Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.0% → 91.1%

Time: 14.3s

Alternatives: 17

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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: 91.1% accurate, 0.1× speedup

Math

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

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) z) (- a y)))
       (+ 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) / z) * (a - y));
	} 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(Float64(t - x) / z) * Float64(a - y)));
	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[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $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. div-sub 77.1%

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

      7. associate-/l* 78.4%

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

      8. associate-/l* 85.4%

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

      9. distribute-rgt-out-- 85.4%

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

   5. Simplified 85.4%

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

   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 91.8%

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

Alternative 2: 91.1% accurate, 0.3× speedup

Math

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

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) z) (- a y))))))

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) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: 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) / z) * (a - y))
    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) / z) * (a - y));
	}
	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) / z) * (a - y))
	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(Float64(t - x) / z) * Float64(a - y)));
	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) / z) * (a - y));
	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[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $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. div-sub 77.1%

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

      7. associate-/l* 78.4%

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

      8. associate-/l* 85.4%

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

      9. distribute-rgt-out-- 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 91.7%

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

Alternative 3: 91.1% accurate, 0.3× speedup

Math

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

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) z) (- a y)))
       (+ 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) / z) * (a - y));
	} 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) / z) * (a - y))
    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) / z) * (a - y));
	} 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) / z) * (a - y))
	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(Float64(t - x) / z) * Float64(a - y)));
	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) / z) * (a - y));
	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[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $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. div-sub 77.1%

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

      7. associate-/l* 78.4%

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

      8. associate-/l* 85.4%

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

      9. distribute-rgt-out-- 85.4%

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

   5. Simplified 85.4%

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

   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 91.8%

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

Alternative 4: 66.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x - t}}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-63}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) a)))))
   (if (<= a -7.2e+131)
     t_1
     (if (<= a -9.8e+53)
       (/ (- y a) (/ z (- x t)))
       (if (<= a -1.5e-32)
         (+ x (/ y (/ a (- t x))))
         (if (<= a 5.8e-63)
           (+ t (/ (* y (- x t)) z))
           (if (<= a 1.8e-35)
             (* y (/ (- t x) (- a z)))
             (if (<= a 3.8e+86) (* t (/ (- y z) (- a z))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -7.2e+131) {
		tmp = t_1;
	} else if (a <= -9.8e+53) {
		tmp = (y - a) / (z / (x - t));
	} else if (a <= -1.5e-32) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 5.8e-63) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.8e-35) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 3.8e+86) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * ((y - z) / a))
    if (a <= (-7.2d+131)) then
        tmp = t_1
    else if (a <= (-9.8d+53)) then
        tmp = (y - a) / (z / (x - t))
    else if (a <= (-1.5d-32)) then
        tmp = x + (y / (a / (t - x)))
    else if (a <= 5.8d-63) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 1.8d-35) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 3.8d+86) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -7.2e+131) {
		tmp = t_1;
	} else if (a <= -9.8e+53) {
		tmp = (y - a) / (z / (x - t));
	} else if (a <= -1.5e-32) {
		tmp = x + (y / (a / (t - x)));
	} else if (a <= 5.8e-63) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 1.8e-35) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 3.8e+86) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / a))
	tmp = 0
	if a <= -7.2e+131:
		tmp = t_1
	elif a <= -9.8e+53:
		tmp = (y - a) / (z / (x - t))
	elif a <= -1.5e-32:
		tmp = x + (y / (a / (t - x)))
	elif a <= 5.8e-63:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 1.8e-35:
		tmp = y * ((t - x) / (a - z))
	elif a <= 3.8e+86:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -7.2e+131)
		tmp = t_1;
	elseif (a <= -9.8e+53)
		tmp = Float64(Float64(y - a) / Float64(z / Float64(x - t)));
	elseif (a <= -1.5e-32)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (a <= 5.8e-63)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 1.8e-35)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 3.8e+86)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -7.2e+131)
		tmp = t_1;
	elseif (a <= -9.8e+53)
		tmp = (y - a) / (z / (x - t));
	elseif (a <= -1.5e-32)
		tmp = x + (y / (a / (t - x)));
	elseif (a <= 5.8e-63)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 1.8e-35)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 3.8e+86)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e+131], t$95$1, If[LessEqual[a, -9.8e+53], N[(N[(y - a), $MachinePrecision] / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-32], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-63], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-35], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+86], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.20000000000000063e131 or 3.79999999999999978e86 < a

   1. Initial program 90.8%

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

   3. Taylor expanded in t around inf 85.9%

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

   4. Taylor expanded in a around inf 63.1%

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

      1. associate-/l* 74.0%

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

   6. Simplified 74.0%

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

   if -7.20000000000000063e131 < a < -9.80000000000000036e53

   1. Initial program 56.0%

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

   3. Taylor expanded in z around inf 58.6%

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

      1. associate--l+ 58.6%

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

      2. distribute-lft-out-- 58.6%

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

      3. div-sub 58.6%

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

      4. mul-1-neg 58.6%

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

      5. unsub-neg 58.6%

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

      6. div-sub 58.6%

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

      7. associate-/l* 65.5%

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

      8. associate-/l* 85.4%

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

      9. distribute-rgt-out-- 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around 0 37.9%

