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

Percentage Accurate: 68.3% → 90.6%

Time: 19.4s

Alternatives: 16

Speedup: 0.3×

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: 68.3% 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: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_1 -2e-296)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (+ t (/ (* (- y a) (- x t)) z))
       (+ x (* (- t x) (/ (- y z) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -2e-296) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = x + ((t - x) * ((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 = x + (((y - z) * (t - x)) / (a - z))
    if (t_1 <= (-2d-296)) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else if (t_1 <= 0.0d0) then
        tmp = t + (((y - a) * (x - t)) / z)
    else
        tmp = x + ((t - x) * ((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 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -2e-296) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_1 <= -2e-296:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	elif t_1 <= 0.0:
		tmp = t + (((y - a) * (x - t)) / z)
	else:
		tmp = x + ((t - x) * ((y - z) / (a - 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 <= -2e-296)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -2e-296)
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	elseif (t_1 <= 0.0)
		tmp = t + (((y - a) * (x - t)) / z);
	else
		tmp = x + ((t - x) * ((y - z) / (a - 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[LessEqual[t$95$1, -2e-296], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -2e-296

   1. Initial program 77.8%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

      1. *-commutative 92.6%

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

      2. clear-num 92.5%

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

      3. un-div-inv 92.7%

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

   5. Applied egg-rr 92.7%

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

   if -2e-296 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.8%

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

      1. associate-*l/ 9.1%

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

   3. Simplified 9.1%

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

   4. Taylor expanded in z around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. associate-*r/ 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-lft-out-- 99.7%

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

      7. associate-*r/ 99.7%

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

      8. mul-1-neg 99.7%

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

      9. unsub-neg 99.7%

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

      10. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

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

   1. Initial program 70.0%

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

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-296}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 2: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-296} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -2e-296) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (* (- y a) (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) * (t - x)) / (a - z))
    if ((t_1 <= (-2d-296)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + (((y - a) * (x - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -2e-296) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -2e-296) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -2e-296) || !(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(y - a) * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -2e-296) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-296], 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[(y - a), $MachinePrecision] * N[(x - t), $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))) < -2e-296 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.5%

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

      1. associate-*l/ 90.8%

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

   3. Simplified 90.8%

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

   if -2e-296 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.8%

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

      1. associate-*l/ 9.1%

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

   3. Simplified 9.1%

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

   4. Taylor expanded in z around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. associate-*r/ 99.7%

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

      5. div-sub 99.7%

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

      6. distribute-lft-out-- 99.7%

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

      7. associate-*r/ 99.7%

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

      8. mul-1-neg 99.7%

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

      9. unsub-neg 99.7%

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

      10. distribute-rgt-out-- 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -2 \cdot 10^{-296} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 3: 47.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -5e-15)
     x
     (if (<= a 1.35e-211)
       t_1
       (if (<= a 1.4e-167)
         (* x (/ y z))
         (if (<= a 1.1e+37)
           t_1
           (if (<= a 4e+60)
             (/ t (/ a (- y z)))
             (if (<= a 3.4e+87) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -5e-15) {
		tmp = x;
	} else if (a <= 1.35e-211) {
		tmp = t_1;
	} else if (a <= 1.4e-167) {
		tmp = x * (y / z);
	} else if (a <= 1.1e+37) {
		tmp = t_1;
	} else if (a <= 4e+60) {
		tmp = t / (a / (y - z));
	} else if (a <= 3.4e+87) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-5d-15)) then
        tmp = x
    else if (a <= 1.35d-211) then
        tmp = t_1
    else if (a <= 1.4d-167) then
        tmp = x * (y / z)
    else if (a <= 1.1d+37) then
        tmp = t_1
    else if (a <= 4d+60) then
        tmp = t / (a / (y - z))
    else if (a <= 3.4d+87) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -5e-15) {
		tmp = x;
	} else if (a <= 1.35e-211) {
		tmp = t_1;
	} else if (a <= 1.4e-167) {
		tmp = x * (y / z);
	} else if (a <= 1.1e+37) {
		tmp = t_1;
	} else if (a <= 4e+60) {
		tmp = t / (a / (y - z));
	} else if (a <= 3.4e+87) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -5e-15:
		tmp = x
	elif a <= 1.35e-211:
		tmp = t_1
	elif a <= 1.4e-167:
		tmp = x * (y / z)
	elif a <= 1.1e+37:
		tmp = t_1
	elif a <= 4e+60:
		tmp = t / (a / (y - z))
	elif a <= 3.4e+87:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -5e-15)
		tmp = x;
	elseif (a <= 1.35e-211)
		tmp = t_1;
	elseif (a <= 1.4e-167)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.1e+37)
		tmp = t_1;
	elseif (a <= 4e+60)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (a <= 3.4e+87)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -5e-15)
		tmp = x;
	elseif (a <= 1.35e-211)
		tmp = t_1;
	elseif (a <= 1.4e-167)
		tmp = x * (y / z);
	elseif (a <= 1.1e+37)
		tmp = t_1;
	elseif (a <= 4e+60)
		tmp = t / (a / (y - z));
	elseif (a <= 3.4e+87)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e-15], x, If[LessEqual[a, 1.35e-211], t$95$1, If[LessEqual[a, 1.4e-167], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+37], t$95$1, If[LessEqual[a, 4e+60], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+87], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.99999999999999999e-15 or 3.4000000000000002e87 < a

