Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.5% → 90.5%

Time: 17.9s

Alternatives: 20

Speedup: 0.9×

Specification

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.5% accurate, 1.0× speedup

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-246} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-246) (not (<= t_1 0.0)))
     (fma (/ (- y z) (- a z)) (- t x) x)
     (+ t (/ (* (- t x) (- a 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 <= -5e-246) || !(t_1 <= 0.0)) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-246) || !(t_1 <= 0.0))
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-246], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.9999999999999997e-246 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 71.3%

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

      1. +-commutative 71.3%

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

      2. associate-*l/ 89.4%

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

      3. fma-def 89.5%

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

   3. Simplified 89.5%

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

   if -4.9999999999999997e-246 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 13.7%

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

      1. +-commutative 13.7%

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

      2. associate-*l/ 13.8%

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

      3. fma-def 13.8%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in z around -inf 99.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-246} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 2: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-246} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-246) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (* (- t x) (- a 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 <= -5e-246) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-5d-246)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-246) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - 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 <= -5e-246) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -5e-246) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - 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 <= -5e-246) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-246], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.9999999999999997e-246 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 71.3%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   if -4.9999999999999997e-246 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 13.7%

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

      1. +-commutative 13.7%

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

      2. associate-*l/ 13.8%

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

      3. fma-def 13.8%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in z around -inf 99.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-246} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 3: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+92} \lor \neg \left(z \leq 1.62 \cdot 10^{+146}\right) \land z \leq 9.5 \cdot 10^{+190}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ x (/ z (- y a))))))
   (if (<= z -4.5e+25)
     t_1
     (if (<= z 2.6e-157)
       (+ x (/ (- t x) (/ a (- y z))))
       (if (or (<= z 4.2e+92) (and (not (<= z 1.62e+146)) (<= z 9.5e+190)))
         (+ x (/ (- y z) (/ (- a z) t)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (z <= -4.5e+25) {
		tmp = t_1;
	} else if (z <= 2.6e-157) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if ((z <= 4.2e+92) || (!(z <= 1.62e+146) && (z <= 9.5e+190))) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x / (z / (y - a)))
    if (z <= (-4.5d+25)) then
        tmp = t_1
    else if (z <= 2.6d-157) then
        tmp = x + ((t - x) / (a / (y - z)))
    else if ((z <= 4.2d+92) .or. (.not. (z <= 1.62d+146)) .and. (z <= 9.5d+190)) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (z <= -4.5e+25) {
		tmp = t_1;
	} else if (z <= 2.6e-157) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if ((z <= 4.2e+92) || (!(z <= 1.62e+146) && (z <= 9.5e+190))) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x / (z / (y - a)))
	tmp = 0
	if z <= -4.5e+25:
		tmp = t_1
	elif z <= 2.6e-157:
		tmp = x + ((t - x) / (a / (y - z)))
	elif (z <= 4.2e+92) or (not (z <= 1.62e+146) and (z <= 9.5e+190)):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -4.5e+25)
		tmp = t_1;
	elseif (z <= 2.6e-157)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	elseif ((z <= 4.2e+92) || (!(z <= 1.62e+146) && (z <= 9.5e+190)))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x / (z / (y - a)));
	tmp = 0.0;
	if (z <= -4.5e+25)
		tmp = t_1;
	elseif (z <= 2.6e-157)
		tmp = x + ((t - x) / (a / (y - z)));
	elseif ((z <= 4.2e+92) || (~((z <= 1.62e+146)) && (z <= 9.5e+190)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+25], t$95$1, If[LessEqual[z, 2.6e-157], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.2e+92], And[N[Not[LessEqual[z, 1.62e+146]], $MachinePrecision], LessEqual[z, 9.5e+190]]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5000000000000003e25 or 4.19999999999999972e92 < z < 1.62e146 or 9.4999999999999995e190 < z

   1. Initial program 43.8%

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

      1. +-commutative 43.8%

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

      2. associate-*l/ 69.8%

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

      3. fma-def 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in z around inf 66.5%

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

      1. associate-/l* 85.3%

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

      2. distribute-lft-out-- 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in t around 0 69.2%

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

      1. associate-/l* 81.2%

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

   9. Simplified 81.2%

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

   if -4.5000000000000003e25 < z < 2.59999999999999988e-157

   1. Initial program 92.1%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 78.6%

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

      1. associate-/l* 85.0%

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

   6. Simplified 85.0%

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

   if 2.59999999999999988e-157 < z < 4.19999999999999972e92 or 1.62e146 < z < 9.4999999999999995e190

