Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.0% → 91.0%

Time: 14.6s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-204}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-257}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -2e-204)
     (fma (- y z) t_1 x)
     (if (<= t_2 2e-257)
       (- t (* (- t x) (/ (- y a) z)))
       (+ x (/ (- y z) (/ (- a z) (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -2e-204) {
		tmp = fma((y - z), t_1, x);
	} else if (t_2 <= 2e-257) {
		tmp = t - ((t - x) * ((y - a) / z));
	} else {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -2e-204)
		tmp = fma(Float64(y - z), t_1, x);
	elseif (t_2 <= 2e-257)
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-204], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, 2e-257], N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-204

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. fma-define 93.9%

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

   3. Simplified 93.9%

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

   if -2e-204 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-257

   1. Initial program 10.6%

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

   3. Taylor expanded in z around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. distribute-lft-out-- 77.1%

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

      3. div-sub 77.1%

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

      4. mul-1-neg 77.1%

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

      5. unsub-neg 77.1%

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

      6. distribute-rgt-out-- 77.1%

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

      7. associate-/l* 90.8%

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

   5. Simplified 90.8%

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

   if 2e-257 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.2%

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

      1. clear-num 92.0%

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

      2. un-div-inv 92.3%

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

   4. Applied egg-rr 92.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-204}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-257}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-204} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-257}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-204) (not (<= t_1 2e-257)))
     t_1
     (- t (* (- t x) (/ (- y a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-204) || !(t_1 <= 2e-257)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * ((y - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-204)) .or. (.not. (t_1 <= 2d-257))) then
        tmp = t_1
    else
        tmp = t - ((t - x) * ((y - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-204) || !(t_1 <= 2e-257)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-204) or not (t_1 <= 2e-257):
		tmp = t_1
	else:
		tmp = t - ((t - x) * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-204) || !(t_1 <= 2e-257))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-204) || ~((t_1 <= 2e-257)))
		tmp = t_1;
	else
		tmp = t - ((t - x) * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-204], N[Not[LessEqual[t$95$1, 2e-257]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-204 or 2e-257 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.0%

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

   if -2e-204 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-257

   1. Initial program 10.6%

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

   3. Taylor expanded in z around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. distribute-lft-out-- 77.1%

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

      3. div-sub 77.1%

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

      4. mul-1-neg 77.1%

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

      5. unsub-neg 77.1%

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

      6. distribute-rgt-out-- 77.1%

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

      7. associate-/l* 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-204} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-257}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-257}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-204)
     t_1
     (if (<= t_1 2e-257)
       (- t (* (- t x) (/ (- y a) z)))
       (+ x (/ (- y 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 <= -2e-204) {
		tmp = t_1;
	} else if (t_1 <= 2e-257) {
		tmp = t - ((t - x) * ((y - a) / z));
	} else {
		tmp = x + ((y - 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 <= (-2d-204)) then
        tmp = t_1
    else if (t_1 <= 2d-257) then
        tmp = t - ((t - x) * ((y - a) / z))
    else
        tmp = x + ((y - 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 <= -2e-204) {
		tmp = t_1;
	} else if (t_1 <= 2e-257) {
		tmp = t - ((t - x) * ((y - a) / z));
	} else {
		tmp = x + ((y - 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 <= -2e-204:
		tmp = t_1
	elif t_1 <= 2e-257:
		tmp = t - ((t - x) * ((y - a) / z))
	else:
		tmp = x + ((y - 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 <= -2e-204)
		tmp = t_1;
	elseif (t_1 <= 2e-257)
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - 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 <= -2e-204)
		tmp = t_1;
	elseif (t_1 <= 2e-257)
		tmp = t - ((t - x) * ((y - a) / z));
	else
		tmp = x + ((y - 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[LessEqual[t$95$1, -2e-204], t$95$1, If[LessEqual[t$95$1, 2e-257], N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-204

