Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.8% → 92.7%

Time: 15.9s

Alternatives: 18

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.8% 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: 92.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-207}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

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 -1e-207)
     (fma (- y z) t_1 x)
     (if (<= t_2 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

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 <= -1e-207) {
		tmp = fma((y - z), t_1, x);
	} else if (t_2 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	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 <= -1e-207)
		tmp = fma(Float64(y - z), t_1, x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	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, -1e-207], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $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)))) < -9.99999999999999925e-208

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. fma-define 95.0%

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

   3. Simplified 95.0%

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

   if -9.99999999999999925e-208 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.9%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. associate--l+ 87.8%

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

      2. distribute-lft-out-- 87.8%

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

      3. div-sub 87.8%

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

      4. mul-1-neg 87.8%

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

      5. unsub-neg 87.8%

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

      6. div-sub 87.8%

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

      7. associate-/l* 90.9%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

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

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

      2. associate-*l/ 73.6%

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

      3. associate-*r/ 94.1%

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

      4. clear-num 94.1%

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

      5. un-div-inv 94.1%

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

   4. Applied egg-rr 94.1%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-207}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-207} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-207) (not (<= t_1 0.0)))
     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 <= -1e-207) || !(t_1 <= 0.0)) {
		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 <= (-1d-207)) .or. (.not. (t_1 <= 0.0d0))) 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 <= -1e-207) || !(t_1 <= 0.0)) {
		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 <= -1e-207) or not (t_1 <= 0.0):
		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 <= -1e-207) || !(t_1 <= 0.0))
		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 <= -1e-207) || ~((t_1 <= 0.0)))
		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, -1e-207], N[Not[LessEqual[t$95$1, 0.0]], $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)))) < -9.99999999999999925e-208 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.2%

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

   if -9.99999999999999925e-208 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.9%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. associate--l+ 87.8%

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

      2. distribute-lft-out-- 87.8%

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

      3. div-sub 87.8%

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

      4. mul-1-neg 87.8%

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

      5. unsub-neg 87.8%

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

      6. div-sub 87.8%

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

      7. associate-/l* 90.9%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-207} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e-207)
     t_1
     (if (<= t_1 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-207) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-1d-207)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e-207) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -1e-207:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e-207)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e-207)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-207], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $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)))) < -9.99999999999999925e-208

   1. Initial program 95.0%

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

   if -9.99999999999999925e-208 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.9%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. associate--l+ 87.8%

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

      2. distribute-lft-out-- 87.8%

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

      3. div-sub 87.8%

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

      4. mul-1-neg 87.8%

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

      5. unsub-neg 87.8%

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

      6. div-sub 87.8%

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

      7. associate-/l* 90.9%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

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

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

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

      2. associate-*l/ 73.6%

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

      3. associate-*r/ 94.1%

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

      4. clear-num 94.1%

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

      5. un-div-inv 94.1%

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

   4. Applied egg-rr 94.1%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-207}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 35.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-161}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y z))) (t_2 (* t (/ y (- a z)))))
   (if (<= a -9e+142)
     x
     (if (<= a -5.8e-178)
       t_2
       (if (<= a 9.5e-232)
         t_1
         (if (<= a 4.5e-161)
           t_2
           (if (<= a 8.5e-89)
             t_1
             (if (<= a 4.2e-24) t_2 (if (<= a 7.2e+136) t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double t_2 = t * (y / (a - z));
	double tmp;
	if (a <= -9e+142) {
		tmp = x;
	} else if (a <= -5.8e-178) {
		tmp = t_2;
	} else if (a <= 9.5e-232) {
		tmp = t_1;
	} else if (a <= 4.5e-161) {
		tmp = t_2;
	} else if (a <= 8.5e-89) {
		tmp = t_1;
	} else if (a <= 4.2e-24) {
		tmp = t_2;
	} else if (a <= 7.2e+136) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / z)
    t_2 = t * (y / (a - z))
    if (a <= (-9d+142)) then
        tmp = x
    else if (a <= (-5.8d-178)) then
        tmp = t_2
    else if (a <= 9.5d-232) then
        tmp = t_1
    else if (a <= 4.5d-161) then
        tmp = t_2
    else if (a <= 8.5d-89) then
        tmp = t_1
    else if (a <= 4.2d-24) then
        tmp = t_2
    else if (a <= 7.2d+136) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double t_2 = t * (y / (a - z));
	double tmp;
	if (a <= -9e+142) {
		tmp = x;
	} else if (a <= -5.8e-178) {
		tmp = t_2;
	} else if (a <= 9.5e-232) {
		tmp = t_1;
	} else if (a <= 4.5e-161) {
		tmp = t_2;
	} else if (a <= 8.5e-89) {
		tmp = t_1;
	} else if (a <= 4.2e-24) {
		tmp = t_2;
	} else if (a <= 7.2e+136) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	t_2 = t * (y / (a - z))
	tmp = 0
	if a <= -9e+142:
		tmp = x
	elif a <= -5.8e-178:
		tmp = t_2
	elif a <= 9.5e-232:
		tmp = t_1
	elif a <= 4.5e-161:
		tmp = t_2
	elif a <= 8.5e-89:
		tmp = t_1
	elif a <= 4.2e-24:
		tmp = t_2
	elif a <= 7.2e+136:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	t_2 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (a <= -9e+142)
		tmp = x;
	elseif (a <= -5.8e-178)
		tmp = t_2;
	elseif (a <= 9.5e-232)
		tmp = t_1;
	elseif (a <= 4.5e-161)
		tmp = t_2;
	elseif (a <= 8.5e-89)
		tmp = t_1;
	elseif (a <= 4.2e-24)
		tmp = t_2;
	elseif (a <= 7.2e+136)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	t_2 = t * (y / (a - z));
	tmp = 0.0;
	if (a <= -9e+142)
		tmp = x;
	elseif (a <= -5.8e-178)
		tmp = t_2;
	elseif (a <= 9.5e-232)
		tmp = t_1;
	elseif (a <= 4.5e-161)
		tmp = t_2;
	elseif (a <= 8.5e-89)
		tmp = t_1;
	elseif (a <= 4.2e-24)
		tmp = t_2;
	elseif (a <= 7.2e+136)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+142], x, If[LessEqual[a, -5.8e-178], t$95$2, If[LessEqual[a, 9.5e-232], t$95$1, If[LessEqual[a, 4.5e-161], t$95$2, If[LessEqual[a, 8.5e-89], t$95$1, If[LessEqual[a, 4.2e-24], t$95$2, If[LessEqual[a, 7.2e+136], t, x]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.9999999999999998e142 or 7.20000000000000011e136 < a