   1. Initial program 69.7%

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

      1. associate-/l* 85.9%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in t around inf 80.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+25}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+92} \lor \neg \left(z \leq 1.62 \cdot 10^{+146}\right) \land z \leq 9.5 \cdot 10^{+190}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 4: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3600:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1560000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+74} \lor \neg \left(x \leq 2.8 \cdot 10^{+132}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ x (/ z y)))))
   (if (<= x -5.6e+88)
     t_1
     (if (<= x -3600.0)
       (+ x (/ t (/ a y)))
       (if (<= x 1560000.0)
         (* t (/ (- y z) (- a z)))
         (if (or (<= x 1.02e+74) (not (<= x 2.8e+132)))
           (- x (/ x (/ a y)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / y));
	double tmp;
	if (x <= -5.6e+88) {
		tmp = t_1;
	} else if (x <= -3600.0) {
		tmp = x + (t / (a / y));
	} else if (x <= 1560000.0) {
		tmp = t * ((y - z) / (a - z));
	} else if ((x <= 1.02e+74) || !(x <= 2.8e+132)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x / (z / y))
    if (x <= (-5.6d+88)) then
        tmp = t_1
    else if (x <= (-3600.0d0)) then
        tmp = x + (t / (a / y))
    else if (x <= 1560000.0d0) then
        tmp = t * ((y - z) / (a - z))
    else if ((x <= 1.02d+74) .or. (.not. (x <= 2.8d+132))) then
        tmp = x - (x / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / y));
	double tmp;
	if (x <= -5.6e+88) {
		tmp = t_1;
	} else if (x <= -3600.0) {
		tmp = x + (t / (a / y));
	} else if (x <= 1560000.0) {
		tmp = t * ((y - z) / (a - z));
	} else if ((x <= 1.02e+74) || !(x <= 2.8e+132)) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x / (z / y))
	tmp = 0
	if x <= -5.6e+88:
		tmp = t_1
	elif x <= -3600.0:
		tmp = x + (t / (a / y))
	elif x <= 1560000.0:
		tmp = t * ((y - z) / (a - z))
	elif (x <= 1.02e+74) or not (x <= 2.8e+132):
		tmp = x - (x / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x / Float64(z / y)))
	tmp = 0.0
	if (x <= -5.6e+88)
		tmp = t_1;
	elseif (x <= -3600.0)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (x <= 1560000.0)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif ((x <= 1.02e+74) || !(x <= 2.8e+132))
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x / (z / y));
	tmp = 0.0;
	if (x <= -5.6e+88)
		tmp = t_1;
	elseif (x <= -3600.0)
		tmp = x + (t / (a / y));
	elseif (x <= 1560000.0)
		tmp = t * ((y - z) / (a - z));
	elseif ((x <= 1.02e+74) || ~((x <= 2.8e+132)))
		tmp = x - (x / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+88], t$95$1, If[LessEqual[x, -3600.0], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1560000.0], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.02e+74], N[Not[LessEqual[x, 2.8e+132]], $MachinePrecision]], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.59999999999999977e88 or 1.02000000000000005e74 < x < 2.7999999999999999e132

   1. Initial program 48.1%

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

      1. +-commutative 48.1%

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

      2. associate-*l/ 75.2%

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

      3. fma-def 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in z around inf 54.3%

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

      1. associate-/l* 73.3%

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

      2. distribute-lft-out-- 73.3%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in t around 0 54.4%

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

      1. associate-/l* 69.7%

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

   9. Simplified 69.7%

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

   10. Taylor expanded in a around 0 51.0%

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

       1. +-commutative 51.0%

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

       2. associate-/l* 62.9%

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

   12. Simplified 62.9%

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

   if -5.59999999999999977e88 < x < -3600

   1. Initial program 88.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 99.2%

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

   5. Taylor expanded in z around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-/l* 83.1%

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

   7. Simplified 83.1%

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

   if -3600 < x < 1.56e6

   1. Initial program 76.4%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. associate-*l/ 77.4%

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

      3. *-commutative 77.4%

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

   6. Simplified 77.4%

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

   if 1.56e6 < x < 1.02000000000000005e74 or 2.7999999999999999e132 < x

   1. Initial program 58.2%

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

      1. associate-*l/ 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in z around 0 55.5%

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

      1. associate-/l* 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in t around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. associate-/l* 58.8%