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

      1. mul-1-neg 37.9%

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

      2. associate-*r/ 57.5%

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

      3. *-commutative 57.5%

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

      4. associate-/r/ 57.3%

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

      5. distribute-neg-frac2 57.3%

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

      6. distribute-neg-frac2 57.3%

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

   8. Simplified 57.3%

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

   if -9.80000000000000036e53 < a < -1.5e-32

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 70.5%

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

      1. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

      1. clear-num 70.4%

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

      2. un-div-inv 70.4%

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

   7. Applied egg-rr 70.4%

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

   if -1.5e-32 < a < 5.7999999999999995e-63

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf 84.5%

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

      1. associate--l+ 84.5%

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

      2. distribute-lft-out-- 84.5%

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

      3. div-sub 85.3%

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

      4. mul-1-neg 85.3%

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

      5. unsub-neg 85.3%

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

      6. div-sub 84.5%

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

      7. associate-/l* 85.7%

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

      8. associate-/l* 82.3%

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

      9. distribute-rgt-out-- 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in y around inf 83.0%

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

   if 5.7999999999999995e-63 < a < 1.80000000000000009e-35

   1. Initial program 88.8%

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

      1. clear-num 88.6%

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

      2. un-div-inv 88.9%

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

   4. Applied egg-rr 88.9%

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

   5. Taylor expanded in y around inf 78.4%

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

      1. div-sub 78.4%

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

   7. Simplified 78.4%

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

   if 1.80000000000000009e-35 < a < 3.79999999999999978e86

   1. Initial program 75.9%

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

   3. Taylor expanded in x around 0 53.2%

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

      1. associate-/l* 67.1%

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

   5. Simplified 67.1%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+131}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x - t}}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-63}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+96}:\\ \;\;\;\;t - t \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -0.0275:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-62}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+83}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) a)))))
   (if (<= a -7.5e+130)
     t_1
     (if (<= a -7.5e+96)
       (- t (* t (/ (- y a) z)))
       (if (<= a -0.0275)
         (+ x (/ (* (- y z) t) a))
         (if (<= a -1.42e-62)
           (* y (/ (- t x) (- a z)))
           (if (<= a 1.6e-62)
             (+ t (/ (* y (- x t)) z))
             (if (<= a 3.1e+83) (* t (/ (- y z) (- a z))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -7.5e+130) {
		tmp = t_1;
	} else if (a <= -7.5e+96) {
		tmp = t - (t * ((y - a) / z));
	} else if (a <= -0.0275) {
		tmp = x + (((y - z) * t) / a);
	} else if (a <= -1.42e-62) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.6e-62) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 3.1e+83) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * ((y - z) / a))
    if (a <= (-7.5d+130)) then
        tmp = t_1
    else if (a <= (-7.5d+96)) then
        tmp = t - (t * ((y - a) / z))
    else if (a <= (-0.0275d0)) then
        tmp = x + (((y - z) * t) / a)
    else if (a <= (-1.42d-62)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 1.6d-62) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 3.1d+83) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -7.5e+130) {
		tmp = t_1;
	} else if (a <= -7.5e+96) {
		tmp = t - (t * ((y - a) / z));
	} else if (a <= -0.0275) {
		tmp = x + (((y - z) * t) / a);
	} else if (a <= -1.42e-62) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 1.6e-62) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 3.1e+83) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / a))
	tmp = 0
	if a <= -7.5e+130:
		tmp = t_1
	elif a <= -7.5e+96:
		tmp = t - (t * ((y - a) / z))
	elif a <= -0.0275:
		tmp = x + (((y - z) * t) / a)
	elif a <= -1.42e-62:
		tmp = y * ((t - x) / (a - z))
	elif a <= 1.6e-62:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 3.1e+83:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -7.5e+130)
		tmp = t_1;
	elseif (a <= -7.5e+96)
		tmp = Float64(t - Float64(t * Float64(Float64(y - a) / z)));
	elseif (a <= -0.0275)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / a));
	elseif (a <= -1.42e-62)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 1.6e-62)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 3.1e+83)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -7.5e+130)
		tmp = t_1;
	elseif (a <= -7.5e+96)
		tmp = t - (t * ((y - a) / z));
	elseif (a <= -0.0275)
		tmp = x + (((y - z) * t) / a);
	elseif (a <= -1.42e-62)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 1.6e-62)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 3.1e+83)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e+130], t$95$1, If[LessEqual[a, -7.5e+96], N[(t - N[(t * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.0275], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.42e-62], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-62], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+83], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.5000000000000003e130 or 3.09999999999999992e83 < a