   1. Initial program 94.4%

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

   3. Taylor expanded in a around inf 65.0%

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

   if -8.9999999999999998e142 < a < -5.7999999999999995e-178 or 9.50000000000000033e-232 < a < 4.4999999999999996e-161 or 8.49999999999999937e-89 < a < 4.1999999999999999e-24

   1. Initial program 78.0%

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

   3. Taylor expanded in y around inf 45.7%

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

      1. div-sub 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in t around inf 32.3%

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

      1. associate-/l* 37.3%

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

   8. Simplified 37.3%

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

   if -5.7999999999999995e-178 < a < 9.50000000000000033e-232 or 4.4999999999999996e-161 < a < 8.49999999999999937e-89

   1. Initial program 66.4%

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

   3. Taylor expanded in x around inf 37.3%

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

      1. mul-1-neg 37.3%

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

      2. unsub-neg 37.3%

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

   5. Simplified 37.3%

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

   6. Taylor expanded in a around 0 49.6%

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

   if 4.1999999999999999e-24 < a < 7.20000000000000011e136

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 29.5%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-161}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_3 := x \cdot \frac{y}{z}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-227}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 2000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z))))
        (t_2 (* x (- 1.0 (/ y a))))
        (t_3 (* x (/ y z))))
   (if (<= a -3.6e-5)
     t_2
     (if (<= a -5.8e-178)
       t_1
       (if (<= a 1.5e-227)
         t_3
         (if (<= a 1.75e-161)
           t_1
           (if (<= a 1.9e-88) t_3 (if (<= a 2000000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double t_3 = x * (y / z);
	double tmp;
	if (a <= -3.6e-5) {
		tmp = t_2;
	} else if (a <= -5.8e-178) {
		tmp = t_1;
	} else if (a <= 1.5e-227) {
		tmp = t_3;
	} else if (a <= 1.75e-161) {
		tmp = t_1;
	} else if (a <= 1.9e-88) {
		tmp = t_3;
	} else if (a <= 2000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    t_3 = x * (y / z)
    if (a <= (-3.6d-5)) then
        tmp = t_2
    else if (a <= (-5.8d-178)) then
        tmp = t_1
    else if (a <= 1.5d-227) then
        tmp = t_3
    else if (a <= 1.75d-161) then
        tmp = t_1
    else if (a <= 1.9d-88) then
        tmp = t_3
    else if (a <= 2000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double t_3 = x * (y / z);
	double tmp;
	if (a <= -3.6e-5) {
		tmp = t_2;
	} else if (a <= -5.8e-178) {
		tmp = t_1;
	} else if (a <= 1.5e-227) {
		tmp = t_3;
	} else if (a <= 1.75e-161) {
		tmp = t_1;
	} else if (a <= 1.9e-88) {
		tmp = t_3;
	} else if (a <= 2000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	t_2 = x * (1.0 - (y / a))
	t_3 = x * (y / z)
	tmp = 0
	if a <= -3.6e-5:
		tmp = t_2
	elif a <= -5.8e-178:
		tmp = t_1
	elif a <= 1.5e-227:
		tmp = t_3
	elif a <= 1.75e-161:
		tmp = t_1
	elif a <= 1.9e-88:
		tmp = t_3
	elif a <= 2000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_3 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (a <= -3.6e-5)
		tmp = t_2;
	elseif (a <= -5.8e-178)
		tmp = t_1;
	elseif (a <= 1.5e-227)
		tmp = t_3;
	elseif (a <= 1.75e-161)
		tmp = t_1;
	elseif (a <= 1.9e-88)
		tmp = t_3;
	elseif (a <= 2000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	t_2 = x * (1.0 - (y / a));
	t_3 = x * (y / z);
	tmp = 0.0;
	if (a <= -3.6e-5)
		tmp = t_2;
	elseif (a <= -5.8e-178)
		tmp = t_1;
	elseif (a <= 1.5e-227)
		tmp = t_3;
	elseif (a <= 1.75e-161)
		tmp = t_1;
	elseif (a <= 1.9e-88)
		tmp = t_3;
	elseif (a <= 2000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e-5], t$95$2, If[LessEqual[a, -5.8e-178], t$95$1, If[LessEqual[a, 1.5e-227], t$95$3, If[LessEqual[a, 1.75e-161], t$95$1, If[LessEqual[a, 1.9e-88], t$95$3, If[LessEqual[a, 2000000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.60000000000000009e-5 or 2e9 < a