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

   9. Simplified 58.8%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+88}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -3600:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1560000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+74} \lor \neg \left(x \leq 2.8 \cdot 10^{+132}\right):\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 5: 71.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+147} \lor \neg \left(z \leq 1.06 \cdot 10^{+191}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ x (/ z (- y a))))))
   (if (<= z -1.16e+25)
     t_1
     (if (<= z 2.6e+58)
       (+ x (* (- t x) (/ y a)))
       (if (or (<= z 9.8e+147) (not (<= z 1.06e+191)))
         t_1
         (* t (/ (- y z) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (z <= -1.16e+25) {
		tmp = t_1;
	} else if (z <= 2.6e+58) {
		tmp = x + ((t - x) * (y / a));
	} else if ((z <= 9.8e+147) || !(z <= 1.06e+191)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x / (z / (y - a)))
    if (z <= (-1.16d+25)) then
        tmp = t_1
    else if (z <= 2.6d+58) then
        tmp = x + ((t - x) * (y / a))
    else if ((z <= 9.8d+147) .or. (.not. (z <= 1.06d+191))) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (z <= -1.16e+25) {
		tmp = t_1;
	} else if (z <= 2.6e+58) {
		tmp = x + ((t - x) * (y / a));
	} else if ((z <= 9.8e+147) || !(z <= 1.06e+191)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x / (z / (y - a)))
	tmp = 0
	if z <= -1.16e+25:
		tmp = t_1
	elif z <= 2.6e+58:
		tmp = x + ((t - x) * (y / a))
	elif (z <= 9.8e+147) or not (z <= 1.06e+191):
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -1.16e+25)
		tmp = t_1;
	elseif (z <= 2.6e+58)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif ((z <= 9.8e+147) || !(z <= 1.06e+191))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x / (z / (y - a)));
	tmp = 0.0;
	if (z <= -1.16e+25)
		tmp = t_1;
	elseif (z <= 2.6e+58)
		tmp = x + ((t - x) * (y / a));
	elseif ((z <= 9.8e+147) || ~((z <= 1.06e+191)))
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.16e+25], t$95$1, If[LessEqual[z, 2.6e+58], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 9.8e+147], N[Not[LessEqual[z, 1.06e+191]], $MachinePrecision]], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15999999999999992e25 or 2.59999999999999988e58 < z < 9.7999999999999996e147 or 1.06000000000000003e191 < z

   1. Initial program 44.9%

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

      1. +-commutative 44.9%

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

      2. associate-*l/ 72.1%

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

      3. fma-def 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in z around inf 65.9%

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

      1. associate-/l* 85.1%

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

      2. distribute-lft-out-- 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in t around 0 69.0%

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

      1. associate-/l* 79.0%

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

   9. Simplified 79.0%

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

   if -1.15999999999999992e25 < z < 2.59999999999999988e58

   1. Initial program 89.4%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 74.9%

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

   if 9.7999999999999996e147 < z < 1.06000000000000003e191

   1. Initial program 33.7%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around 0 23.9%

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

      1. *-commutative 23.9%

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

      2. associate-*l/ 75.8%

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

      3. *-commutative 75.8%

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

   6. Simplified 75.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+25}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+147} \lor \neg \left(z \leq 1.06 \cdot 10^{+191}\right):\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 6: 70.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+146} \lor \neg \left(z \leq 5.5 \cdot 10^{+191}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ x (/ z (- y a))))))
   (if (<= z -2.2e+25)
     t_1
     (if (<= z 3.9e+58)
       (+ x (/ y (/ a (- t x))))
       (if (or (<= z 3.35e+146) (not (<= z 5.5e+191)))
         t_1
         (* t (/ (- y z) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (z <= -2.2e+25) {
		tmp = t_1;
	} else if (z <= 3.9e+58) {
		tmp = x + (y / (a / (t - x)));
	} else if ((z <= 3.35e+146) || !(z <= 5.5e+191)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x / (z / (y - a)))
    if (z <= (-2.2d+25)) then
        tmp = t_1
    else if (z <= 3.9d+58) then
        tmp = x + (y / (a / (t - x)))
    else if ((z <= 3.35d+146) .or. (.not. (z <= 5.5d+191))) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (z <= -2.2e+25) {
		tmp = t_1;
	} else if (z <= 3.9e+58) {
		tmp = x + (y / (a / (t - x)));
	} else if ((z <= 3.35e+146) || !(z <= 5.5e+191)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x / (z / (y - a)))
	tmp = 0
	if z <= -2.2e+25:
		tmp = t_1
	elif z <= 3.9e+58:
		tmp = x + (y / (a / (t - x)))
	elif (z <= 3.35e+146) or not (z <= 5.5e+191):
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -2.2e+25)
		tmp = t_1;
	elseif (z <= 3.9e+58)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif ((z <= 3.35e+146) || !(z <= 5.5e+191))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x / (z / (y - a)));
	tmp = 0.0;
	if (z <= -2.2e+25)
		tmp = t_1;
	elseif (z <= 3.9e+58)
		tmp = x + (y / (a / (t - x)));
	elseif ((z <= 3.35e+146) || ~((z <= 5.5e+191)))
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+25], t$95$1, If[LessEqual[z, 3.9e+58], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.35e+146], N[Not[LessEqual[z, 5.5e+191]], $MachinePrecision]], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e25 or 3.9000000000000001e58 < z < 3.35000000000000003e146 or 5.5000000000000002e191 < z

   1. Initial program 44.9%

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

      1. +-commutative 44.9%

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

      2. associate-*l/ 72.1%

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

      3. fma-def 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in z around inf 65.9%

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

      1. associate-/l* 85.1%

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

      2. distribute-lft-out-- 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in t around 0 69.0%