   1. Initial program 64.1%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in a around inf 49.2%

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

   if -4.99999999999999999e-15 < a < 1.35e-211 or 1.39999999999999993e-167 < a < 1.1e37 or 3.9999999999999998e60 < a < 3.4000000000000002e87

   1. Initial program 69.8%

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

      1. associate-*l/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in a around 0 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

      4. associate-/l* 52.0%

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

   6. Simplified 52.0%

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

   7. Taylor expanded in t around inf 53.2%

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

   if 1.35e-211 < a < 1.39999999999999993e-167

   1. Initial program 61.4%

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

      1. associate-*l/ 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in z around inf 80.5%

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

   5. Taylor expanded in x around inf 70.9%

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

   6. Taylor expanded in y around inf 70.9%

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

   if 1.1e37 < a < 3.9999999999999998e60

   1. Initial program 87.4%

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

      1. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in x around 0 59.8%

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

   5. Taylor expanded in a around inf 59.9%

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

      1. associate-/l* 60.1%

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

   7. Simplified 60.1%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-211}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-261}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-294}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 4.25 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= x -5.8e+81)
     (* x (/ (- y a) z))
     (if (<= x -1.3e-261)
       (/ (- t) (/ (- a z) z))
       (if (<= x -5.8e-294)
         (* t (/ y a))
         (if (<= x 4.25e-274)
           t_1
           (if (<= x 5.8e-235)
             (/ (* (- y z) t) a)
             (if (<= x 3e-61) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (x <= -5.8e+81) {
		tmp = x * ((y - a) / z);
	} else if (x <= -1.3e-261) {
		tmp = -t / ((a - z) / z);
	} else if (x <= -5.8e-294) {
		tmp = t * (y / a);
	} else if (x <= 4.25e-274) {
		tmp = t_1;
	} else if (x <= 5.8e-235) {
		tmp = ((y - z) * t) / a;
	} else if (x <= 3e-61) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (x <= (-5.8d+81)) then
        tmp = x * ((y - a) / z)
    else if (x <= (-1.3d-261)) then
        tmp = -t / ((a - z) / z)
    else if (x <= (-5.8d-294)) then
        tmp = t * (y / a)
    else if (x <= 4.25d-274) then
        tmp = t_1
    else if (x <= 5.8d-235) then
        tmp = ((y - z) * t) / a
    else if (x <= 3d-61) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (x <= -5.8e+81) {
		tmp = x * ((y - a) / z);
	} else if (x <= -1.3e-261) {
		tmp = -t / ((a - z) / z);
	} else if (x <= -5.8e-294) {
		tmp = t * (y / a);
	} else if (x <= 4.25e-274) {
		tmp = t_1;
	} else if (x <= 5.8e-235) {
		tmp = ((y - z) * t) / a;
	} else if (x <= 3e-61) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if x <= -5.8e+81:
		tmp = x * ((y - a) / z)
	elif x <= -1.3e-261:
		tmp = -t / ((a - z) / z)
	elif x <= -5.8e-294:
		tmp = t * (y / a)
	elif x <= 4.25e-274:
		tmp = t_1
	elif x <= 5.8e-235:
		tmp = ((y - z) * t) / a
	elif x <= 3e-61:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (x <= -5.8e+81)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (x <= -1.3e-261)
		tmp = Float64(Float64(-t) / Float64(Float64(a - z) / z));
	elseif (x <= -5.8e-294)
		tmp = Float64(t * Float64(y / a));
	elseif (x <= 4.25e-274)
		tmp = t_1;
	elseif (x <= 5.8e-235)
		tmp = Float64(Float64(Float64(y - z) * t) / a);
	elseif (x <= 3e-61)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (x <= -5.8e+81)
		tmp = x * ((y - a) / z);
	elseif (x <= -1.3e-261)
		tmp = -t / ((a - z) / z);
	elseif (x <= -5.8e-294)
		tmp = t * (y / a);
	elseif (x <= 4.25e-274)
		tmp = t_1;
	elseif (x <= 5.8e-235)
		tmp = ((y - z) * t) / a;
	elseif (x <= 3e-61)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+81], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e-261], N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-294], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.25e-274], t$95$1, If[LessEqual[x, 5.8e-235], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[x, 3e-61], t$95$1, x]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.7999999999999999e81