   1. Initial program 89.5%

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

   3. Taylor expanded in x around inf 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in z around 0 55.0%

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

   if -3.60000000000000009e-5 < a < -5.7999999999999995e-178 or 1.5e-227 < a < 1.7500000000000001e-161 or 1.90000000000000006e-88 < a < 2e9

   1. Initial program 72.7%

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

   3. Taylor expanded in y around inf 49.7%

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

      1. div-sub 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in t around inf 38.6%

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

      1. associate-/l* 42.7%

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

   8. Simplified 42.7%

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

   if -5.7999999999999995e-178 < a < 1.5e-227 or 1.7500000000000001e-161 < a < 1.90000000000000006e-88

   1. Initial program 66.4%

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

   3. Taylor expanded in x around inf 37.3%

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

      1. mul-1-neg 37.3%

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

      2. unsub-neg 37.3%

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

   5. Simplified 37.3%

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

   6. Taylor expanded in a around 0 49.6%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-161}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2000000000:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.66 \cdot 10^{-108} \lor \neg \left(a \leq 2 \cdot 10^{-70} \lor \neg \left(a \leq 1.35 \cdot 10^{-5}\right) \land a \leq 2.05 \cdot 10^{+97}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.66e-108)
         (not (or (<= a 2e-70) (and (not (<= a 1.35e-5)) (<= a 2.05e+97)))))
   (+ x (/ (- y z) (/ (- a z) t)))
   (+ t (* (/ (- t x) z) (- a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.66e-108) || !((a <= 2e-70) || (!(a <= 1.35e-5) && (a <= 2.05e+97)))) {
		tmp = x + ((y - z) / ((a - z) / t));
	} 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) :: tmp
    if ((a <= (-1.66d-108)) .or. (.not. (a <= 2d-70) .or. (.not. (a <= 1.35d-5)) .and. (a <= 2.05d+97))) then
        tmp = x + ((y - z) / ((a - z) / t))
    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 tmp;
	if ((a <= -1.66e-108) || !((a <= 2e-70) || (!(a <= 1.35e-5) && (a <= 2.05e+97)))) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.66e-108) or not ((a <= 2e-70) or (not (a <= 1.35e-5) and (a <= 2.05e+97))):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.66e-108) || !((a <= 2e-70) || (!(a <= 1.35e-5) && (a <= 2.05e+97))))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	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)
	tmp = 0.0;
	if ((a <= -1.66e-108) || ~(((a <= 2e-70) || (~((a <= 1.35e-5)) && (a <= 2.05e+97)))))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.66e-108], N[Not[Or[LessEqual[a, 2e-70], And[N[Not[LessEqual[a, 1.35e-5]], $MachinePrecision], LessEqual[a, 2.05e+97]]]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 a < -1.65999999999999993e-108 or 1.99999999999999999e-70 < a < 1.3499999999999999e-5 or 2.04999999999999994e97 < a

   1. Initial program 89.3%

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

      1. clear-num 89.1%

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

      2. un-div-inv 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in t around inf 81.6%

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

   if -1.65999999999999993e-108 < a < 1.99999999999999999e-70 or 1.3499999999999999e-5 < a < 2.04999999999999994e97