   1. Initial program 93.8%

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

   if -2e-204 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-257

   1. Initial program 10.6%

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

   3. Taylor expanded in z around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. distribute-lft-out-- 77.1%

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

      3. div-sub 77.1%

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

      4. mul-1-neg 77.1%

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

      5. unsub-neg 77.1%

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

      6. distribute-rgt-out-- 77.1%

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

      7. associate-/l* 90.8%

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

   5. Simplified 90.8%

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

   if 2e-257 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.2%

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

      1. clear-num 92.0%

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

      2. un-div-inv 92.3%

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

   4. Applied egg-rr 92.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-204}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-257}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{-z}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+35}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+181}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- z)))))
   (if (<= y -5.2e+181)
     t_1
     (if (<= y -2.6e+84)
       (* x (/ y z))
       (if (<= y 2.5e+35)
         (+ x t)
         (if (<= y 1.7e+154) (* t (/ y a)) (if (<= y 9e+181) (+ x t) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -z);
	double tmp;
	if (y <= -5.2e+181) {
		tmp = t_1;
	} else if (y <= -2.6e+84) {
		tmp = x * (y / z);
	} else if (y <= 2.5e+35) {
		tmp = x + t;
	} else if (y <= 1.7e+154) {
		tmp = t * (y / a);
	} else if (y <= 9e+181) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / -z)
    if (y <= (-5.2d+181)) then
        tmp = t_1
    else if (y <= (-2.6d+84)) then
        tmp = x * (y / z)
    else if (y <= 2.5d+35) then
        tmp = x + t
    else if (y <= 1.7d+154) then
        tmp = t * (y / a)
    else if (y <= 9d+181) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -z);
	double tmp;
	if (y <= -5.2e+181) {
		tmp = t_1;
	} else if (y <= -2.6e+84) {
		tmp = x * (y / z);
	} else if (y <= 2.5e+35) {
		tmp = x + t;
	} else if (y <= 1.7e+154) {
		tmp = t * (y / a);
	} else if (y <= 9e+181) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / -z)
	tmp = 0
	if y <= -5.2e+181:
		tmp = t_1
	elif y <= -2.6e+84:
		tmp = x * (y / z)
	elif y <= 2.5e+35:
		tmp = x + t
	elif y <= 1.7e+154:
		tmp = t * (y / a)
	elif y <= 9e+181:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(-z)))
	tmp = 0.0
	if (y <= -5.2e+181)
		tmp = t_1;
	elseif (y <= -2.6e+84)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 2.5e+35)
		tmp = Float64(x + t);
	elseif (y <= 1.7e+154)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 9e+181)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / -z);
	tmp = 0.0;
	if (y <= -5.2e+181)
		tmp = t_1;
	elseif (y <= -2.6e+84)
		tmp = x * (y / z);
	elseif (y <= 2.5e+35)
		tmp = x + t;
	elseif (y <= 1.7e+154)
		tmp = t * (y / a);
	elseif (y <= 9e+181)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+181], t$95$1, If[LessEqual[y, -2.6e+84], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+35], N[(x + t), $MachinePrecision], If[LessEqual[y, 1.7e+154], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+181], N[(x + t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2e181 or 9e181 < y

   1. Initial program 87.9%

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

   3. Taylor expanded in x around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. associate-/l* 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in a around 0 46.4%

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

      1. associate-*r/ 46.4%

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

      2. *-commutative 46.4%

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

      3. neg-mul-1 46.4%

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

      4. distribute-lft-neg-in 46.4%

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

      5. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   9. Taylor expanded in y around inf 46.2%

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

       1. mul-1-neg 46.2%

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

       2. associate-/l* 55.5%

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

       3. distribute-rgt-neg-in 55.5%

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

   11. Simplified 55.5%

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

   if -5.2e181 < y < -2.6000000000000001e84

   1. Initial program 83.9%

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

   3. Taylor expanded in y around -inf 62.8%

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

   4. Taylor expanded in t around 0 46.7%

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

      1. associate-*r/ 46.7%

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

      2. mul-1-neg 46.7%

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

      3. distribute-lft-neg-out 46.7%

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

      4. *-commutative 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in a around 0 40.4%

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

      1. associate-/l* 48.4%

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

   9. Simplified 48.4%

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

   if -2.6000000000000001e84 < y < 2.50000000000000011e35 or 1.69999999999999987e154 < y < 9e181

   1. Initial program 75.1%

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

      1. clear-num 74.8%

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

      2. un-div-inv 75.1%

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

   4. Applied egg-rr 75.1%

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

   5. Taylor expanded in t around inf 67.5%

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

   6. Taylor expanded in z around inf 51.9%

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

   if 2.50000000000000011e35 < y < 1.69999999999999987e154

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0 54.4%

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

      1. *-commutative 54.4%

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

      2. associate-/l* 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in z around 0 38.9%

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

      1. associate-/l* 44.2%

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

   8. Simplified 44.2%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+181}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+35}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+181}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \left(t - x\right) \cdot \frac{y - a}{z}\\ t_2 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (- t x) (/ (- y a) z))))
        (t_2 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -7.2e+131)
     t_2
     (if (<= a -9.2e+53)
       t_1
       (if (<= a -1.95e-17)
         (+ x (* (- y z) (/ (- t x) a)))
         (if (<= a 1.48e-61) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) * ((y - a) / z));
	double t_2 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -7.2e+131) {
		tmp = t_2;
	} else if (a <= -9.2e+53) {
		tmp = t_1;
	} else if (a <= -1.95e-17) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 1.48e-61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - ((t - x) * ((y - a) / z))
    t_2 = x + ((y - z) / ((a - z) / t))
    if (a <= (-7.2d+131)) then
        tmp = t_2
    else if (a <= (-9.2d+53)) then
        tmp = t_1
    else if (a <= (-1.95d-17)) then
        tmp = x + ((y - z) * ((t - x) / a))
    else if (a <= 1.48d-61) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((t - x) * ((y - a) / z));
	double t_2 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -7.2e+131) {
		tmp = t_2;
	} else if (a <= -9.2e+53) {
		tmp = t_1;
	} else if (a <= -1.95e-17) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else if (a <= 1.48e-61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((t - x) * ((y - a) / z))
	t_2 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if a <= -7.2e+131:
		tmp = t_2
	elif a <= -9.2e+53:
		tmp = t_1
	elif a <= -1.95e-17:
		tmp = x + ((y - z) * ((t - x) / a))
	elif a <= 1.48e-61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)))
	t_2 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -7.2e+131)
		tmp = t_2;
	elseif (a <= -9.2e+53)
		tmp = t_1;
	elseif (a <= -1.95e-17)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	elseif (a <= 1.48e-61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((t - x) * ((y - a) / z));
	t_2 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (a <= -7.2e+131)
		tmp = t_2;
	elseif (a <= -9.2e+53)
		tmp = t_1;
	elseif (a <= -1.95e-17)
		tmp = x + ((y - z) * ((t - x) / a));
	elseif (a <= 1.48e-61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e+131], t$95$2, If[LessEqual[a, -9.2e+53], t$95$1, If[LessEqual[a, -1.95e-17], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.48e-61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.20000000000000063e131 or 1.4799999999999999e-61 < a

   1. Initial program 87.6%

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

      1. clear-num 86.7%

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

      2. un-div-inv 86.8%

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

   4. Applied egg-rr 86.8%

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

   5. Taylor expanded in t around inf 80.4%

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

   if -7.20000000000000063e131 < a < -9.20000000000000079e53 or -1.94999999999999995e-17 < a < 1.4799999999999999e-61