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

      1. associate-/l* 79.0%

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

   9. Simplified 79.0%

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

   if -2.2000000000000001e25 < z < 3.9000000000000001e58

   1. Initial program 89.4%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 70.6%

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

      1. associate-/l* 75.6%

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

   6. Simplified 75.6%

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

   if 3.35000000000000003e146 < z < 5.5000000000000002e191

   1. Initial program 33.7%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around 0 23.9%

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

      1. *-commutative 23.9%

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

      2. associate-*l/ 75.8%

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

      3. *-commutative 75.8%

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

   6. Simplified 75.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+25}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+146} \lor \neg \left(z \leq 5.5 \cdot 10^{+191}\right):\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 7: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+148} \lor \neg \left(z \leq 2 \cdot 10^{+191}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ x (/ z (- y a))))))
   (if (<= z -5.2e+25)
     t_1
     (if (<= z 8.2e+58)
       (+ x (/ (- t x) (/ a (- y z))))
       (if (or (<= z 2e+148) (not (<= z 2e+191)))
         t_1
         (* t (/ (- y z) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (z <= -5.2e+25) {
		tmp = t_1;
	} else if (z <= 8.2e+58) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if ((z <= 2e+148) || !(z <= 2e+191)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x / (z / (y - a)))
    if (z <= (-5.2d+25)) then
        tmp = t_1
    else if (z <= 8.2d+58) then
        tmp = x + ((t - x) / (a / (y - z)))
    else if ((z <= 2d+148) .or. (.not. (z <= 2d+191))) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (z <= -5.2e+25) {
		tmp = t_1;
	} else if (z <= 8.2e+58) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else if ((z <= 2e+148) || !(z <= 2e+191)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x / (z / (y - a)))
	tmp = 0
	if z <= -5.2e+25:
		tmp = t_1
	elif z <= 8.2e+58:
		tmp = x + ((t - x) / (a / (y - z)))
	elif (z <= 2e+148) or not (z <= 2e+191):
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (z <= -5.2e+25)
		tmp = t_1;
	elseif (z <= 8.2e+58)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	elseif ((z <= 2e+148) || !(z <= 2e+191))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x / (z / (y - a)));
	tmp = 0.0;
	if (z <= -5.2e+25)
		tmp = t_1;
	elseif (z <= 8.2e+58)
		tmp = x + ((t - x) / (a / (y - z)));
	elseif ((z <= 2e+148) || ~((z <= 2e+191)))
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+25], t$95$1, If[LessEqual[z, 8.2e+58], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2e+148], N[Not[LessEqual[z, 2e+191]], $MachinePrecision]], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999997e25 or 8.2e58 < z < 2.0000000000000001e148 or 2.00000000000000015e191 < z

   1. Initial program 44.9%

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

      1. +-commutative 44.9%

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

      2. associate-*l/ 72.1%

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

      3. fma-def 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in z around inf 65.9%

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

      1. associate-/l* 85.1%

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

      2. distribute-lft-out-- 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in t around 0 69.0%

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

      1. associate-/l* 79.0%

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

   9. Simplified 79.0%

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

   if -5.1999999999999997e25 < z < 8.2e58

   1. Initial program 89.4%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around inf 73.3%

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

      1. associate-/l* 78.4%

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

   6. Simplified 78.4%

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

   if 2.0000000000000001e148 < z < 2.00000000000000015e191

   1. Initial program 33.7%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around 0 23.9%

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

      1. *-commutative 23.9%

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

      2. associate-*l/ 75.8%

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

      3. *-commutative 75.8%

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

   6. Simplified 75.8%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+148} \lor \neg \left(z \leq 2 \cdot 10^{+191}\right):\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 8: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{if}\;x \leq -8 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -880:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1300000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ x (/ z (- y a))))))
   (if (<= x -8e+88)
     t_1
     (if (<= x -880.0)
       (+ x (/ t (/ a y)))
       (if (<= x 1300000.0)
         (* t (/ (- y z) (- a z)))
         (if (<= x 9.4e+72) (- x (/ x (/ a y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (x <= -8e+88) {
		tmp = t_1;
	} else if (x <= -880.0) {
		tmp = x + (t / (a / y));
	} else if (x <= 1300000.0) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 9.4e+72) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (x / (z / (y - a)))
    if (x <= (-8d+88)) then
        tmp = t_1
    else if (x <= (-880.0d0)) then
        tmp = x + (t / (a / y))
    else if (x <= 1300000.0d0) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 9.4d+72) then
        tmp = x - (x / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (x / (z / (y - a)));
	double tmp;
	if (x <= -8e+88) {
		tmp = t_1;
	} else if (x <= -880.0) {
		tmp = x + (t / (a / y));
	} else if (x <= 1300000.0) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 9.4e+72) {
		tmp = x - (x / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (x / (z / (y - a)))
	tmp = 0
	if x <= -8e+88:
		tmp = t_1
	elif x <= -880.0:
		tmp = x + (t / (a / y))
	elif x <= 1300000.0:
		tmp = t * ((y - z) / (a - z))
	elif x <= 9.4e+72:
		tmp = x - (x / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(x / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (x <= -8e+88)
		tmp = t_1;
	elseif (x <= -880.0)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (x <= 1300000.0)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 9.4e+72)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (x / (z / (y - a)));
	tmp = 0.0;
	if (x <= -8e+88)
		tmp = t_1;
	elseif (x <= -880.0)
		tmp = x + (t / (a / y));
	elseif (x <= 1300000.0)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 9.4e+72)
		tmp = x - (x / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(x / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+88], t$95$1, If[LessEqual[x, -880.0], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1300000.0], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.4e+72], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.99999999999999968e88 or 9.40000000000000069e72 < x