   1. Initial program 67.2%

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

   3. Taylor expanded in z around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. distribute-lft-out-- 73.3%

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

      3. div-sub 74.3%

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

      4. mul-1-neg 74.3%

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

      5. unsub-neg 74.3%

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

      6. div-sub 73.3%

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

      7. associate-/l* 78.8%

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

      8. associate-/l* 78.6%

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

      9. distribute-rgt-out-- 80.7%

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

   5. Simplified 80.7%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.66 \cdot 10^{-108} \lor \neg \left(a \leq 2 \cdot 10^{-70} \lor \neg \left(a \leq 1.35 \cdot 10^{-5}\right) \land a \leq 2.05 \cdot 10^{+97}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -0.00019:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 5000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -0.00019)
     t_2
     (if (<= a 1.7e-135)
       t_1
       (if (<= a 5.8e-89)
         (* x (/ (- y a) z))
         (if (<= a 5000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -0.00019) {
		tmp = t_2;
	} else if (a <= 1.7e-135) {
		tmp = t_1;
	} else if (a <= 5.8e-89) {
		tmp = x * ((y - a) / z);
	} else if (a <= 5000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((t - x) / (a / (y - z)))
    if (a <= (-0.00019d0)) then
        tmp = t_2
    else if (a <= 1.7d-135) then
        tmp = t_1
    else if (a <= 5.8d-89) then
        tmp = x * ((y - a) / z)
    else if (a <= 5000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -0.00019) {
		tmp = t_2;
	} else if (a <= 1.7e-135) {
		tmp = t_1;
	} else if (a <= 5.8e-89) {
		tmp = x * ((y - a) / z);
	} else if (a <= 5000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -0.00019:
		tmp = t_2
	elif a <= 1.7e-135:
		tmp = t_1
	elif a <= 5.8e-89:
		tmp = x * ((y - a) / z)
	elif a <= 5000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -0.00019)
		tmp = t_2;
	elseif (a <= 1.7e-135)
		tmp = t_1;
	elseif (a <= 5.8e-89)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 5000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -0.00019)
		tmp = t_2;
	elseif (a <= 1.7e-135)
		tmp = t_1;
	elseif (a <= 5.8e-89)
		tmp = x * ((y - a) / z);
	elseif (a <= 5000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00019], t$95$2, If[LessEqual[a, 1.7e-135], t$95$1, If[LessEqual[a, 5.8e-89], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9000000000000001e-4 or 5e9 < a

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*l/ 68.5%

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

      3. associate-*r/ 91.3%

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

      4. clear-num 91.2%

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

      5. un-div-inv 91.3%

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

   4. Applied egg-rr 91.3%

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

   5. Taylor expanded in a around inf 76.3%

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

   if -1.9000000000000001e-4 < a < 1.69999999999999995e-135 or 5.79999999999999984e-89 < a < 5e9

   1. Initial program 70.3%

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

   3. Taylor expanded in x around 0 56.0%

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

      1. associate-/l* 69.8%

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

   5. Simplified 69.8%

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

   if 1.69999999999999995e-135 < a < 5.79999999999999984e-89

   1. Initial program 65.0%

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

   3. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in z around inf 73.6%

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

      1. associate-*r/ 73.6%

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

      2. neg-mul-1 73.6%

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

      3. sub-neg 73.6%

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

      4. distribute-lft-out-- 73.6%

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

      5. sub-neg 73.6%

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

      6. mul-1-neg 73.6%

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

      7. neg-mul-1 73.6%

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

      8. remove-double-neg 73.6%

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

   8. Simplified 73.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00019:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 5000000000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ (- y z) (/ a t)))))
   (if (<= a -8e+145)
     t_2
     (if (<= a 1.85e-135)
       t_1
       (if (<= a 5.7e-89) (* x (/ (- y a) z)) (if (<= a 7.6e+134) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -8e+145) {
		tmp = t_2;
	} else if (a <= 1.85e-135) {
		tmp = t_1;
	} else if (a <= 5.7e-89) {
		tmp = x * ((y - a) / z);
	} else if (a <= 7.6e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + ((y - z) / (a / t))
    if (a <= (-8d+145)) then
        tmp = t_2
    else if (a <= 1.85d-135) then
        tmp = t_1
    else if (a <= 5.7d-89) then
        tmp = x * ((y - a) / z)
    else if (a <= 7.6d+134) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + ((y - z) / (a / t));
	double tmp;
	if (a <= -8e+145) {
		tmp = t_2;
	} else if (a <= 1.85e-135) {
		tmp = t_1;
	} else if (a <= 5.7e-89) {
		tmp = x * ((y - a) / z);
	} else if (a <= 7.6e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + ((y - z) / (a / t))
	tmp = 0
	if a <= -8e+145:
		tmp = t_2
	elif a <= 1.85e-135:
		tmp = t_1
	elif a <= 5.7e-89:
		tmp = x * ((y - a) / z)
	elif a <= 7.6e+134:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(y - z) / Float64(a / t)))
	tmp = 0.0
	if (a <= -8e+145)
		tmp = t_2;
	elseif (a <= 1.85e-135)
		tmp = t_1;
	elseif (a <= 5.7e-89)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 7.6e+134)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + ((y - z) / (a / t));
	tmp = 0.0;
	if (a <= -8e+145)
		tmp = t_2;
	elseif (a <= 1.85e-135)
		tmp = t_1;
	elseif (a <= 5.7e-89)
		tmp = x * ((y - a) / z);
	elseif (a <= 7.6e+134)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+145], t$95$2, If[LessEqual[a, 1.85e-135], t$95$1, If[LessEqual[a, 5.7e-89], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+134], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.9999999999999999e145 or 7.59999999999999997e134 < a