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 80.9%

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

      1. associate--l+ 80.9%

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

      2. distribute-lft-out-- 80.9%

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

      3. div-sub 81.6%

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

      4. mul-1-neg 81.6%

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

      5. unsub-neg 81.6%

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

      6. distribute-rgt-out-- 81.6%

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

      7. associate-/l* 87.8%

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

   5. Simplified 87.8%

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

   if -9.20000000000000079e53 < a < -1.94999999999999995e-17

   1. Initial program 93.6%

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

   3. Taylor expanded in a around inf 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-/l* 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+131}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+53}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-17}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-61}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+35}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+180}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))) (t_2 (* t (/ y a))))
   (if (<= y -6.8e+181)
     t_2
     (if (<= y -3.2e+85)
       t_1
       (if (<= y 2.5e+35)
         (+ x t)
         (if (<= y 3.8e+153) t_2 (if (<= y 1.6e+180) (+ x t) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double t_2 = t * (y / a);
	double tmp;
	if (y <= -6.8e+181) {
		tmp = t_2;
	} else if (y <= -3.2e+85) {
		tmp = t_1;
	} else if (y <= 2.5e+35) {
		tmp = x + t;
	} else if (y <= 3.8e+153) {
		tmp = t_2;
	} else if (y <= 1.6e+180) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / z)
    t_2 = t * (y / a)
    if (y <= (-6.8d+181)) then
        tmp = t_2
    else if (y <= (-3.2d+85)) then
        tmp = t_1
    else if (y <= 2.5d+35) then
        tmp = x + t
    else if (y <= 3.8d+153) then
        tmp = t_2
    else if (y <= 1.6d+180) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double t_2 = t * (y / a);
	double tmp;
	if (y <= -6.8e+181) {
		tmp = t_2;
	} else if (y <= -3.2e+85) {
		tmp = t_1;
	} else if (y <= 2.5e+35) {
		tmp = x + t;
	} else if (y <= 3.8e+153) {
		tmp = t_2;
	} else if (y <= 1.6e+180) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	t_2 = t * (y / a)
	tmp = 0
	if y <= -6.8e+181:
		tmp = t_2
	elif y <= -3.2e+85:
		tmp = t_1
	elif y <= 2.5e+35:
		tmp = x + t
	elif y <= 3.8e+153:
		tmp = t_2
	elif y <= 1.6e+180:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	t_2 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -6.8e+181)
		tmp = t_2;
	elseif (y <= -3.2e+85)
		tmp = t_1;
	elseif (y <= 2.5e+35)
		tmp = Float64(x + t);
	elseif (y <= 3.8e+153)
		tmp = t_2;
	elseif (y <= 1.6e+180)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	t_2 = t * (y / a);
	tmp = 0.0;
	if (y <= -6.8e+181)
		tmp = t_2;
	elseif (y <= -3.2e+85)
		tmp = t_1;
	elseif (y <= 2.5e+35)
		tmp = x + t;
	elseif (y <= 3.8e+153)
		tmp = t_2;
	elseif (y <= 1.6e+180)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+181], t$95$2, If[LessEqual[y, -3.2e+85], t$95$1, If[LessEqual[y, 2.5e+35], N[(x + t), $MachinePrecision], If[LessEqual[y, 3.8e+153], t$95$2, If[LessEqual[y, 1.6e+180], N[(x + t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.80000000000000062e181 or 2.50000000000000011e35 < y < 3.79999999999999966e153

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-/l* 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in z around 0 40.7%

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

      1. associate-/l* 49.4%

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

   8. Simplified 49.4%

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

   if -6.80000000000000062e181 < y < -3.20000000000000018e85 or 1.59999999999999997e180 < y

   1. Initial program 81.7%

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

   3. Taylor expanded in y around -inf 67.3%

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

   4. Taylor expanded in t around 0 34.9%

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

      1. associate-*r/ 34.9%

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

      2. mul-1-neg 34.9%

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

      3. distribute-lft-neg-out 34.9%

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

      4. *-commutative 34.9%

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

   6. Simplified 34.9%

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

   7. Taylor expanded in a around 0 34.1%

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

      1. associate-/l* 45.8%

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

   9. Simplified 45.8%

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

   if -3.20000000000000018e85 < y < 2.50000000000000011e35 or 3.79999999999999966e153 < y < 1.59999999999999997e180

   1. Initial program 75.1%

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

      1. clear-num 74.8%

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

      2. un-div-inv 75.1%

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

   4. Applied egg-rr 75.1%

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

   5. Taylor expanded in t around inf 67.5%

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

   6. Taylor expanded in z around inf 51.9%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+181}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+35}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+180}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-71}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -5.8e+82)
     t_1
     (if (<= y -1.35e+57)
       (+ x t)
       (if (<= y -2.8e-17)
         (+ x (* t (/ y a)))
         (if (<= y 6.2e-71) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -5.8e+82) {
		tmp = t_1;
	} else if (y <= -1.35e+57) {
		tmp = x + t;
	} else if (y <= -2.8e-17) {
		tmp = x + (t * (y / a));
	} else if (y <= 6.2e-71) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    if (y <= (-5.8d+82)) then
        tmp = t_1
    else if (y <= (-1.35d+57)) then
        tmp = x + t
    else if (y <= (-2.8d-17)) then
        tmp = x + (t * (y / a))
    else if (y <= 6.2d-71) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -5.8e+82) {
		tmp = t_1;
	} else if (y <= -1.35e+57) {
		tmp = x + t;
	} else if (y <= -2.8e-17) {
		tmp = x + (t * (y / a));
	} else if (y <= 6.2e-71) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -5.8e+82:
		tmp = t_1
	elif y <= -1.35e+57:
		tmp = x + t
	elif y <= -2.8e-17:
		tmp = x + (t * (y / a))
	elif y <= 6.2e-71:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -5.8e+82)
		tmp = t_1;
	elseif (y <= -1.35e+57)
		tmp = Float64(x + t);
	elseif (y <= -2.8e-17)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (y <= 6.2e-71)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -5.8e+82)
		tmp = t_1;
	elseif (y <= -1.35e+57)
		tmp = x + t;
	elseif (y <= -2.8e-17)
		tmp = x + (t * (y / a));
	elseif (y <= 6.2e-71)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+82], t$95$1, If[LessEqual[y, -1.35e+57], N[(x + t), $MachinePrecision], If[LessEqual[y, -2.8e-17], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-71], N[(x + t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000003e82 or 6.20000000000000004e-71 < y