   1. Initial program 48.3%

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

      1. +-commutative 48.3%

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

      2. associate-*l/ 69.8%

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

      3. fma-def 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around inf 48.4%

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

      1. associate-/l* 65.3%

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

      2. distribute-lft-out-- 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in t around 0 48.5%

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

      1. associate-/l* 63.1%

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

   9. Simplified 63.1%

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

   if -7.99999999999999968e88 < x < -880

   1. Initial program 88.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 99.2%

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

   5. Taylor expanded in z around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-/l* 83.1%

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

   7. Simplified 83.1%

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

   if -880 < x < 1.3e6

   1. Initial program 76.4%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around 0 61.9%

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

      1. *-commutative 61.9%

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

      2. associate-*l/ 77.4%

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

      3. *-commutative 77.4%

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

   6. Simplified 77.4%

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

   if 1.3e6 < x < 9.40000000000000069e72

   1. Initial program 73.6%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in z around 0 69.2%

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

      1. associate-/l* 69.6%

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

   6. Simplified 69.6%

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

   7. Taylor expanded in t around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. associate-/l* 69.6%

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

   9. Simplified 69.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+88}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \mathbf{elif}\;x \leq -880:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 1300000:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 9: 56.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0023:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 7.9 \cdot 10^{-50}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+19} \lor \neg \left(a \leq 8 \cdot 10^{+172}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{-z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.0023)
   (+ x (/ t (/ a y)))
   (if (<= a 7.9e-50)
     (+ t (/ x (/ z y)))
     (if (or (<= a 8.6e+19) (not (<= a 8e+172)))
       (+ x (/ (* y t) a))
       (+ t (/ x (/ (- z) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.0023) {
		tmp = x + (t / (a / y));
	} else if (a <= 7.9e-50) {
		tmp = t + (x / (z / y));
	} else if ((a <= 8.6e+19) || !(a <= 8e+172)) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t + (x / (-z / 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 (a <= (-0.0023d0)) then
        tmp = x + (t / (a / y))
    else if (a <= 7.9d-50) then
        tmp = t + (x / (z / y))
    else if ((a <= 8.6d+19) .or. (.not. (a <= 8d+172))) then
        tmp = x + ((y * t) / a)
    else
        tmp = t + (x / (-z / 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 (a <= -0.0023) {
		tmp = x + (t / (a / y));
	} else if (a <= 7.9e-50) {
		tmp = t + (x / (z / y));
	} else if ((a <= 8.6e+19) || !(a <= 8e+172)) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t + (x / (-z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.0023:
		tmp = x + (t / (a / y))
	elif a <= 7.9e-50:
		tmp = t + (x / (z / y))
	elif (a <= 8.6e+19) or not (a <= 8e+172):
		tmp = x + ((y * t) / a)
	else:
		tmp = t + (x / (-z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.0023)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (a <= 7.9e-50)
		tmp = Float64(t + Float64(x / Float64(z / y)));
	elseif ((a <= 8.6e+19) || !(a <= 8e+172))
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(t + Float64(x / Float64(Float64(-z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.0023)
		tmp = x + (t / (a / y));
	elseif (a <= 7.9e-50)
		tmp = t + (x / (z / y));
	elseif ((a <= 8.6e+19) || ~((a <= 8e+172)))
		tmp = x + ((y * t) / a);
	else
		tmp = t + (x / (-z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.0023], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.9e-50], N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 8.6e+19], N[Not[LessEqual[a, 8e+172]], $MachinePrecision]], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.0023

   1. Initial program 71.1%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 82.5%

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

   5. Taylor expanded in z around 0 55.8%

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

      1. +-commutative 55.8%

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

      2. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   if -0.0023 < a < 7.9000000000000002e-50

   1. Initial program 65.2%

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

      1. +-commutative 65.2%

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

      2. associate-*l/ 77.6%

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

      3. fma-def 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in z around inf 75.5%