   1. Initial program 52.5%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in z around inf 49.4%

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

   5. Taylor expanded in x around inf 55.1%

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

   6. Taylor expanded in y around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. distribute-frac-neg 55.1%

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

      3. +-commutative 55.1%

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

      4. distribute-frac-neg 55.1%

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

      5. sub-neg 55.1%

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

      6. div-sub 55.2%

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

   8. Simplified 55.2%

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

   if -5.7999999999999999e81 < x < -1.3000000000000001e-261

   1. Initial program 76.3%

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

      1. associate-*l/ 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in x around 0 51.4%

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

   5. Taylor expanded in y around 0 39.5%

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

      1. mul-1-neg 39.5%

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

      2. associate-/l* 49.2%

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

   7. Simplified 49.2%

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

   if -1.3000000000000001e-261 < x < -5.8000000000000001e-294

   1. Initial program 74.2%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 66.2%

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

   5. Taylor expanded in z around 0 48.6%

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

      1. associate-/l* 65.9%

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

   7. Simplified 65.9%

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

      1. associate-/r/ 65.9%

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

   9. Applied egg-rr 65.9%

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

   if -5.8000000000000001e-294 < x < 4.24999999999999989e-274 or 5.80000000000000018e-235 < x < 3.00000000000000012e-61

   1. Initial program 73.7%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in a around 0 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. associate-/l* 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in t around inf 57.2%