   1. Initial program 83.5%

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

   3. Taylor expanded in y around inf 74.1%

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

      1. div-sub 74.1%

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

   5. Simplified 74.1%

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

   if -5.8000000000000003e82 < y < -1.3499999999999999e57 or -2.7999999999999999e-17 < y < 6.20000000000000004e-71

   1. Initial program 75.7%

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

      1. clear-num 75.5%

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

      2. un-div-inv 75.9%

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

   4. Applied egg-rr 75.9%

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

   5. Taylor expanded in t around inf 72.0%

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

   6. Taylor expanded in z around inf 60.3%

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

   if -1.3499999999999999e57 < y < -2.7999999999999999e-17

   1. Initial program 75.6%

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

      1. clear-num 75.4%

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

      2. un-div-inv 75.9%

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

   4. Applied egg-rr 75.9%

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

   5. Taylor expanded in t around inf 67.8%

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

   6. Taylor expanded in z around 0 60.8%

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

      1. +-commutative 60.8%

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

      2. associate-/l* 60.8%

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

   8. Simplified 60.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-71}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -350000000 \lor \neg \left(z \leq 3.8 \cdot 10^{-87}\right) \land \left(z \leq 225000000 \lor \neg \left(z \leq 6 \cdot 10^{+45}\right)\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -350000000.0)
         (and (not (<= z 3.8e-87)) (or (<= z 225000000.0) (not (<= z 6e+45)))))
   (* t (- 1.0 (/ y z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -350000000.0) || (!(z <= 3.8e-87) && ((z <= 225000000.0) || !(z <= 6e+45)))) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (t * (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 <= (-350000000.0d0)) .or. (.not. (z <= 3.8d-87)) .and. (z <= 225000000.0d0) .or. (.not. (z <= 6d+45))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (t * (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 <= -350000000.0) || (!(z <= 3.8e-87) && ((z <= 225000000.0) || !(z <= 6e+45)))) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -350000000.0) or (not (z <= 3.8e-87) and ((z <= 225000000.0) or not (z <= 6e+45))):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -350000000.0) || (!(z <= 3.8e-87) && ((z <= 225000000.0) || !(z <= 6e+45))))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -350000000.0) || (~((z <= 3.8e-87)) && ((z <= 225000000.0) || ~((z <= 6e+45)))))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -350000000.0], And[N[Not[LessEqual[z, 3.8e-87]], $MachinePrecision], Or[LessEqual[z, 225000000.0], N[Not[LessEqual[z, 6e+45]], $MachinePrecision]]]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e8 or 3.8e-87 < z < 2.25e8 or 6.00000000000000021e45 < z

   1. Initial program 67.0%

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

   3. Taylor expanded in t around inf 61.8%

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

   4. Taylor expanded in a around 0 57.6%

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

      1. mul-1-neg 57.6%

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

      2. unsub-neg 57.6%

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

   6. Simplified 57.6%

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

   if -3.5e8 < z < 3.8e-87 or 2.25e8 < z < 6.00000000000000021e45

   1. Initial program 94.9%

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

      1. clear-num 94.1%

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

      2. un-div-inv 94.4%

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

   4. Applied egg-rr 94.4%

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

   5. Taylor expanded in t around inf 74.7%

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

   6. Taylor expanded in z around 0 63.1%

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

      1. +-commutative 63.1%

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

      2. associate-/l* 69.0%

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

   8. Simplified 69.0%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000000 \lor \neg \left(z \leq 3.8 \cdot 10^{-87}\right) \land \left(z \leq 225000000 \lor \neg \left(z \leq 6 \cdot 10^{+45}\right)\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -0.03:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -1.7e+131)
     x
     (if (<= a -4.6e+91)
       t_1
       (if (<= a -0.03) x (if (<= a 3.2e+101) t_1 (+ x t)))))))

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 <= -1.7e+131) {
		tmp = x;
	} else if (a <= -4.6e+91) {
		tmp = t_1;
	} else if (a <= -0.03) {
		tmp = x;
	} else if (a <= 3.2e+101) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-1.7d+131)) then
        tmp = x
    else if (a <= (-4.6d+91)) then
        tmp = t_1
    else if (a <= (-0.03d0)) then
        tmp = x
    else if (a <= 3.2d+101) then
        tmp = t_1
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -1.7e+131) {
		tmp = x;
	} else if (a <= -4.6e+91) {
		tmp = t_1;
	} else if (a <= -0.03) {
		tmp = x;
	} else if (a <= 3.2e+101) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -1.7e+131:
		tmp = x
	elif a <= -4.6e+91:
		tmp = t_1
	elif a <= -0.03:
		tmp = x
	elif a <= 3.2e+101:
		tmp = t_1
	else:
		tmp = x + t
	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 <= -1.7e+131)
		tmp = x;
	elseif (a <= -4.6e+91)
		tmp = t_1;
	elseif (a <= -0.03)
		tmp = x;
	elseif (a <= 3.2e+101)
		tmp = t_1;
	else
		tmp = Float64(x + t);
	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 <= -1.7e+131)
		tmp = x;
	elseif (a <= -4.6e+91)
		tmp = t_1;
	elseif (a <= -0.03)
		tmp = x;
	elseif (a <= 3.2e+101)
		tmp = t_1;
	else
		tmp = x + t;
	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, -1.7e+131], x, If[LessEqual[a, -4.6e+91], t$95$1, If[LessEqual[a, -0.03], x, If[LessEqual[a, 3.2e+101], t$95$1, N[(x + t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.69999999999999993e131 or -4.59999999999999982e91 < a < -0.029999999999999999