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

      1. associate-/l* 86.6%

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

      2. distribute-lft-out-- 86.6%

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

   6. Simplified 86.6%

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

   7. Taylor expanded in t around 0 68.6%

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

      1. associate-/l* 76.5%

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

   9. Simplified 76.5%

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

   10. Taylor expanded in a around 0 67.7%

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

       1. +-commutative 67.7%

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

       2. associate-/l* 75.7%

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

   12. Simplified 75.7%

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

   if 7.9000000000000002e-50 < a < 8.6e19 or 8.0000000000000007e172 < a

   1. Initial program 66.1%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 83.5%

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

   5. Taylor expanded in z around 0 66.2%

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

   if 8.6e19 < a < 8.0000000000000007e172

   1. Initial program 67.3%

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

      1. +-commutative 67.3%

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

      2. associate-*l/ 83.1%

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

      3. fma-def 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in z around inf 44.5%

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

      1. associate-/l* 58.2%

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

      2. distribute-lft-out-- 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in t around 0 47.8%

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

      1. associate-/l* 55.8%

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

   9. Simplified 55.8%

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

   10. Taylor expanded in y around 0 53.6%

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

       1. associate-*r/ 53.6%

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

       2. neg-mul-1 53.6%

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

   12. Simplified 53.6%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0023:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 7.9 \cdot 10^{-50}:\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+19} \lor \neg \left(a \leq 8 \cdot 10^{+172}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{-z}{a}}\\ \end{array} \]

Alternative 10: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-31} \lor \neg \left(a \leq 2.4 \cdot 10^{-194}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.9e-31) (not (<= a 2.4e-194)))
   (+ x (/ (- y z) (/ (- a z) t)))
   (+ t (/ (* (- t x) (- a y)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.9e-31) || !(a <= 2.4e-194)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.9d-31)) .or. (.not. (a <= 2.4d-194))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.9e-31) || !(a <= 2.4e-194)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.9e-31) or not (a <= 2.4e-194):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.9e-31) || !(a <= 2.4e-194))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.9e-31) || ~((a <= 2.4e-194)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.9e-31], N[Not[LessEqual[a, 2.4e-194]], $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] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9000000000000001e-31 or 2.4e-194 < a

   1. Initial program 67.3%

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

      1. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in t around inf 75.7%

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

   if -2.9000000000000001e-31 < a < 2.4e-194

   1. Initial program 66.6%

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

      1. +-commutative 66.6%

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

      2. associate-*l/ 75.8%

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

      3. fma-def 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in z around -inf 83.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-31} \lor \neg \left(a \leq 2.4 \cdot 10^{-194}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 11: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-9} \lor \neg \left(a \leq 1.3 \cdot 10^{-109}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e-9) (not (<= a 1.3e-109)))
   (+ 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 <= -2.8e-9) || !(a <= 1.3e-109)) {
		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 <= (-2.8d-9)) .or. (.not. (a <= 1.3d-109))) 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 <= -2.8e-9) || !(a <= 1.3e-109)) {
		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 <= -2.8e-9) or not (a <= 1.3e-109):
		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 <= -2.8e-9) || !(a <= 1.3e-109))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(Float64(t - x) / Float64(z / Float64(a - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e-9) || ~((a <= 1.3e-109)))
		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, -2.8e-9], N[Not[LessEqual[a, 1.3e-109]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(t - x), $MachinePrecision] / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.79999999999999984e-9 or 1.2999999999999999e-109 < a

   1. Initial program 69.3%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in t around inf 77.2%

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

   if -2.79999999999999984e-9 < a < 1.2999999999999999e-109

   1. Initial program 64.0%

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

      1. +-commutative 64.0%

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

      2. associate-*l/ 76.9%

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

      3. fma-def 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in z around inf 79.1%

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

      1. associate-/l* 89.7%

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

      2. distribute-lft-out-- 89.7%

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

   6. Simplified 89.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-9} \lor \neg \left(a \leq 1.3 \cdot 10^{-109}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \]

Alternative 12: 55.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26} \lor \neg \left(z \leq 4.8 \cdot 10^{+57}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+26) (not (<= z 4.8e+57)))
   (* t (- 1.0 (/ y z)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+26) || !(z <= 4.8e+57)) {
		tmp = t * (1.0 - (y / z));
	} 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 ((z <= (-4.2d+26)) .or. (.not. (z <= 4.8d+57))) then
        tmp = t * (1.0d0 - (y / z))
    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 ((z <= -4.2e+26) || !(z <= 4.8e+57)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+26) or not (z <= 4.8e+57):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+26) || !(z <= 4.8e+57))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	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 ((z <= -4.2e+26) || ~((z <= 4.8e+57)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+26], N[Not[LessEqual[z, 4.8e+57]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e26 or 4.80000000000000009e57 < z

   1. Initial program 44.4%

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

      1. associate-*l/ 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in a around 0 36.6%

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

      1. mul-1-neg 36.6%

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

      2. associate-/l* 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in t around inf 59.3%