   1. Initial program 94.4%

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

      1. clear-num 94.2%

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

      2. un-div-inv 94.1%

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

   4. Applied egg-rr 94.1%

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

   5. Taylor expanded in t around inf 86.6%

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

   6. Taylor expanded in a around inf 82.9%

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

   if -7.9999999999999999e145 < a < 1.8499999999999999e-135 or 5.7000000000000002e-89 < a < 7.59999999999999997e134

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0 50.4%

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

      1. associate-/l* 63.5%

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

   5. Simplified 63.5%

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

   if 1.8499999999999999e-135 < a < 5.7000000000000002e-89

   1. Initial program 65.0%

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

   3. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in z around inf 73.6%

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

      1. associate-*r/ 73.6%

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

      2. neg-mul-1 73.6%

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

      3. sub-neg 73.6%

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

      4. distribute-lft-out-- 73.6%

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

      5. sub-neg 73.6%

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

      6. mul-1-neg 73.6%

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

      7. neg-mul-1 73.6%

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

      8. remove-double-neg 73.6%

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

   8. Simplified 73.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+145}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+142}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -9e+142)
     (- x (* z (/ t (- a z))))
     (if (<= a 1.22e-135)
       t_1
       (if (<= a 5.7e-89)
         (* x (/ (- y a) z))
         (if (<= a 1.35e+135) t_1 (+ x (/ (- y z) (/ a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -9e+142) {
		tmp = x - (z * (t / (a - z)));
	} else if (a <= 1.22e-135) {
		tmp = t_1;
	} else if (a <= 5.7e-89) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.35e+135) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-9d+142)) then
        tmp = x - (z * (t / (a - z)))
    else if (a <= 1.22d-135) then
        tmp = t_1
    else if (a <= 5.7d-89) then
        tmp = x * ((y - a) / z)
    else if (a <= 1.35d+135) then
        tmp = t_1
    else
        tmp = x + ((y - z) / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -9e+142) {
		tmp = x - (z * (t / (a - z)));
	} else if (a <= 1.22e-135) {
		tmp = t_1;
	} else if (a <= 5.7e-89) {
		tmp = x * ((y - a) / z);
	} else if (a <= 1.35e+135) {
		tmp = t_1;
	} else {
		tmp = x + ((y - z) / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -9e+142:
		tmp = x - (z * (t / (a - z)))
	elif a <= 1.22e-135:
		tmp = t_1
	elif a <= 5.7e-89:
		tmp = x * ((y - a) / z)
	elif a <= 1.35e+135:
		tmp = t_1
	else:
		tmp = x + ((y - z) / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (a <= -9e+142)
		tmp = Float64(x - Float64(z * Float64(t / Float64(a - z))));
	elseif (a <= 1.22e-135)
		tmp = t_1;
	elseif (a <= 5.7e-89)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (a <= 1.35e+135)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (a <= -9e+142)
		tmp = x - (z * (t / (a - z)));
	elseif (a <= 1.22e-135)
		tmp = t_1;
	elseif (a <= 5.7e-89)
		tmp = x * ((y - a) / z);
	elseif (a <= 1.35e+135)
		tmp = t_1;
	else
		tmp = x + ((y - z) / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+142], N[(x - N[(z * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e-135], t$95$1, If[LessEqual[a, 5.7e-89], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+135], t$95$1, N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.9999999999999998e142

   1. Initial program 96.0%

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

      1. clear-num 95.3%

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

      2. un-div-inv 95.3%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in t around inf 88.0%

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

   6. Taylor expanded in y around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. *-commutative 74.8%

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

      3. associate-*r/ 85.4%

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

      4. unsub-neg 85.4%

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

   8. Simplified 85.4%

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

   if -8.9999999999999998e142 < a < 1.22e-135 or 5.7000000000000002e-89 < a < 1.34999999999999992e135