   1. Initial program 90.7%

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

   3. Taylor expanded in a around inf 55.9%

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

   if -1.69999999999999993e131 < a < -4.59999999999999982e91 or -0.029999999999999999 < a < 3.20000000000000005e101

   1. Initial program 74.7%

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

   3. Taylor expanded in t around inf 64.7%

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

   4. Taylor expanded in a around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. unsub-neg 56.2%

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

   6. Simplified 56.2%

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

   if 3.20000000000000005e101 < a

   1. Initial program 86.3%

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

      1. clear-num 83.6%

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

      2. un-div-inv 83.8%

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

   4. Applied egg-rr 83.8%

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

   5. Taylor expanded in t around inf 84.1%

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

   6. Taylor expanded in z around inf 56.7%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -0.03:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+101}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+101}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e+131)
   x
   (if (<= a -1.3e+40)
     (* x (/ (- y a) z))
     (if (<= a -7.2e-15)
       (* y (/ (- t x) a))
       (if (<= a 2.15e+101) (* t (- 1.0 (/ y z))) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e+131) {
		tmp = x;
	} else if (a <= -1.3e+40) {
		tmp = x * ((y - a) / z);
	} else if (a <= -7.2e-15) {
		tmp = y * ((t - x) / a);
	} else if (a <= 2.15e+101) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8d+131)) then
        tmp = x
    else if (a <= (-1.3d+40)) then
        tmp = x * ((y - a) / z)
    else if (a <= (-7.2d-15)) then
        tmp = y * ((t - x) / a)
    else if (a <= 2.15d+101) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e+131) {
		tmp = x;
	} else if (a <= -1.3e+40) {
		tmp = x * ((y - a) / z);
	} else if (a <= -7.2e-15) {
		tmp = y * ((t - x) / a);
	} else if (a <= 2.15e+101) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e+131:
		tmp = x
	elif a <= -1.3e+40:
		tmp = x * ((y - a) / z)
	elif a <= -7.2e-15:
		tmp = y * ((t - x) / a)
	elif a <= 2.15e+101:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e+131)
		tmp = x;
	elseif (a <= -1.3e+40)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= -7.2e-15)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (a <= 2.15e+101)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8e+131)
		tmp = x;
	elseif (a <= -1.3e+40)
		tmp = x * ((y - a) / z);
	elseif (a <= -7.2e-15)
		tmp = y * ((t - x) / a);
	elseif (a <= 2.15e+101)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e+131], x, If[LessEqual[a, -1.3e+40], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.2e-15], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e+101], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.9999999999999993e131

   1. Initial program 94.5%

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

   3. Taylor expanded in a around inf 61.9%

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

   if -7.9999999999999993e131 < a < -1.3e40

   1. Initial program 59.0%

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

   3. Taylor expanded in z around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. distribute-lft-out-- 55.0%

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

      3. div-sub 55.0%

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

      4. mul-1-neg 55.0%

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

      5. unsub-neg 55.0%

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

      6. distribute-rgt-out-- 55.0%

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

      7. associate-/l* 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in t around 0 35.5%

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

      1. associate-*r/ 47.4%

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

   8. Simplified 47.4%

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

   if -1.3e40 < a < -7.2000000000000002e-15

   1. Initial program 92.7%

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

   3. Taylor expanded in y around -inf 56.2%

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

      1. associate-/l* 62.5%

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

      2. clear-num 62.4%

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

      3. div-inv 62.6%

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

      4. add-cube-cbrt 62.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{a - z}{t - x}} \]

      5. *-un-lft-identity 62.0%

         \[\leadsto \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{a - z}{t - x}}} \]

      6. times-frac 62.1%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}}} \]

      7. pow2 62.1%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}} \]

   5. Applied egg-rr 62.1%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}}} \]
   6. Step-by-step derivation

      1. /-rgt-identity 62.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}} \]

      2. associate-*r/ 62.0%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{\frac{a - z}{t - x}}} \]

      3. unpow2 62.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{\frac{a - z}{t - x}} \]

      4. rem-3cbrt-lft 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in a around inf 49.4%