   1. Initial program 89.6%

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

   3. Taylor expanded in t around inf 84.8%

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

   4. Taylor expanded in a around inf 62.4%

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

      1. associate-/l* 73.1%

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

   6. Simplified 73.1%

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

   if -7.5000000000000003e130 < a < -7.4999999999999996e96

   1. Initial program 61.0%

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

   3. Taylor expanded in z around inf 56.6%

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

      1. associate--l+ 56.6%

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

      2. distribute-lft-out-- 56.6%

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

      3. div-sub 56.6%

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

      4. mul-1-neg 56.6%

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

      5. unsub-neg 56.6%

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

      6. div-sub 56.6%

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

      7. associate-/l* 67.3%

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

      8. associate-/l* 88.7%

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

      9. distribute-rgt-out-- 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in t around inf 46.1%

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

      1. associate-/l* 66.4%

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

   8. Simplified 66.4%

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

   if -7.4999999999999996e96 < a < -0.0275000000000000001

   1. Initial program 87.0%

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

   3. Taylor expanded in t around inf 65.8%

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

   4. Taylor expanded in a around inf 65.8%

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

   if -0.0275000000000000001 < a < -1.42e-62

   1. Initial program 85.5%

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

      1. clear-num 86.6%

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

      2. un-div-inv 85.7%

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

   4. Applied egg-rr 85.7%

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

   5. Taylor expanded in y around inf 86.3%

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

      1. div-sub 86.3%

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

   7. Simplified 86.3%

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

   if -1.42e-62 < a < 1.60000000000000011e-62

   1. Initial program 72.7%

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

   3. Taylor expanded in z around inf 85.7%

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

      1. associate--l+ 85.7%

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

      2. distribute-lft-out-- 85.7%

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

      3. div-sub 86.6%

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

      4. mul-1-neg 86.6%

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

      5. unsub-neg 86.6%

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

      6. div-sub 85.7%

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

      7. associate-/l* 87.0%

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

      8. associate-/l* 83.5%

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

      9. distribute-rgt-out-- 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in y around inf 84.2%

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

   if 1.60000000000000011e-62 < a < 3.09999999999999992e83

   1. Initial program 79.2%

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

   3. Taylor expanded in x around 0 49.3%

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

      1. associate-/l* 59.3%

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

   5. Simplified 59.3%

      \[\leadsto \color{blue}{t \cdot \frac{y - z}{a - z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+130}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+96}:\\ \;\;\;\;t - t \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -0.0275:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-62}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+83}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -750000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-87}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 170000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- x t)) z)))
   (if (<= z -3.5e+99)
     t
     (if (<= z -1.15e+73)
       t_1
       (if (<= z -750000000.0)
         t
         (if (<= z 3.7e-87)
           (+ x (* t (/ y a)))
           (if (<= z 170000000.0) t_1 (+ x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / z;
	double tmp;
	if (z <= -3.5e+99) {
		tmp = t;
	} else if (z <= -1.15e+73) {
		tmp = t_1;
	} else if (z <= -750000000.0) {
		tmp = t;
	} else if (z <= 3.7e-87) {
		tmp = x + (t * (y / a));
	} else if (z <= 170000000.0) {
		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 = (y * (x - t)) / z
    if (z <= (-3.5d+99)) then
        tmp = t
    else if (z <= (-1.15d+73)) then
        tmp = t_1
    else if (z <= (-750000000.0d0)) then
        tmp = t
    else if (z <= 3.7d-87) then
        tmp = x + (t * (y / a))
    else if (z <= 170000000.0d0) 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 = (y * (x - t)) / z;
	double tmp;
	if (z <= -3.5e+99) {
		tmp = t;
	} else if (z <= -1.15e+73) {
		tmp = t_1;
	} else if (z <= -750000000.0) {
		tmp = t;
	} else if (z <= 3.7e-87) {
		tmp = x + (t * (y / a));
	} else if (z <= 170000000.0) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (x - t)) / z
	tmp = 0
	if z <= -3.5e+99:
		tmp = t
	elif z <= -1.15e+73:
		tmp = t_1
	elif z <= -750000000.0:
		tmp = t
	elif z <= 3.7e-87:
		tmp = x + (t * (y / a))
	elif z <= 170000000.0:
		tmp = t_1
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(x - t)) / z)
	tmp = 0.0
	if (z <= -3.5e+99)
		tmp = t;
	elseif (z <= -1.15e+73)
		tmp = t_1;
	elseif (z <= -750000000.0)
		tmp = t;
	elseif (z <= 3.7e-87)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 170000000.0)
		tmp = t_1;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (x - t)) / z;
	tmp = 0.0;
	if (z <= -3.5e+99)
		tmp = t;
	elseif (z <= -1.15e+73)
		tmp = t_1;
	elseif (z <= -750000000.0)
		tmp = t;
	elseif (z <= 3.7e-87)
		tmp = x + (t * (y / a));
	elseif (z <= 170000000.0)
		tmp = t_1;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -3.5e+99], t, If[LessEqual[z, -1.15e+73], t$95$1, If[LessEqual[z, -750000000.0], t, If[LessEqual[z, 3.7e-87], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 170000000.0], t$95$1, N[(x + t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4999999999999998e99 or -1.15e73 < z < -7.5e8

