1. Initial program 86.1%

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

   2. Taylor expanded in a around inf 46.3%

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

   if -1.02000000000000001e-20 < a < 2.30000000000000002e111

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 34.8%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.02 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 24.7% 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 81.0%

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

2. Taylor expanded in z around inf 24.6%

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

3. Final simplification 24.6%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023228 
(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)))))