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0 50.4%

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

      1. associate-/l* 63.5%

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

   5. Simplified 63.5%

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

   if 1.22e-135 < a < 5.7000000000000002e-89

   1. Initial program 65.0%

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

   3. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in z around inf 73.6%

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

      1. associate-*r/ 73.6%

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

      2. neg-mul-1 73.6%

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

      3. sub-neg 73.6%

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

      4. distribute-lft-out-- 73.6%

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

      5. sub-neg 73.6%

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

      6. mul-1-neg 73.6%

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

      7. neg-mul-1 73.6%

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

      8. remove-double-neg 73.6%

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

   8. Simplified 73.6%

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

   if 1.34999999999999992e135 < a

   1. Initial program 93.2%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 93.2%

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

   4. Applied egg-rr 93.2%

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

   5. Taylor expanded in t around inf 85.5%

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

   6. Taylor expanded in a around inf 81.2%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+142}:\\ \;\;\;\;x - z \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+135}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+178}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -1.1e+178)
     t
     (if (<= z 2.6e+44)
       t_1
       (if (<= z 9.6e+77) (* x (/ y z)) (if (<= z 8.2e+96) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.1e+178) {
		tmp = t;
	} else if (z <= 2.6e+44) {
		tmp = t_1;
	} else if (z <= 9.6e+77) {
		tmp = x * (y / z);
	} else if (z <= 8.2e+96) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-1.1d+178)) then
        tmp = t
    else if (z <= 2.6d+44) then
        tmp = t_1
    else if (z <= 9.6d+77) then
        tmp = x * (y / z)
    else if (z <= 8.2d+96) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.1e+178) {
		tmp = t;
	} else if (z <= 2.6e+44) {
		tmp = t_1;
	} else if (z <= 9.6e+77) {
		tmp = x * (y / z);
	} else if (z <= 8.2e+96) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.1e+178:
		tmp = t
	elif z <= 2.6e+44:
		tmp = t_1
	elif z <= 9.6e+77:
		tmp = x * (y / z)
	elif z <= 8.2e+96:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.1e+178)
		tmp = t;
	elseif (z <= 2.6e+44)
		tmp = t_1;
	elseif (z <= 9.6e+77)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 8.2e+96)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.1e+178)
		tmp = t;
	elseif (z <= 2.6e+44)
		tmp = t_1;
	elseif (z <= 9.6e+77)
		tmp = x * (y / z);
	elseif (z <= 8.2e+96)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+178], t, If[LessEqual[z, 2.6e+44], t$95$1, If[LessEqual[z, 9.6e+77], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+96], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999999e178 or 8.19999999999999996e96 < 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 48.4%

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

   if -1.09999999999999999e178 < z < 2.5999999999999999e44 or 9.5999999999999994e77 < z < 8.19999999999999996e96

   1. Initial program 88.9%

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

      1. clear-num 88.8%

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

      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 t around inf 72.9%

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

   6. Taylor expanded in z around 0 50.1%

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

   if 2.5999999999999999e44 < z < 9.5999999999999994e77

   1. Initial program 66.9%

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

   3. Taylor expanded in x around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in a around 0 63.3%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+178}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+96}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+178}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -1.1e+178)
     t
     (if (<= z 2.15e+44)
       t_1
       (if (<= z 1.25e+78) (* x (/ (- y a) z)) (if (<= z 2.2e+99) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.1e+178) {
		tmp = t;
	} else if (z <= 2.15e+44) {
		tmp = t_1;
	} else if (z <= 1.25e+78) {
		tmp = x * ((y - a) / z);
	} else if (z <= 2.2e+99) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-1.1d+178)) then
        tmp = t
    else if (z <= 2.15d+44) then
        tmp = t_1
    else if (z <= 1.25d+78) then
        tmp = x * ((y - a) / z)
    else if (z <= 2.2d+99) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.1e+178) {
		tmp = t;
	} else if (z <= 2.15e+44) {
		tmp = t_1;
	} else if (z <= 1.25e+78) {
		tmp = x * ((y - a) / z);
	} else if (z <= 2.2e+99) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.1e+178:
		tmp = t
	elif z <= 2.15e+44:
		tmp = t_1
	elif z <= 1.25e+78:
		tmp = x * ((y - a) / z)
	elif z <= 2.2e+99:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.1e+178)
		tmp = t;
	elseif (z <= 2.15e+44)
		tmp = t_1;
	elseif (z <= 1.25e+78)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 2.2e+99)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.1e+178)
		tmp = t;
	elseif (z <= 2.15e+44)
		tmp = t_1;
	elseif (z <= 1.25e+78)
		tmp = x * ((y - a) / z);
	elseif (z <= 2.2e+99)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+178], t, If[LessEqual[z, 2.15e+44], t$95$1, If[LessEqual[z, 1.25e+78], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+99], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999999e178 or 2.19999999999999978e99 < 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 48.4%

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

   if -1.09999999999999999e178 < z < 2.14999999999999991e44 or 1.24999999999999996e78 < z < 2.19999999999999978e99