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

   if 4.24999999999999989e-274 < x < 5.80000000000000018e-235

   1. Initial program 99.1%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in x around 0 73.4%

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

   5. Taylor expanded in a around inf 73.4%

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

   if 3.00000000000000012e-61 < x

   1. Initial program 62.3%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in a around inf 38.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-261}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-294}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 4.25 \cdot 10^{-274}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 52.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{\frac{-z}{x}}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ y (/ (- z) x)))))
   (if (<= a -1.65e+103)
     x
     (if (<= a 3.4e+17)
       t_1
       (if (<= a 2.8e+58) (/ t (/ a (- y z))) (if (<= a 2.8e+86) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y / (-z / x));
	double tmp;
	if (a <= -1.65e+103) {
		tmp = x;
	} else if (a <= 3.4e+17) {
		tmp = t_1;
	} else if (a <= 2.8e+58) {
		tmp = t / (a / (y - z));
	} else if (a <= 2.8e+86) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (y / (-z / x))
    if (a <= (-1.65d+103)) then
        tmp = x
    else if (a <= 3.4d+17) then
        tmp = t_1
    else if (a <= 2.8d+58) then
        tmp = t / (a / (y - z))
    else if (a <= 2.8d+86) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y / (-z / x));
	double tmp;
	if (a <= -1.65e+103) {
		tmp = x;
	} else if (a <= 3.4e+17) {
		tmp = t_1;
	} else if (a <= 2.8e+58) {
		tmp = t / (a / (y - z));
	} else if (a <= 2.8e+86) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (y / (-z / x))
	tmp = 0
	if a <= -1.65e+103:
		tmp = x
	elif a <= 3.4e+17:
		tmp = t_1
	elif a <= 2.8e+58:
		tmp = t / (a / (y - z))
	elif a <= 2.8e+86:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(y / Float64(Float64(-z) / x)))
	tmp = 0.0
	if (a <= -1.65e+103)
		tmp = x;
	elseif (a <= 3.4e+17)
		tmp = t_1;
	elseif (a <= 2.8e+58)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (a <= 2.8e+86)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (y / (-z / x));
	tmp = 0.0;
	if (a <= -1.65e+103)
		tmp = x;
	elseif (a <= 3.4e+17)
		tmp = t_1;
	elseif (a <= 2.8e+58)
		tmp = t / (a / (y - z));
	elseif (a <= 2.8e+86)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+103], x, If[LessEqual[a, 3.4e+17], t$95$1, If[LessEqual[a, 2.8e+58], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+86], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65000000000000004e103 or 2.80000000000000004e86 < a

   1. Initial program 61.7%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in a around inf 54.3%

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

   if -1.65000000000000004e103 < a < 3.4e17 or 2.7999999999999998e58 < a < 2.80000000000000004e86

   1. Initial program 69.2%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in z around inf 64.1%

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

   5. Taylor expanded in a around 0 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. associate-/l* 67.0%

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

      4. unsub-neg 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in t around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-neg-frac 60.4%

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

   10. Simplified 60.4%

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

   if 3.4e17 < a < 2.7999999999999998e58

   1. Initial program 86.2%

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

      1. associate-*l/ 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in x around 0 63.6%

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

   5. Taylor expanded in a around inf 48.5%

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

      1. associate-/l* 48.5%

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

   7. Simplified 48.5%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+86}:\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 47.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -8 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -8e-12)
     x
     (if (<= a 8.5e-212)
       t_1
       (if (<= a 1.4e-167) (* x (/ y z)) (if (<= a 5e+82) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -8e-12) {
		tmp = x;
	} else if (a <= 8.5e-212) {
		tmp = t_1;
	} else if (a <= 1.4e-167) {
		tmp = x * (y / z);
	} else if (a <= 5e+82) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-8d-12)) then
        tmp = x
    else if (a <= 8.5d-212) then
        tmp = t_1
    else if (a <= 1.4d-167) then
        tmp = x * (y / z)
    else if (a <= 5d+82) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -8e-12) {
		tmp = x;
	} else if (a <= 8.5e-212) {
		tmp = t_1;
	} else if (a <= 1.4e-167) {
		tmp = x * (y / z);
	} else if (a <= 5e+82) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -8e-12:
		tmp = x
	elif a <= 8.5e-212:
		tmp = t_1
	elif a <= 1.4e-167:
		tmp = x * (y / z)
	elif a <= 5e+82:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -8e-12)
		tmp = x;
	elseif (a <= 8.5e-212)
		tmp = t_1;
	elseif (a <= 1.4e-167)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 5e+82)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -8e-12)
		tmp = x;
	elseif (a <= 8.5e-212)
		tmp = t_1;
	elseif (a <= 1.4e-167)
		tmp = x * (y / z);
	elseif (a <= 5e+82)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e-12], x, If[LessEqual[a, 8.5e-212], t$95$1, If[LessEqual[a, 1.4e-167], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+82], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.99999999999999984e-12 or 5.00000000000000015e82 < a

   1. Initial program 64.1%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in a around inf 49.2%

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

   if -7.99999999999999984e-12 < a < 8.5000000000000002e-212 or 1.39999999999999993e-167 < a < 5.00000000000000015e82