   1. Initial program 60.3%

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

   3. Taylor expanded in z around inf 48.5%

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

   if -3.4999999999999998e99 < z < -1.15e73 or 3.7000000000000002e-87 < z < 1.7e8

   1. Initial program 85.0%

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

   3. Taylor expanded in z around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. distribute-lft-out-- 74.2%

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

      3. div-sub 78.0%

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

      4. mul-1-neg 78.0%

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

      5. unsub-neg 78.0%

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

      6. div-sub 74.2%

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

      7. associate-/l* 77.6%

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

      8. associate-/l* 73.7%

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

      9. distribute-rgt-out-- 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in y around inf 67.3%

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

      1. sub-neg 67.3%

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

      2. remove-double-neg 67.3%

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

      3. distribute-frac-neg2 67.3%

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

      4. distribute-neg-frac2 67.3%

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

      5. neg-mul-1 67.3%

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

      6. distribute-neg-in 67.3%

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

      7. +-commutative 67.3%

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

      8. neg-mul-1 67.3%

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

      9. sub-neg 67.3%

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

      10. div-sub 67.3%

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

      11. distribute-rgt-neg-in 67.3%

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

      12. associate-*r/ 64.0%

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

      13. distribute-neg-frac2 64.0%

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

   8. Simplified 64.0%

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

   if -7.5e8 < z < 3.7000000000000002e-87

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. associate-/l* 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around inf 61.6%

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

      1. associate-/l* 67.9%

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

   8. Simplified 67.9%

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

   if 1.7e8 < z

   1. Initial program 69.0%

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

   3. Taylor expanded in t around inf 63.7%

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

   4. Taylor expanded in z around inf 54.5%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+73}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq -750000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-87}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 170000000:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ t_2 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y))))
        (t_2 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -7.2e+131)
     t_2
     (if (<= a -9.2e+53)
       t_1
       (if (<= a -4.3e-38)
         t_2
         (if (<= a 1.2e-61) t_1 (+ x (* (- y z) (/ t (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	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 <= -4.3e-38) {
		tmp = t_2;
	} else if (a <= 1.2e-61) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) * (t / (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) :: t_2
    real(8) :: tmp
    t_1 = t + (((t - x) / z) * (a - y))
    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 <= (-4.3d-38)) then
        tmp = t_2
    else if (a <= 1.2d-61) then
        tmp = t_1
    else
        tmp = x + ((y - z) * (t / (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 = t + (((t - x) / z) * (a - y));
	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 <= -4.3e-38) {
		tmp = t_2;
	} else if (a <= 1.2e-61) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	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 <= -4.3e-38:
		tmp = t_2
	elif a <= 1.2e-61:
		tmp = t_1
	else:
		tmp = x + ((y - z) * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	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 <= -4.3e-38)
		tmp = t_2;
	elseif (a <= 1.2e-61)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	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 <= -4.3e-38)
		tmp = t_2;
	elseif (a <= 1.2e-61)
		tmp = t_1;
	else
		tmp = x + ((y - z) * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, 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, -4.3e-38], t$95$2, If[LessEqual[a, 1.2e-61], t$95$1, N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.20000000000000063e131 or -9.20000000000000079e53 < a < -4.3000000000000002e-38

   1. Initial program 92.9%

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

      1. clear-num 93.3%

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

      2. un-div-inv 93.1%

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

   4. Applied egg-rr 93.1%

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

   5. Taylor expanded in t around inf 83.3%

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

   if -7.20000000000000063e131 < a < -9.20000000000000079e53 or -4.3000000000000002e-38 < a < 1.2e-61