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

   if -4.2000000000000002e26 < z < 4.80000000000000009e57

   1. Initial program 89.3%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 75.6%

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

   5. Taylor expanded in z around 0 58.8%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26} \lor \neg \left(z \leq 4.8 \cdot 10^{+57}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 13: 57.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+26} \lor \neg \left(z \leq 1.4 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.85e+26) (not (<= z 1.4e+53)))
   (* t (- 1.0 (/ y z)))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e+26) || !(z <= 1.4e+53)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (t / (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 ((z <= (-2.85d+26)) .or. (.not. (z <= 1.4d+53))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (t / (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 ((z <= -2.85e+26) || !(z <= 1.4e+53)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.85e+26) or not (z <= 1.4e+53):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.85e+26) || !(z <= 1.4e+53))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.85e+26) || ~((z <= 1.4e+53)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.85e+26], N[Not[LessEqual[z, 1.4e+53]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8500000000000002e26 or 1.4e53 < z

   1. Initial program 44.4%

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

      1. associate-*l/ 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in a around 0 36.6%

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

      1. mul-1-neg 36.6%

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

      2. associate-/l* 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in t around inf 59.3%

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

   if -2.8500000000000002e26 < z < 1.4e53

   1. Initial program 89.3%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 75.6%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-/l* 63.9%

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

   7. Simplified 63.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+26} \lor \neg \left(z \leq 1.4 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 14: 60.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26} \lor \neg \left(z \leq 2.6 \cdot 10^{+58}\right):\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+26) (not (<= z 2.6e+58)))
   (+ t (/ x (/ z y)))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+26) || !(z <= 2.6e+58)) {
		tmp = t + (x / (z / y));
	} else {
		tmp = x + (t / (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 ((z <= (-4.2d+26)) .or. (.not. (z <= 2.6d+58))) then
        tmp = t + (x / (z / y))
    else
        tmp = x + (t / (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 ((z <= -4.2e+26) || !(z <= 2.6e+58)) {
		tmp = t + (x / (z / y));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+26) or not (z <= 2.6e+58):
		tmp = t + (x / (z / y))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+26) || !(z <= 2.6e+58))
		tmp = Float64(t + Float64(x / Float64(z / y)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+26) || ~((z <= 2.6e+58)))
		tmp = t + (x / (z / y));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+26], N[Not[LessEqual[z, 2.6e+58]], $MachinePrecision]], N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e26 or 2.59999999999999988e58 < z

   1. Initial program 44.0%

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

      1. +-commutative 44.0%

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

      2. associate-*l/ 73.5%

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

      3. fma-def 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 61.9%

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

      1. associate-/l* 81.8%

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

      2. distribute-lft-out-- 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in t around 0 65.4%

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

      1. associate-/l* 75.5%

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

   9. Simplified 75.5%

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

   10. Taylor expanded in a around 0 61.8%

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

       1. +-commutative 61.8%

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

       2. associate-/l* 68.9%

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

   12. Simplified 68.9%

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

   if -4.2000000000000002e26 < z < 2.59999999999999988e58

   1. Initial program 89.4%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 75.8%

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

   5. Taylor expanded in z around 0 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-/l* 64.2%

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

   7. Simplified 64.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26} \lor \neg \left(z \leq 2.6 \cdot 10^{+58}\right):\\ \;\;\;\;t + \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 15: 47.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.8e-13) x (if (<= a 4.7e+69) (* t (- 1.0 (/ y z))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.8e-13) {
		tmp = x;
	} else if (a <= 4.7e+69) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.8d-13)) then
        tmp = x
    else if (a <= 4.7d+69) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.8e-13) {
		tmp = x;
	} else if (a <= 4.7e+69) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.8e-13:
		tmp = x
	elif a <= 4.7e+69:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.8e-13)
		tmp = x;
	elseif (a <= 4.7e+69)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.8e-13)
		tmp = x;
	elseif (a <= 4.7e+69)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.8e-13], x, If[LessEqual[a, 4.7e+69], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.80000000000000009e-13

   1. Initial program 71.1%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around inf 47.1%

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

   if -7.80000000000000009e-13 < a < 4.69999999999999996e69

   1. Initial program 66.0%

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

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in a around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. associate-/l* 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in t around inf 56.1%

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

   if 4.69999999999999996e69 < a

   1. Initial program 65.0%

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

      1. associate-/l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in t around inf 78.0%

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

   5. Taylor expanded in z around inf 50.1%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 16: 39.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 11000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+26)
   t
   (if (<= z 11000000.0) x (if (<= z 1.9e+220) (+ x t) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+26) {
		tmp = t;
	} else if (z <= 11000000.0) {
		tmp = x;
	} else if (z <= 1.9e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d+26)) then
        tmp = t
    else if (z <= 11000000.0d0) then
        tmp = x
    else if (z <= 1.9d+220) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+26) {
		tmp = t;
	} else if (z <= 11000000.0) {
		tmp = x;
	} else if (z <= 1.9e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+26:
		tmp = t
	elif z <= 11000000.0:
		tmp = x
	elif z <= 1.9e+220:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+26)
		tmp = t;
	elseif (z <= 11000000.0)
		tmp = x;
	elseif (z <= 1.9e+220)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+26)
		tmp = t;
	elseif (z <= 11000000.0)
		tmp = x;
	elseif (z <= 1.9e+220)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+26], t, If[LessEqual[z, 11000000.0], x, If[LessEqual[z, 1.9e+220], N[(x + t), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.60000000000000002e26 or 1.89999999999999992e220 < z