   1. Initial program 70.8%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in a around 0 44.3%

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

      1. +-commutative 44.3%

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

      2. mul-1-neg 44.3%

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

      3. unsub-neg 44.3%

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

      4. associate-/l* 49.2%

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

   6. Simplified 49.2%

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

   7. Taylor expanded in t around inf 50.3%

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

   if 8.5000000000000002e-212 < a < 1.39999999999999993e-167

   1. Initial program 61.4%

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

      1. associate-*l/ 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in z around inf 80.5%

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

   5. Taylor expanded in x around inf 70.9%

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

   6. Taylor expanded in y around inf 70.9%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-212}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 55.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= x -1.25e+43)
     t_1
     (if (<= x 2.6e+27)
       (* t (/ (- y z) (- a z)))
       (if (<= x 3.75e+118) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -1.25e+43) {
		tmp = t_1;
	} else if (x <= 2.6e+27) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 3.75e+118) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    if (x <= (-1.25d+43)) then
        tmp = t_1
    else if (x <= 2.6d+27) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 3.75d+118) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (x <= -1.25e+43) {
		tmp = t_1;
	} else if (x <= 2.6e+27) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 3.75e+118) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if x <= -1.25e+43:
		tmp = t_1
	elif x <= 2.6e+27:
		tmp = t * ((y - z) / (a - z))
	elif x <= 3.75e+118:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (x <= -1.25e+43)
		tmp = t_1;
	elseif (x <= 2.6e+27)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 3.75e+118)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (x <= -1.25e+43)
		tmp = t_1;
	elseif (x <= 2.6e+27)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 3.75e+118)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e+43], t$95$1, If[LessEqual[x, 2.6e+27], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.75e+118], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2500000000000001e43 or 2.60000000000000009e27 < x < 3.75000000000000001e118

   1. Initial program 57.2%

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

      1. associate-*l/ 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in y around inf 54.5%

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

      1. div-sub 57.1%

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

      2. *-commutative 57.1%

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

   6. Simplified 57.1%

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

   if -1.2500000000000001e43 < x < 2.60000000000000009e27

   1. Initial program 78.2%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 55.7%

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

      1. associate-*r/ 68.8%

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

   6. Simplified 68.8%

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

   if 3.75000000000000001e118 < x

   1. Initial program 49.0%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in a around inf 46.7%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+133} \lor \neg \left(z \leq 3.2 \cdot 10^{-57}\right):\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+133) (not (<= z 3.2e-57)))
   (- t (/ y (/ (- z) x)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+133) || !(z <= 3.2e-57)) {
		tmp = t - (y / (-z / x));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.5d+133)) .or. (.not. (z <= 3.2d-57))) then
        tmp = t - (y / (-z / x))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+133) || !(z <= 3.2e-57)) {
		tmp = t - (y / (-z / x));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+133) or not (z <= 3.2e-57):
		tmp = t - (y / (-z / x))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+133) || !(z <= 3.2e-57))
		tmp = Float64(t - Float64(y / Float64(Float64(-z) / x)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e+133) || ~((z <= 3.2e-57)))
		tmp = t - (y / (-z / x));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+133], N[Not[LessEqual[z, 3.2e-57]], $MachinePrecision]], N[(t - N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999985e133 or 3.2000000000000001e-57 < z

   1. Initial program 49.1%

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

      1. associate-*l/ 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in z around inf 62.7%

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

   5. Taylor expanded in a around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. associate-/l* 70.1%

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

      4. unsub-neg 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in t around 0 67.3%

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

      1. mul-1-neg 67.3%

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

      2. distribute-neg-frac 67.3%

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

   10. Simplified 67.3%

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

   if -4.49999999999999985e133 < z < 3.2000000000000001e-57

   1. Initial program 79.7%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in z around 0 67.3%

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

      1. +-commutative 67.3%

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

      2. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+133} \lor \neg \left(z \leq 3.2 \cdot 10^{-57}\right):\\ \;\;\;\;t - \frac{y}{\frac{-z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 9: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+63} \lor \neg \left(z \leq 1.2 \cdot 10^{-61}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e+63) (not (<= z 1.2e-61)))
   (- t (/ y (/ z (- t x))))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+63) || !(z <= 1.2e-61)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.8d+63)) .or. (.not. (z <= 1.2d-61))) then
        tmp = t - (y / (z / (t - x)))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+63) || !(z <= 1.2e-61)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e+63) or not (z <= 1.2e-61):
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e+63) || !(z <= 1.2e-61))
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.8e+63) || ~((z <= 1.2e-61)))
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e+63], N[Not[LessEqual[z, 1.2e-61]], $MachinePrecision]], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999999e63 or 1.2e-61 < z