   1. Initial program 71.4%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. associate--l+ 82.3%

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

      2. distribute-lft-out-- 82.3%

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

      3. div-sub 83.1%

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

      4. mul-1-neg 83.1%

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

      5. unsub-neg 83.1%

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

      6. div-sub 82.3%

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

      7. associate-/l* 84.1%

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

      8. associate-/l* 83.2%

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

      9. distribute-rgt-out-- 87.0%

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

   5. Simplified 87.0%

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

   if 1.2e-61 < a

   1. Initial program 83.9%

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

   3. Taylor expanded in t around inf 77.2%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+131}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+53}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+160}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-7}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.4e+160)
   (+ x (* y (/ (- t x) a)))
   (if (<= x -1.16e+91)
     (/ x (/ z (- y a)))
     (if (<= x -3.6e-7)
       (+ x (* t (/ (- y z) a)))
       (if (<= x 2.15e+125)
         (* t (/ (- y z) (- a z)))
         (* x (+ (/ y (- z a)) 1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.4e+160) {
		tmp = x + (y * ((t - x) / a));
	} else if (x <= -1.16e+91) {
		tmp = x / (z / (y - a));
	} else if (x <= -3.6e-7) {
		tmp = x + (t * ((y - z) / a));
	} else if (x <= 2.15e+125) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * ((y / (z - a)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3.4d+160)) then
        tmp = x + (y * ((t - x) / a))
    else if (x <= (-1.16d+91)) then
        tmp = x / (z / (y - a))
    else if (x <= (-3.6d-7)) then
        tmp = x + (t * ((y - z) / a))
    else if (x <= 2.15d+125) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x * ((y / (z - a)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.4e+160) {
		tmp = x + (y * ((t - x) / a));
	} else if (x <= -1.16e+91) {
		tmp = x / (z / (y - a));
	} else if (x <= -3.6e-7) {
		tmp = x + (t * ((y - z) / a));
	} else if (x <= 2.15e+125) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * ((y / (z - a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.4e+160:
		tmp = x + (y * ((t - x) / a))
	elif x <= -1.16e+91:
		tmp = x / (z / (y - a))
	elif x <= -3.6e-7:
		tmp = x + (t * ((y - z) / a))
	elif x <= 2.15e+125:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * ((y / (z - a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.4e+160)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (x <= -1.16e+91)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	elseif (x <= -3.6e-7)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	elseif (x <= 2.15e+125)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(z - a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.4e+160)
		tmp = x + (y * ((t - x) / a));
	elseif (x <= -1.16e+91)
		tmp = x / (z / (y - a));
	elseif (x <= -3.6e-7)
		tmp = x + (t * ((y - z) / a));
	elseif (x <= 2.15e+125)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * ((y / (z - a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.4e+160], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.16e+91], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.6e-7], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e+125], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.4000000000000003e160

   1. Initial program 66.9%

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

   3. Taylor expanded in z around 0 49.7%

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

      1. associate-/l* 58.0%

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

   5. Simplified 58.0%

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

   if -3.4000000000000003e160 < x < -1.1600000000000001e91

   1. Initial program 65.3%

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

   3. Taylor expanded in x around inf 45.0%

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

      1. mul-1-neg 45.0%

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

      2. unsub-neg 45.0%

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

   5. Simplified 45.0%

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

   6. Taylor expanded in z around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. neg-mul-1 71.9%

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

      3. +-commutative 71.9%

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

      4. neg-mul-1 71.9%

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

      5. remove-double-neg 71.9%

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

      6. neg-mul-1 71.9%

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

      7. sub-neg 71.9%

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

      8. distribute-lft-out-- 71.9%

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

      9. associate-*r/ 71.9%

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

      10. mul-1-neg 71.9%

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

      11. remove-double-neg 71.9%

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

   8. Simplified 71.9%

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

      1. clear-num 71.7%

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

      2. un-div-inv 72.0%

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

   10. Applied egg-rr 72.0%

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

   if -1.1600000000000001e91 < x < -3.59999999999999994e-7

   1. Initial program 83.9%

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

   3. Taylor expanded in t around inf 64.6%

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

   4. Taylor expanded in a around inf 60.8%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

   if -3.59999999999999994e-7 < x < 2.15000000000000018e125

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0 58.1%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   if 2.15000000000000018e125 < x

   1. Initial program 68.5%

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

   3. Taylor expanded in x around inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. unsub-neg 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in y around inf 66.2%

      \[\leadsto x \cdot \left(1 - \color{blue}{\frac{y}{a - z}}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+160}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;x \leq -1.16 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-7}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{+45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.6e+160)
   (* x (- 1.0 (/ y a)))
   (if (<= x -3.9e+89)
     (/ x (/ z (- y a)))
     (if (<= x -3.7e+45)
       (+ x (* t (/ y a)))
       (if (<= x 4.2e+137) (* t (/ (- y z) (- a z))) (* x (/ (- y a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.6e+160) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= -3.9e+89) {
		tmp = x / (z / (y - a));
	} else if (x <= -3.7e+45) {
		tmp = x + (t * (y / a));
	} else if (x <= 4.2e+137) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = 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) :: tmp
    if (x <= (-4.6d+160)) then
        tmp = x * (1.0d0 - (y / a))
    else if (x <= (-3.9d+89)) then
        tmp = x / (z / (y - a))
    else if (x <= (-3.7d+45)) then
        tmp = x + (t * (y / a))
    else if (x <= 4.2d+137) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = 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 tmp;
	if (x <= -4.6e+160) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= -3.9e+89) {
		tmp = x / (z / (y - a));
	} else if (x <= -3.7e+45) {
		tmp = x + (t * (y / a));
	} else if (x <= 4.2e+137) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x * ((y - a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.6e+160:
		tmp = x * (1.0 - (y / a))
	elif x <= -3.9e+89:
		tmp = x / (z / (y - a))
	elif x <= -3.7e+45:
		tmp = x + (t * (y / a))
	elif x <= 4.2e+137:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x * ((y - a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.6e+160)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (x <= -3.9e+89)
		tmp = Float64(x / Float64(z / Float64(y - a)));
	elseif (x <= -3.7e+45)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (x <= 4.2e+137)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x * Float64(Float64(y - a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.6e+160)
		tmp = x * (1.0 - (y / a));
	elseif (x <= -3.9e+89)
		tmp = x / (z / (y - a));
	elseif (x <= -3.7e+45)
		tmp = x + (t * (y / a));
	elseif (x <= 4.2e+137)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x * ((y - a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.6e+160], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.9e+89], N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.7e+45], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+137], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.59999999999999975e160