   1. Initial program 88.9%

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

      1. clear-num 88.8%

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

      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 t around inf 72.9%

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

   6. Taylor expanded in z around 0 50.1%

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

   if 2.14999999999999991e44 < z < 1.24999999999999996e78

   1. Initial program 66.9%

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

   3. Taylor expanded in x around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in z around inf 63.7%

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

      1. associate-*r/ 63.7%

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

      2. neg-mul-1 63.7%

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

      3. sub-neg 63.7%

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

      4. distribute-lft-out-- 63.7%

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

      5. sub-neg 63.7%

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

      6. mul-1-neg 63.7%

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

      7. neg-mul-1 63.7%

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

      8. remove-double-neg 63.7%

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

   8. Simplified 63.7%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+178}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+99}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+178}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -1.12e+178)
     t
     (if (<= z 1.6e+44)
       t_1
       (if (<= z 9.5e+77) (* y (/ x (- z a))) (if (<= z 6e+97) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.12e+178) {
		tmp = t;
	} else if (z <= 1.6e+44) {
		tmp = t_1;
	} else if (z <= 9.5e+77) {
		tmp = y * (x / (z - a));
	} else if (z <= 6e+97) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-1.12d+178)) then
        tmp = t
    else if (z <= 1.6d+44) then
        tmp = t_1
    else if (z <= 9.5d+77) then
        tmp = y * (x / (z - a))
    else if (z <= 6d+97) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.12e+178) {
		tmp = t;
	} else if (z <= 1.6e+44) {
		tmp = t_1;
	} else if (z <= 9.5e+77) {
		tmp = y * (x / (z - a));
	} else if (z <= 6e+97) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.12e+178:
		tmp = t
	elif z <= 1.6e+44:
		tmp = t_1
	elif z <= 9.5e+77:
		tmp = y * (x / (z - a))
	elif z <= 6e+97:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.12e+178)
		tmp = t;
	elseif (z <= 1.6e+44)
		tmp = t_1;
	elseif (z <= 9.5e+77)
		tmp = Float64(y * Float64(x / Float64(z - a)));
	elseif (z <= 6e+97)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.12e+178)
		tmp = t;
	elseif (z <= 1.6e+44)
		tmp = t_1;
	elseif (z <= 9.5e+77)
		tmp = y * (x / (z - a));
	elseif (z <= 6e+97)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+178], t, If[LessEqual[z, 1.6e+44], t$95$1, If[LessEqual[z, 9.5e+77], N[(y * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+97], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12000000000000001e178 or 5.9999999999999997e97 < 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 48.4%

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

   if -1.12000000000000001e178 < z < 1.60000000000000002e44 or 9.4999999999999998e77 < z < 5.9999999999999997e97

   1. Initial program 88.9%

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

      1. clear-num 88.8%

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

      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 t around inf 73.3%

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

   6. Taylor expanded in z around 0 50.4%

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

   if 1.60000000000000002e44 < z < 9.4999999999999998e77

   1. Initial program 70.6%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. div-sub 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around 0 63.0%

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

      1. neg-mul-1 63.0%

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

      2. distribute-neg-frac 63.0%

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

   8. Simplified 63.0%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+178}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+97}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -4.4e+60)
     t_1
     (if (<= x 2.1e+43)
       (* t (/ (- y z) (- a z)))
       (if (<= x 7.2e+168) (* y (/ (- t x) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.4e+60) {
		tmp = t_1;
	} else if (x <= 2.1e+43) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 7.2e+168) {
		tmp = y * ((t - x) / (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 * (1.0d0 - (y / a))
    if (x <= (-4.4d+60)) then
        tmp = t_1
    else if (x <= 2.1d+43) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 7.2d+168) then
        tmp = y * ((t - x) / (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 * (1.0 - (y / a));
	double tmp;
	if (x <= -4.4e+60) {
		tmp = t_1;
	} else if (x <= 2.1e+43) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 7.2e+168) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -4.4e+60:
		tmp = t_1
	elif x <= 2.1e+43:
		tmp = t * ((y - z) / (a - z))
	elif x <= 7.2e+168:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -4.4e+60)
		tmp = t_1;
	elseif (x <= 2.1e+43)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 7.2e+168)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -4.4e+60)
		tmp = t_1;
	elseif (x <= 2.1e+43)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 7.2e+168)
		tmp = y * ((t - x) / (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[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.4e+60], t$95$1, If[LessEqual[x, 2.1e+43], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+168], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.39999999999999992e60 or 7.1999999999999999e168 < x

   1. Initial program 71.9%

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

   3. Taylor expanded in x around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in z around 0 58.1%

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

   if -4.39999999999999992e60 < x < 2.10000000000000002e43

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 55.1%

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

      1. associate-/l* 69.0%

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

   5. Simplified 69.0%

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

   if 2.10000000000000002e43 < x < 7.1999999999999999e168

   1. Initial program 73.5%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. div-sub 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.2e+60)
   (* x (- 1.0 (/ y a)))
   (if (<= x 5.5e+62)
     (* t (/ (- y z) (- a z)))
     (if (<= x 2.3e+157) (* y (/ x (- z a))) (+ x (/ (* y t) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.2e+60) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= 5.5e+62) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 2.3e+157) {
		tmp = y * (x / (z - a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5.2d+60)) then
        tmp = x * (1.0d0 - (y / a))
    else if (x <= 5.5d+62) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 2.3d+157) then
        tmp = y * (x / (z - a))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.2e+60) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= 5.5e+62) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 2.3e+157) {
		tmp = y * (x / (z - a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.2e+60:
		tmp = x * (1.0 - (y / a))
	elif x <= 5.5e+62:
		tmp = t * ((y - z) / (a - z))
	elif x <= 2.3e+157:
		tmp = y * (x / (z - a))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.2e+60)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (x <= 5.5e+62)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 2.3e+157)
		tmp = Float64(y * Float64(x / Float64(z - a)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.2e+60)
		tmp = x * (1.0 - (y / a));
	elseif (x <= 5.5e+62)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 2.3e+157)
		tmp = y * (x / (z - a));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.2e+60], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+62], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+157], N[(y * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.20000000000000016e60