   1. Initial program 48.5%

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

      1. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in z around inf 61.7%

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

   5. Taylor expanded in a around 0 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. associate-/l* 67.0%

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

      4. unsub-neg 67.0%

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

   7. Simplified 67.0%

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

   if -5.7999999999999999e63 < z < 1.2e-61

   1. Initial program 83.2%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. associate-/l* 80.9%

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

   6. Simplified 80.9%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+63} \lor \neg \left(z \leq 1.2 \cdot 10^{-61}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 10: 55.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4e+87)
   (* x (/ (- y a) z))
   (if (<= x 2.55e+115) (* t (/ (- y z) (- a z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e+87) {
		tmp = x * ((y - a) / z);
	} else if (x <= 2.55e+115) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-4d+87)) then
        tmp = x * ((y - a) / z)
    else if (x <= 2.55d+115) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e+87) {
		tmp = x * ((y - a) / z);
	} else if (x <= 2.55e+115) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4e+87:
		tmp = x * ((y - a) / z)
	elif x <= 2.55e+115:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4e+87)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (x <= 2.55e+115)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4e+87)
		tmp = x * ((y - a) / z);
	elseif (x <= 2.55e+115)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4e+87], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.55e+115], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9999999999999998e87

   1. Initial program 52.5%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in z around inf 49.4%

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

   5. Taylor expanded in x around inf 55.1%

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

   6. Taylor expanded in y around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. distribute-frac-neg 55.1%

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

      3. +-commutative 55.1%

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

      4. distribute-frac-neg 55.1%

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

      5. sub-neg 55.1%

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

      6. div-sub 55.2%

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

   8. Simplified 55.2%

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

   if -3.9999999999999998e87 < x < 2.5499999999999998e115

   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/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 52.0%

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

      1. associate-*r/ 64.3%

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

   6. Simplified 64.3%

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

   if 2.5499999999999998e115 < x

   1. Initial program 49.0%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in a around inf 46.7%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 29.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-259}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.26e+85)
   (* y (/ x z))
   (if (<= x -2.7e-259)
     t
     (if (<= x 2.25e-201) (* y (/ t a)) (if (<= x 1.2e-61) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.26e+85) {
		tmp = y * (x / z);
	} else if (x <= -2.7e-259) {
		tmp = t;
	} else if (x <= 2.25e-201) {
		tmp = y * (t / a);
	} else if (x <= 1.2e-61) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.26d+85)) then
        tmp = y * (x / z)
    else if (x <= (-2.7d-259)) then
        tmp = t
    else if (x <= 2.25d-201) then
        tmp = y * (t / a)
    else if (x <= 1.2d-61) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.26e+85) {
		tmp = y * (x / z);
	} else if (x <= -2.7e-259) {
		tmp = t;
	} else if (x <= 2.25e-201) {
		tmp = y * (t / a);
	} else if (x <= 1.2e-61) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.26e+85:
		tmp = y * (x / z)
	elif x <= -2.7e-259:
		tmp = t
	elif x <= 2.25e-201:
		tmp = y * (t / a)
	elif x <= 1.2e-61:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.26e+85)
		tmp = Float64(y * Float64(x / z));
	elseif (x <= -2.7e-259)
		tmp = t;
	elseif (x <= 2.25e-201)
		tmp = Float64(y * Float64(t / a));
	elseif (x <= 1.2e-61)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.26e+85)
		tmp = y * (x / z);
	elseif (x <= -2.7e-259)
		tmp = t;
	elseif (x <= 2.25e-201)
		tmp = y * (t / a);
	elseif (x <= 1.2e-61)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.26e+85], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.7e-259], t, If[LessEqual[x, 2.25e-201], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-61], t, x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.26000000000000003e85