   1. Initial program 66.9%

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

   3. Taylor expanded in z around 0 49.7%

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

      1. associate-/l* 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in x around inf 55.1%

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

      1. mul-1-neg 55.1%

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

   8. Simplified 55.1%

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

   9. Taylor expanded in x around 0 55.1%

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

   if -4.59999999999999975e160 < x < -3.90000000000000011e89

   1. Initial program 65.3%

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

   3. Taylor expanded in x around inf 45.0%

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

      1. mul-1-neg 45.0%

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

      2. unsub-neg 45.0%

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

   5. Simplified 45.0%

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

   6. Taylor expanded in z around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. neg-mul-1 71.9%

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

      3. +-commutative 71.9%

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

      4. neg-mul-1 71.9%

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

      5. remove-double-neg 71.9%

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

      6. neg-mul-1 71.9%

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

      7. sub-neg 71.9%

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

      8. distribute-lft-out-- 71.9%

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

      9. associate-*r/ 71.9%

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

      10. mul-1-neg 71.9%

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

      11. remove-double-neg 71.9%

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

   8. Simplified 71.9%

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

      1. clear-num 71.7%

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

      2. un-div-inv 72.0%

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

   10. Applied egg-rr 72.0%

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

   if -3.90000000000000011e89 < x < -3.69999999999999977e45

   1. Initial program 92.1%

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

   3. Taylor expanded in z around 0 77.7%

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

      1. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in t around inf 69.6%

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

      1. associate-/l* 77.7%

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

   8. Simplified 77.7%

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

   if -3.69999999999999977e45 < x < 4.1999999999999998e137

   1. Initial program 84.9%

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

   3. Taylor expanded in x around 0 56.8%

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

      1. associate-/l* 70.0%

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

   5. Simplified 70.0%

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

   if 4.1999999999999998e137 < x

   1. Initial program 66.5%

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

   3. Taylor expanded in x around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. unsub-neg 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in z around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. neg-mul-1 57.4%

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

      3. +-commutative 57.4%

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

      4. neg-mul-1 57.4%

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

      5. remove-double-neg 57.4%

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

      6. neg-mul-1 57.4%

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

      7. sub-neg 57.4%

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

      8. distribute-lft-out-- 57.4%

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

      9. associate-*r/ 57.4%

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

      10. mul-1-neg 57.4%

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

      11. remove-double-neg 57.4%

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

   8. Simplified 57.4%

      \[\leadsto x \cdot \color{blue}{\frac{y - a}{z}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 10: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -520000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-87}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+113}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -520000000.0)
   t
   (if (<= z 3.8e-87)
     (+ x (* t (/ y a)))
     (if (<= z 4.2e-23) (* x (/ y z)) (if (<= z 5.8e+113) (+ x t) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -520000000.0) {
		tmp = t;
	} else if (z <= 3.8e-87) {
		tmp = x + (t * (y / a));
	} else if (z <= 4.2e-23) {
		tmp = x * (y / z);
	} else if (z <= 5.8e+113) {
		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 (z <= (-520000000.0d0)) then
        tmp = t
    else if (z <= 3.8d-87) then
        tmp = x + (t * (y / a))
    else if (z <= 4.2d-23) then
        tmp = x * (y / z)
    else if (z <= 5.8d+113) 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 (z <= -520000000.0) {
		tmp = t;
	} else if (z <= 3.8e-87) {
		tmp = x + (t * (y / a));
	} else if (z <= 4.2e-23) {
		tmp = x * (y / z);
	} else if (z <= 5.8e+113) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -520000000.0:
		tmp = t
	elif z <= 3.8e-87:
		tmp = x + (t * (y / a))
	elif z <= 4.2e-23:
		tmp = x * (y / z)
	elif z <= 5.8e+113:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -520000000.0)
		tmp = t;
	elseif (z <= 3.8e-87)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 4.2e-23)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 5.8e+113)
		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 (z <= -520000000.0)
		tmp = t;
	elseif (z <= 3.8e-87)
		tmp = x + (t * (y / a));
	elseif (z <= 4.2e-23)
		tmp = x * (y / z);
	elseif (z <= 5.8e+113)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -520000000.0], t, If[LessEqual[z, 3.8e-87], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-23], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+113], N[(x + t), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2e8 or 5.79999999999999968e113 < z