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

      1. associate-/l* 49.3%

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

   10. Simplified 49.3%

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

   if -7.2000000000000002e-15 < a < 2.15e101

   1. Initial program 75.2%

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

   3. Taylor expanded in t around inf 65.1%

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

   4. Taylor expanded in a around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

   6. Simplified 56.4%

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

   if 2.15e101 < a

   1. Initial program 86.3%

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

      1. clear-num 83.6%

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

      2. un-div-inv 83.8%

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

   4. Applied egg-rr 83.8%

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

   5. Taylor expanded in t around inf 84.1%

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

   6. Taylor expanded in z around inf 56.7%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+101}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -120000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6500000000:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= z -120000000.0)
     t_2
     (if (<= z 3.8e-87)
       t_1
       (if (<= z 6500000000.0)
         (/ (* t (- z y)) z)
         (if (<= z 1.05e+46) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -120000000.0) {
		tmp = t_2;
	} else if (z <= 3.8e-87) {
		tmp = t_1;
	} else if (z <= 6500000000.0) {
		tmp = (t * (z - y)) / z;
	} else if (z <= 1.05e+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 + (t * (y / a))
    t_2 = t * (1.0d0 - (y / z))
    if (z <= (-120000000.0d0)) then
        tmp = t_2
    else if (z <= 3.8d-87) then
        tmp = t_1
    else if (z <= 6500000000.0d0) then
        tmp = (t * (z - y)) / z
    else if (z <= 1.05d+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 + (t * (y / a));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -120000000.0) {
		tmp = t_2;
	} else if (z <= 3.8e-87) {
		tmp = t_1;
	} else if (z <= 6500000000.0) {
		tmp = (t * (z - y)) / z;
	} else if (z <= 1.05e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -120000000.0:
		tmp = t_2
	elif z <= 3.8e-87:
		tmp = t_1
	elif z <= 6500000000.0:
		tmp = (t * (z - y)) / z
	elif z <= 1.05e+46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -120000000.0)
		tmp = t_2;
	elseif (z <= 3.8e-87)
		tmp = t_1;
	elseif (z <= 6500000000.0)
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	elseif (z <= 1.05e+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 + (t * (y / a));
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -120000000.0)
		tmp = t_2;
	elseif (z <= 3.8e-87)
		tmp = t_1;
	elseif (z <= 6500000000.0)
		tmp = (t * (z - y)) / z;
	elseif (z <= 1.05e+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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -120000000.0], t$95$2, If[LessEqual[z, 3.8e-87], t$95$1, If[LessEqual[z, 6500000000.0], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.05e+46], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e8 or 1.05e46 < z

   1. Initial program 64.5%

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

   3. Taylor expanded in t around inf 63.1%

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

   4. Taylor expanded in a around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   6. Simplified 58.2%

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

   if -1.2e8 < z < 3.8e-87 or 6.5e9 < z < 1.05e46

   1. Initial program 94.9%

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

      1. clear-num 94.1%

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

      2. un-div-inv 94.4%

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

   4. Applied egg-rr 94.4%

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

   5. Taylor expanded in t around inf 74.7%

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

   6. Taylor expanded in z around 0 63.1%

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

      1. +-commutative 63.1%

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

      2. associate-/l* 69.0%

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

   8. Simplified 69.0%

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

   if 3.8e-87 < z < 6.5e9

   1. Initial program 81.5%

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

   3. Taylor expanded in x around 0 54.1%

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

      1. *-commutative 54.1%

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

      2. associate-/l* 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in a around 0 54.1%

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

      1. associate-*r/ 54.1%

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

      2. *-commutative 54.1%

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

      3. neg-mul-1 54.1%

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

      4. distribute-lft-neg-in 54.1%

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

      5. *-commutative 54.1%

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

   8. Simplified 54.1%

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

   9. Taylor expanded in t around 0 54.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -120000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-87}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6500000000:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -650000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 115000000000:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= z -650000000.0)
     t_2
     (if (<= z 3.3e-87)
       t_1
       (if (<= z 115000000000.0)
         (/ y (/ z (- x t)))
         (if (<= z 4.4e+45) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -650000000.0) {
		tmp = t_2;
	} else if (z <= 3.3e-87) {
		tmp = t_1;
	} else if (z <= 115000000000.0) {
		tmp = y / (z / (x - t));
	} else if (z <= 4.4e+45) {
		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 + (t * (y / a))
    t_2 = t * (1.0d0 - (y / z))
    if (z <= (-650000000.0d0)) then
        tmp = t_2
    else if (z <= 3.3d-87) then
        tmp = t_1
    else if (z <= 115000000000.0d0) then
        tmp = y / (z / (x - t))
    else if (z <= 4.4d+45) 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 + (t * (y / a));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -650000000.0) {
		tmp = t_2;
	} else if (z <= 3.3e-87) {
		tmp = t_1;
	} else if (z <= 115000000000.0) {
		tmp = y / (z / (x - t));
	} else if (z <= 4.4e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -650000000.0:
		tmp = t_2
	elif z <= 3.3e-87:
		tmp = t_1
	elif z <= 115000000000.0:
		tmp = y / (z / (x - t))
	elif z <= 4.4e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -650000000.0)
		tmp = t_2;
	elseif (z <= 3.3e-87)
		tmp = t_1;
	elseif (z <= 115000000000.0)
		tmp = Float64(y / Float64(z / Float64(x - t)));
	elseif (z <= 4.4e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -650000000.0)
		tmp = t_2;
	elseif (z <= 3.3e-87)
		tmp = t_1;
	elseif (z <= 115000000000.0)
		tmp = y / (z / (x - t));
	elseif (z <= 4.4e+45)
		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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -650000000.0], t$95$2, If[LessEqual[z, 3.3e-87], t$95$1, If[LessEqual[z, 115000000000.0], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e8 or 4.4000000000000001e45 < z

   1. Initial program 64.5%

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

   3. Taylor expanded in t around inf 63.1%

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

   4. Taylor expanded in a around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   6. Simplified 58.2%

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

   if -6.5e8 < z < 3.3e-87 or 1.15e11 < z < 4.4000000000000001e45

   1. Initial program 94.9%

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

      1. clear-num 94.1%

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

      2. un-div-inv 94.4%

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

   4. Applied egg-rr 94.4%

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

   5. Taylor expanded in t around inf 74.7%

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

   6. Taylor expanded in z around 0 63.1%

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

      1. +-commutative 63.1%

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

      2. associate-/l* 69.0%

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

   8. Simplified 69.0%

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

   if 3.3e-87 < z < 1.15e11

   1. Initial program 81.5%

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

   3. Taylor expanded in y around -inf 68.3%

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

      1. associate-/l* 72.4%

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

      2. clear-num 72.4%

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

      3. div-inv 72.5%

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

      4. add-cube-cbrt 71.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{a - z}{t - x}} \]