   1. Initial program 44.6%

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

      1. associate-*l/ 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in z around inf 58.6%

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

   if -2.60000000000000002e26 < z < 1.1e7

   1. Initial program 90.8%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around inf 37.9%

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

   if 1.1e7 < z < 1.89999999999999992e220

   1. Initial program 49.9%

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

      1. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in t around inf 69.0%

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

   5. Taylor expanded in z around inf 45.2%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 11000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 37.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-92}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e-92)
   (+ x t)
   (if (<= z 2.4e-141) (* t (/ y a)) (if (<= z 1.7e+220) (+ x t) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e-92) {
		tmp = x + t;
	} else if (z <= 2.4e-141) {
		tmp = t * (y / a);
	} else if (z <= 1.7e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.6d-92)) then
        tmp = x + t
    else if (z <= 2.4d-141) then
        tmp = t * (y / a)
    else if (z <= 1.7d+220) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e-92) {
		tmp = x + t;
	} else if (z <= 2.4e-141) {
		tmp = t * (y / a);
	} else if (z <= 1.7e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e-92:
		tmp = x + t
	elif z <= 2.4e-141:
		tmp = t * (y / a)
	elif z <= 1.7e+220:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e-92)
		tmp = Float64(x + t);
	elseif (z <= 2.4e-141)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.7e+220)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e-92)
		tmp = x + t;
	elseif (z <= 2.4e-141)
		tmp = t * (y / a);
	elseif (z <= 1.7e+220)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e-92], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.4e-141], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+220], N[(x + t), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.60000000000000016e-92 or 2.4000000000000001e-141 < z < 1.7e220

   1. Initial program 61.0%

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

      1. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in t around inf 67.5%

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

   5. Taylor expanded in z around inf 45.3%

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

   if -3.60000000000000016e-92 < z < 2.4000000000000001e-141

   1. Initial program 97.0%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 46.3%

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

   5. Taylor expanded in z around 0 39.5%

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

   if 1.7e220 < z

   1. Initial program 18.4%

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

      1. associate-*l/ 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in z around inf 74.9%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-92}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 39.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+102}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.12e+57)
   (/ x (/ z y))
   (if (<= y 4.1e+102) (+ x t) (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.12e+57) {
		tmp = x / (z / y);
	} else if (y <= 4.1e+102) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.12d+57)) then
        tmp = x / (z / y)
    else if (y <= 4.1d+102) then
        tmp = x + t
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.12e+57) {
		tmp = x / (z / y);
	} else if (y <= 4.1e+102) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.12e+57:
		tmp = x / (z / y)
	elif y <= 4.1e+102:
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.12e+57)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 4.1e+102)
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.12e+57)
		tmp = x / (z / y);
	elseif (y <= 4.1e+102)
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.12e+57], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+102], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12000000000000003e57

   1. Initial program 57.1%

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

      1. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in a around 0 36.6%

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

      1. mul-1-neg 36.6%

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

      2. associate-/l* 50.9%

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

   6. Simplified 50.9%

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

   7. Taylor expanded in x around -inf 25.6%

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

      1. associate-/l* 40.7%

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

   9. Simplified 40.7%

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

   if -1.12000000000000003e57 < y < 4.1e102

   1. Initial program 69.5%

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

      1. associate-/l* 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in t around inf 69.9%

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

   5. Taylor expanded in z around inf 46.5%

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

   if 4.1e102 < y

   1. Initial program 67.8%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in t around inf 75.4%

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

   5. Taylor expanded in z around 0 44.8%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+102}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 19: 39.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+25) t (if (<= z 3.4e+58) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+25) {
		tmp = t;
	} else if (z <= 3.4e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.7d+25)) then
        tmp = t
    else if (z <= 3.4d+58) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+25) {
		tmp = t;
	} else if (z <= 3.4e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+25:
		tmp = t
	elif z <= 3.4e+58:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+25)
		tmp = t;
	elseif (z <= 3.4e+58)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+25)
		tmp = t;
	elseif (z <= 3.4e+58)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+25], t, If[LessEqual[z, 3.4e+58], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e25 or 3.4000000000000001e58 < z

   1. Initial program 44.0%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 51.6%

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

   if -2.7e25 < z < 3.4000000000000001e58

   1. Initial program 89.4%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around inf 37.0%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 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 67.1%

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

   1. associate-*l/ 83.8%

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

3. Simplified 83.8%

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

4. Taylor expanded in z around inf 30.5%

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

5. Final simplification 30.5%

   \[\leadsto t \]

Developer target: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))