   1. Initial program 61.5%

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

   3. Taylor expanded in z around inf 51.3%

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

   if -5.2e8 < z < 3.8e-87

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. associate-/l* 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around inf 61.6%

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

      1. associate-/l* 67.9%

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

   8. Simplified 67.9%

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

   if 3.8e-87 < z < 4.2000000000000002e-23

   1. Initial program 81.6%

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

   3. Taylor expanded in x around inf 57.7%

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

      1. mul-1-neg 57.7%

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

      2. unsub-neg 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in a around 0 58.7%

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

   if 4.2000000000000002e-23 < z < 5.79999999999999968e113

   1. Initial program 90.5%

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

   3. Taylor expanded in t around inf 76.7%

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

   4. Taylor expanded in z around inf 48.4%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -520000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-87}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+113}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-40} \lor \neg \left(a \leq 8 \cdot 10^{-63}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.4e-40) (not (<= a 8e-63)))
   (+ x (* (- y z) (/ t (- a z))))
   (+ t (/ (* y (- x t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.4e-40) || !(a <= 8e-63)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} 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 <= (-5.4d-40)) .or. (.not. (a <= 8d-63))) then
        tmp = x + ((y - z) * (t / (a - z)))
    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 <= -5.4e-40) || !(a <= 8e-63)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.4e-40) or not (a <= 8e-63):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.4e-40) || !(a <= 8e-63))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.4e-40) || ~((a <= 8e-63)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.4e-40], N[Not[LessEqual[a, 8e-63]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4e-40 or 8.00000000000000053e-63 < a

   1. Initial program 84.8%

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

   3. Taylor expanded in t around inf 76.0%

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

   if -5.4e-40 < a < 8.00000000000000053e-63

   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. div-sub 85.1%

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

      7. associate-/l* 86.4%

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

      8. associate-/l* 83.0%

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

      9. distribute-rgt-out-- 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in y around inf 83.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-40} \lor \neg \left(a \leq 8 \cdot 10^{-63}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -520000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -520000000.0)
   t
   (if (<= z 9e-87)
     (* x (- 1.0 (/ y a)))
     (if (<= z 4.2e-23) (* x (/ y z)) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -520000000.0) {
		tmp = t;
	} else if (z <= 9e-87) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.2e-23) {
		tmp = x * (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 (z <= (-520000000.0d0)) then
        tmp = t
    else if (z <= 9d-87) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 4.2d-23) then
        tmp = x * (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 (z <= -520000000.0) {
		tmp = t;
	} else if (z <= 9e-87) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 4.2e-23) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -520000000.0:
		tmp = t
	elif z <= 9e-87:
		tmp = x * (1.0 - (y / a))
	elif z <= 4.2e-23:
		tmp = x * (y / z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -520000000.0)
		tmp = t;
	elseif (z <= 9e-87)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 4.2e-23)
		tmp = Float64(x * 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 (z <= -520000000.0)
		tmp = t;
	elseif (z <= 9e-87)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 4.2e-23)
		tmp = x * (y / z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -520000000.0], t, If[LessEqual[z, 9e-87], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-23], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2e8

   1. Initial program 64.0%

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

   3. Taylor expanded in z around inf 44.0%

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

   if -5.2e8 < z < 8.99999999999999915e-87

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 72.4%

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

      1. associate-/l* 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in x around inf 53.0%

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

      1. mul-1-neg 53.0%

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

   8. Simplified 53.0%

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

   9. Taylor expanded in x around 0 53.0%

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

   if 8.99999999999999915e-87 < z < 4.2000000000000002e-23

   1. Initial program 80.3%

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

   3. Taylor expanded in x around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in a around 0 62.5%

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

   if 4.2000000000000002e-23 < z

   1. Initial program 69.7%

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

   3. Taylor expanded in t around inf 63.5%

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

   4. Taylor expanded in z around inf 52.6%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -520000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+47} \lor \neg \left(x \leq 2.85 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.8e+47) (not (<= x 2.85e+125)))
   (* x (+ (/ y (- z a)) 1.0))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.8e+47) || !(x <= 2.85e+125)) {
		tmp = x * ((y / (z - a)) + 1.0);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.8d+47)) .or. (.not. (x <= 2.85d+125))) then
        tmp = x * ((y / (z - a)) + 1.0d0)
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.8e+47) || !(x <= 2.85e+125)) {
		tmp = x * ((y / (z - a)) + 1.0);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.8e+47) or not (x <= 2.85e+125):
		tmp = x * ((y / (z - a)) + 1.0)
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.8e+47) || !(x <= 2.85e+125))
		tmp = Float64(x * Float64(Float64(y / Float64(z - a)) + 1.0));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.8e+47) || ~((x <= 2.85e+125)))
		tmp = x * ((y / (z - a)) + 1.0);
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.8e+47], N[Not[LessEqual[x, 2.85e+125]], $MachinePrecision]], N[(x * N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999988e47 or 2.8499999999999998e125 < x