      5. *-un-lft-identity 71.6%

         \[\leadsto \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{a - z}{t - x}}} \]

      6. times-frac 71.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}}} \]

      7. pow2 71.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}} \]

   5. Applied egg-rr 71.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}}} \]
   6. Step-by-step derivation

      1. /-rgt-identity 71.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{\frac{a - z}{t - x}} \]

      2. associate-*r/ 71.6%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{\frac{a - z}{t - x}}} \]

      3. unpow2 71.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{\frac{a - z}{t - x}} \]

      4. rem-3cbrt-lft 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in a around 0 63.6%

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

      1. neg-mul-1 63.6%

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

      2. distribute-neg-frac 63.6%

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

   10. Simplified 63.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -650000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-87}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 115000000000:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-71}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -1.65e+82)
     t_1
     (if (<= y -7.8e-91)
       (* (- y z) (/ t (- a z)))
       (if (<= y 6.4e-71) (+ x t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -1.65e+82) {
		tmp = t_1;
	} else if (y <= -7.8e-91) {
		tmp = (y - z) * (t / (a - z));
	} else if (y <= 6.4e-71) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    if (y <= (-1.65d+82)) then
        tmp = t_1
    else if (y <= (-7.8d-91)) then
        tmp = (y - z) * (t / (a - z))
    else if (y <= 6.4d-71) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -1.65e+82) {
		tmp = t_1;
	} else if (y <= -7.8e-91) {
		tmp = (y - z) * (t / (a - z));
	} else if (y <= 6.4e-71) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -1.65e+82:
		tmp = t_1
	elif y <= -7.8e-91:
		tmp = (y - z) * (t / (a - z))
	elif y <= 6.4e-71:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.65e+82)
		tmp = t_1;
	elseif (y <= -7.8e-91)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (y <= 6.4e-71)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -1.65e+82)
		tmp = t_1;
	elseif (y <= -7.8e-91)
		tmp = (y - z) * (t / (a - z));
	elseif (y <= 6.4e-71)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+82], t$95$1, If[LessEqual[y, -7.8e-91], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-71], N[(x + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999e82 or 6.3999999999999998e-71 < y

   1. Initial program 83.5%

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

   3. Taylor expanded in y around inf 74.1%

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

      1. div-sub 74.1%

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

   5. Simplified 74.1%

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

   if -1.6499999999999999e82 < y < -7.79999999999999987e-91

   1. Initial program 78.7%

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

   3. Taylor expanded in x around 0 37.6%

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

      1. *-commutative 37.6%

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

      2. associate-/l* 54.4%

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

   5. Simplified 54.4%

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

   if -7.79999999999999987e-91 < y < 6.3999999999999998e-71

   1. Initial program 74.6%

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

      1. clear-num 74.4%

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

      2. un-div-inv 74.5%

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

   4. Applied egg-rr 74.5%

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

   5. Taylor expanded in t around inf 72.1%

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

   6. Taylor expanded in z around inf 60.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-91}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-71}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-17} \lor \neg \left(a \leq 2.15 \cdot 10^{+84}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.6e-17) (not (<= a 2.15e+84)))
   (+ x (* (- y z) (/ (- t x) a)))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e-17) || !(a <= 2.15e+84)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.6d-17)) .or. (.not. (a <= 2.15d+84))) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.6e-17) || !(a <= 2.15e+84)) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.6e-17) or not (a <= 2.15e+84):
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.6e-17) || !(a <= 2.15e+84))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.6e-17) || ~((a <= 2.15e+84)))
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.6e-17], N[Not[LessEqual[a, 2.15e+84]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.60000000000000003e-17 or 2.1499999999999998e84 < a

   1. Initial program 86.6%

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

   3. Taylor expanded in a around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   if -2.60000000000000003e-17 < a < 2.1499999999999998e84

   1. Initial program 74.5%

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

   3. Taylor expanded in z around inf 77.6%

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

      1. associate--l+ 77.6%

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

      2. distribute-lft-out-- 77.6%

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

      3. div-sub 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. distribute-rgt-out-- 78.3%

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

      7. associate-/l* 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in y around inf 75.8%

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

      1. associate-/l* 78.6%

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

   8. Simplified 78.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-17} \lor \neg \left(a \leq 2.15 \cdot 10^{+84}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-40} \lor \neg \left(a \leq 3.7 \cdot 10^{-62}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e-40) (not (<= a 3.7e-62)))
   (+ x (/ (- y z) (/ (- a z) t)))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-40) || !(a <= 3.7e-62)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.8d-40)) .or. (.not. (a <= 3.7d-62))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-40) || !(a <= 3.7e-62)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e-40) or not (a <= 3.7e-62):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e-40) || !(a <= 3.7e-62))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e-40) || ~((a <= 3.7e-62)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e-40], N[Not[LessEqual[a, 3.7e-62]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8e-40 or 3.6999999999999998e-62 < a

   1. Initial program 84.8%

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

      1. clear-num 84.0%

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

      2. un-div-inv 84.0%

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

   4. Applied egg-rr 84.0%

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

   5. Taylor expanded in t around inf 75.2%

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

   if -2.8e-40 < a < 3.6999999999999998e-62

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 85.1%

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

      1. associate--l+ 85.1%

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

      2. distribute-lft-out-- 85.1%

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

      3. div-sub 86.0%

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

      4. mul-1-neg 86.0%

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

      5. unsub-neg 86.0%

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

      6. distribute-rgt-out-- 86.0%

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

      7. associate-/l* 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around inf 83.6%