   1. Initial program 74.7%

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

   3. Taylor expanded in x around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in z around 0 58.8%

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

   if -5.20000000000000016e60 < x < 5.4999999999999997e62

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0 55.4%

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

      1. associate-/l* 68.9%

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

   5. Simplified 68.9%

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

   if 5.4999999999999997e62 < x < 2.30000000000000004e157

   1. Initial program 73.8%

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

   3. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in t around 0 68.0%

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

      1. neg-mul-1 68.0%

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

      2. distribute-neg-frac 68.0%

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

   8. Simplified 68.0%

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

   if 2.30000000000000004e157 < x

   1. Initial program 66.3%

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

      1. clear-num 66.2%

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

      2. un-div-inv 66.2%

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

   4. Applied egg-rr 66.2%

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

   5. Taylor expanded in t around inf 55.2%

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

   6. Taylor expanded in z around 0 55.3%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \frac{x}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-164} \lor \neg \left(t \leq 1.36 \cdot 10^{-135}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e-164) (not (<= t 1.36e-135)))
   (+ x (/ (- y z) (/ (- a z) t)))
   (* x (+ (/ (- y z) (- z a)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e-164) || !(t <= 1.36e-135)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = x * (((y - z) / (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 ((t <= (-2.8d-164)) .or. (.not. (t <= 1.36d-135))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = x * (((y - z) / (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 ((t <= -2.8e-164) || !(t <= 1.36e-135)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.8e-164) or not (t <= 1.36e-135):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.8e-164) || !(t <= 1.36e-135))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.8e-164) || ~((t <= 1.36e-135)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = x * (((y - z) / (z - a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.8e-164], N[Not[LessEqual[t, 1.36e-135]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8000000000000001e-164 or 1.36e-135 < t

   1. Initial program 83.2%

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

      1. clear-num 83.0%

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

      2. un-div-inv 83.1%

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

   4. Applied egg-rr 83.1%

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

   5. Taylor expanded in t around inf 74.9%

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

   if -2.8000000000000001e-164 < t < 1.36e-135

   1. Initial program 72.9%

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

   3. Taylor expanded in x around inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-164} \lor \neg \left(t \leq 1.36 \cdot 10^{-135}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.12e-13)
   x
   (if (<= a 1.06e-88) (* x (/ y z)) (if (<= a 7.6e+134) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.12e-13) {
		tmp = x;
	} else if (a <= 1.06e-88) {
		tmp = x * (y / z);
	} else if (a <= 7.6e+134) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.12d-13)) then
        tmp = x
    else if (a <= 1.06d-88) then
        tmp = x * (y / z)
    else if (a <= 7.6d+134) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.12e-13) {
		tmp = x;
	} else if (a <= 1.06e-88) {
		tmp = x * (y / z);
	} else if (a <= 7.6e+134) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.12e-13:
		tmp = x
	elif a <= 1.06e-88:
		tmp = x * (y / z)
	elif a <= 7.6e+134:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.12e-13)
		tmp = x;
	elseif (a <= 1.06e-88)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 7.6e+134)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.12e-13)
		tmp = x;
	elseif (a <= 1.06e-88)
		tmp = x * (y / z);
	elseif (a <= 7.6e+134)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.12e-13], x, If[LessEqual[a, 1.06e-88], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.6e+134], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12e-13 or 7.59999999999999997e134 < a

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 51.2%

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

   if -1.12e-13 < a < 1.06e-88

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf 27.8%

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

      1. mul-1-neg 27.8%

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

      2. unsub-neg 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in a around 0 36.5%

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

   if 1.06e-88 < a < 7.59999999999999997e134

   1. Initial program 77.4%

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

   3. Taylor expanded in z around inf 26.8%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.3e-5) x (if (<= a 7.6e+134) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e-5) {
		tmp = x;
	} else if (a <= 7.6e+134) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.3d-5)) then
        tmp = x
    else if (a <= 7.6d+134) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3e-5) {
		tmp = x;
	} else if (a <= 7.6e+134) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.3e-5:
		tmp = x
	elif a <= 7.6e+134:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3e-5)
		tmp = x;
	elseif (a <= 7.6e+134)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.3e-5)
		tmp = x;
	elseif (a <= 7.6e+134)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3e-5], x, If[LessEqual[a, 7.6e+134], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.29999999999999992e-5 or 7.59999999999999997e134 < a

   1. Initial program 92.5%

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

   3. Taylor expanded in a around inf 52.1%

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

   if -1.29999999999999992e-5 < a < 7.59999999999999997e134

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 29.7%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+134}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 25.8% 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 80.3%

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

3. Taylor expanded in z around inf 21.8%

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

4. Final simplification 21.8%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024078 
(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)))))