   1. Initial program 70.4%

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

   3. Taylor expanded in x around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in y around inf 60.4%

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

   if -2.79999999999999988e47 < x < 2.8499999999999998e125

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0 56.8%

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

      1. associate-/l* 70.2%

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

   5. Simplified 70.2%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+47} \lor \neg \left(x \leq 2.85 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+171}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-80} \lor \neg \left(a \leq 3.6 \cdot 10^{-63}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+171)
   x
   (if (or (<= a -1.95e-80) (not (<= a 3.6e-63))) (+ x t) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+171) {
		tmp = x;
	} else if ((a <= -1.95e-80) || !(a <= 3.6e-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 <= (-2.1d+171)) then
        tmp = x
    else if ((a <= (-1.95d-80)) .or. (.not. (a <= 3.6d-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 <= -2.1e+171) {
		tmp = x;
	} else if ((a <= -1.95e-80) || !(a <= 3.6e-63)) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e+171:
		tmp = x
	elif (a <= -1.95e-80) or not (a <= 3.6e-63):
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+171)
		tmp = x;
	elseif ((a <= -1.95e-80) || !(a <= 3.6e-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 <= -2.1e+171)
		tmp = x;
	elseif ((a <= -1.95e-80) || ~((a <= 3.6e-63)))
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+171], x, If[Or[LessEqual[a, -1.95e-80], N[Not[LessEqual[a, 3.6e-63]], $MachinePrecision]], N[(x + t), $MachinePrecision], t]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1000000000000001e171

   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 -2.1000000000000001e171 < a < -1.9499999999999999e-80 or 3.60000000000000008e-63 < a

   1. Initial program 82.2%

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

   3. Taylor expanded in t around inf 70.0%

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

   4. Taylor expanded in z around inf 43.0%

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

   if -1.9499999999999999e-80 < a < 3.60000000000000008e-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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+171}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-80} \lor \neg \left(a \leq 3.6 \cdot 10^{-63}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+85} \lor \neg \left(y \leq 10^{+120}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.3e+85) (not (<= y 1e+120))) (* x (/ y z)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.3e+85) || !(y <= 1e+120)) {
		tmp = x * (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 ((y <= (-5.3d+85)) .or. (.not. (y <= 1d+120))) then
        tmp = x * (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 ((y <= -5.3e+85) || !(y <= 1e+120)) {
		tmp = x * (y / z);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.3e+85) or not (y <= 1e+120):
		tmp = x * (y / z)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.3e+85) || !(y <= 1e+120))
		tmp = Float64(x * 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 ((y <= -5.3e+85) || ~((y <= 1e+120)))
		tmp = x * (y / z);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.3e+85], N[Not[LessEqual[y, 1e+120]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2999999999999999e85 or 9.9999999999999998e119 < y

   1. Initial program 83.9%

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

   3. Taylor expanded in x around inf 40.4%

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

      1. mul-1-neg 40.4%

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

      2. unsub-neg 40.4%

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

   5. Simplified 40.4%

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

   6. Taylor expanded in a around 0 39.8%

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

   if -5.2999999999999999e85 < y < 9.9999999999999998e119

   1. Initial program 77.0%

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

   3. Taylor expanded in t around inf 68.6%

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

   4. Taylor expanded in z around inf 50.6%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+85} \lor \neg \left(y \leq 10^{+120}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 38.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-32} \lor \neg \left(a \leq 5 \cdot 10^{+85}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.2e-32) (not (<= a 5e+85))) x t))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.2e-32) || !(a <= 5e+85)) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7.2d-32)) .or. (.not. (a <= 5d+85))) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.2e-32) || !(a <= 5e+85)) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.2e-32) or not (a <= 5e+85):
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.2e-32) || !(a <= 5e+85))
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.2e-32) || ~((a <= 5e+85)))
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.2e-32], N[Not[LessEqual[a, 5e+85]], $MachinePrecision]], x, t]

Derivation

1. Split input into 2 regimes

2. if a < -7.19999999999999986e-32 or 5.0000000000000001e85 < 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 -7.19999999999999986e-32 < a < 5.0000000000000001e85

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-32} \lor \neg \left(a \leq 5 \cdot 10^{+85}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. 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)))))