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

      1. associate-/l* 84.8%

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

   8. Simplified 84.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-40} \lor \neg \left(a \leq 3.7 \cdot 10^{-62}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-17} \lor \neg \left(a \leq 2.2 \cdot 10^{+86}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.1e-17) (not (<= a 2.2e+86)))
   (+ x (* (- t x) (/ y a)))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.1e-17) || !(a <= 2.2e+86)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.1d-17)) .or. (.not. (a <= 2.2d+86))) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t + (y * ((x - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.1e-17) || !(a <= 2.2e+86)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.1e-17) or not (a <= 2.2e+86):
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.1e-17) || !(a <= 2.2e+86))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.1e-17) || ~((a <= 2.2e+86)))
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.1e-17], N[Not[LessEqual[a, 2.2e+86]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.09999999999999992e-17 or 2.20000000000000003e86 < a

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. associate-/l* 67.3%

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

   5. Simplified 67.3%

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

   if -2.09999999999999992e-17 < a < 2.20000000000000003e86

   1. Initial program 74.5%

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

   3. Taylor expanded in z around inf 77.6%

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

      1. associate--l+ 77.6%

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

      2. distribute-lft-out-- 77.6%

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

      3. div-sub 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. distribute-rgt-out-- 78.3%

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

      7. associate-/l* 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in y around inf 75.8%

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

      1. associate-/l* 78.6%

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

   8. Simplified 78.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-17} \lor \neg \left(a \leq 2.2 \cdot 10^{+86}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-80} \lor \neg \left(a \leq 2.6 \cdot 10^{-63}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e+172)
   x
   (if (or (<= a -7.6e-80) (not (<= a 2.6e-63))) (+ x t) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e+172) {
		tmp = x;
	} else if ((a <= -7.6e-80) || !(a <= 2.6e-63)) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.4d+172)) then
        tmp = x
    else if ((a <= (-7.6d-80)) .or. (.not. (a <= 2.6d-63))) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e+172) {
		tmp = x;
	} else if ((a <= -7.6e-80) || !(a <= 2.6e-63)) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e+172:
		tmp = x
	elif (a <= -7.6e-80) or not (a <= 2.6e-63):
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e+172)
		tmp = x;
	elseif ((a <= -7.6e-80) || !(a <= 2.6e-63))
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.4e+172)
		tmp = x;
	elseif ((a <= -7.6e-80) || ~((a <= 2.6e-63)))
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e+172], x, If[Or[LessEqual[a, -7.6e-80], N[Not[LessEqual[a, 2.6e-63]], $MachinePrecision]], N[(x + t), $MachinePrecision], t]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4000000000000001e172

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf 67.8%

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

   if -2.4000000000000001e172 < a < -7.59999999999999933e-80 or 2.6000000000000001e-63 < a

   1. Initial program 82.2%

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

      1. clear-num 81.2%

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

      2. un-div-inv 81.2%

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

   4. Applied egg-rr 81.2%

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

   5. Taylor expanded in t around inf 69.0%

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

   6. Taylor expanded in z around inf 43.0%

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

   if -7.59999999999999933e-80 < a < 2.6000000000000001e-63

   1. Initial program 72.8%

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

   3. Taylor expanded in z around inf 42.1%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-80} \lor \neg \left(a \leq 2.6 \cdot 10^{-63}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+100} \lor \neg \left(y \leq 2.3 \cdot 10^{+35}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.02e+100) (not (<= y 2.3e+35))) (* t (/ y a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.02e+100) || !(y <= 2.3e+35)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.02d+100)) .or. (.not. (y <= 2.3d+35))) then
        tmp = t * (y / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.02e+100) || !(y <= 2.3e+35)) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.02e+100) or not (y <= 2.3e+35):
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.02e+100) || !(y <= 2.3e+35))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.02e+100) || ~((y <= 2.3e+35)))
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.02e+100], N[Not[LessEqual[y, 2.3e+35]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0199999999999999e100 or 2.2999999999999998e35 < y

   1. Initial program 86.8%

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

   3. Taylor expanded in x around 0 48.9%

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

      1. *-commutative 48.9%

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

      2. associate-/l* 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in z around 0 29.0%

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

      1. associate-/l* 35.9%

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

   8. Simplified 35.9%

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

   if -1.0199999999999999e100 < y < 2.2999999999999998e35

   1. Initial program 75.0%

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

      1. clear-num 74.6%

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

      2. un-div-inv 75.0%

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

   4. Applied egg-rr 75.0%

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

   5. Taylor expanded in t around inf 66.7%

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

   6. Taylor expanded in z around inf 51.8%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+100} \lor \neg \left(y \leq 2.3 \cdot 10^{+35}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e-32) x (if (<= a 2.4e+86) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e-32) {
		tmp = x;
	} else if (a <= 2.4e+86) {
		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 <= (-3.6d-32)) then
        tmp = x
    else if (a <= 2.4d+86) 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 <= -3.6e-32) {
		tmp = x;
	} else if (a <= 2.4e+86) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e-32:
		tmp = x
	elif a <= 2.4e+86:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e-32)
		tmp = x;
	elseif (a <= 2.4e+86)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e-32)
		tmp = x;
	elseif (a <= 2.4e+86)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e-32], x, If[LessEqual[a, 2.4e+86], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.59999999999999993e-32 or 2.4e86 < a

   1. Initial program 86.0%

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

   3. Taylor expanded in a around inf 45.3%

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

   if -3.59999999999999993e-32 < a < 2.4e86

   1. Initial program 74.7%

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

   3. Taylor expanded in z around inf 38.7%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.5%

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

3. Taylor expanded in z around inf 28.7%

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

4. Final simplification 28.7%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(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)))))