   1. Initial program 52.5%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in z around inf 49.4%

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

   5. Taylor expanded in x around inf 55.1%

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

   6. Taylor expanded in y around inf 42.4%

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

      1. *-rgt-identity 42.4%

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

      2. *-commutative 42.4%

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

      3. times-frac 42.7%

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

      4. /-rgt-identity 42.7%

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

   8. Simplified 42.7%

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

   if -1.26000000000000003e85 < x < -2.69999999999999984e-259 or 2.2500000000000001e-201 < x < 1.2e-61

   1. Initial program 74.9%

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

      1. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around inf 42.8%

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

   if -2.69999999999999984e-259 < x < 2.2500000000000001e-201

   1. Initial program 79.7%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around 0 59.1%

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

   5. Taylor expanded in z around 0 33.4%

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

      1. associate-/l* 42.6%

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

   7. Simplified 42.6%

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

      1. associate-/r/ 40.1%

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

   9. Applied egg-rr 40.1%

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

   10. Taylor expanded in y around 0 33.4%

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

       1. *-commutative 33.4%

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

       2. associate-*l/ 42.5%

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

   12. Simplified 42.5%

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

   if 1.2e-61 < x

   1. Initial program 62.3%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in a around inf 38.9%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-259}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-201}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 29.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-258}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.5e+81)
   (* x (/ y z))
   (if (<= x -1.95e-258)
     t
     (if (<= x 1.25e-192) (* y (/ t a)) (if (<= x 1.5e-61) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.5e+81) {
		tmp = x * (y / z);
	} else if (x <= -1.95e-258) {
		tmp = t;
	} else if (x <= 1.25e-192) {
		tmp = y * (t / a);
	} else if (x <= 1.5e-61) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-8.5d+81)) then
        tmp = x * (y / z)
    else if (x <= (-1.95d-258)) then
        tmp = t
    else if (x <= 1.25d-192) then
        tmp = y * (t / a)
    else if (x <= 1.5d-61) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.5e+81) {
		tmp = x * (y / z);
	} else if (x <= -1.95e-258) {
		tmp = t;
	} else if (x <= 1.25e-192) {
		tmp = y * (t / a);
	} else if (x <= 1.5e-61) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.5e+81:
		tmp = x * (y / z)
	elif x <= -1.95e-258:
		tmp = t
	elif x <= 1.25e-192:
		tmp = y * (t / a)
	elif x <= 1.5e-61:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.5e+81)
		tmp = Float64(x * Float64(y / z));
	elseif (x <= -1.95e-258)
		tmp = t;
	elseif (x <= 1.25e-192)
		tmp = Float64(y * Float64(t / a));
	elseif (x <= 1.5e-61)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8.5e+81)
		tmp = x * (y / z);
	elseif (x <= -1.95e-258)
		tmp = t;
	elseif (x <= 1.25e-192)
		tmp = y * (t / a);
	elseif (x <= 1.5e-61)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.5e+81], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.95e-258], t, If[LessEqual[x, 1.25e-192], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-61], t, x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.49999999999999986e81

   1. Initial program 52.5%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in z around inf 49.4%

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

   5. Taylor expanded in x around inf 55.1%

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

   6. Taylor expanded in y around inf 48.0%

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

   if -8.49999999999999986e81 < x < -1.95000000000000002e-258 or 1.25e-192 < x < 1.50000000000000006e-61

   1. Initial program 74.9%

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

      1. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around inf 42.8%

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

   if -1.95000000000000002e-258 < x < 1.25e-192

   1. Initial program 79.7%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around 0 59.1%

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

   5. Taylor expanded in z around 0 33.4%

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

      1. associate-/l* 42.6%

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

   7. Simplified 42.6%

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

      1. associate-/r/ 40.1%

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

   9. Applied egg-rr 40.1%

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

   10. Taylor expanded in y around 0 33.4%

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

       1. *-commutative 33.4%

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

       2. associate-*l/ 42.5%

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

   12. Simplified 42.5%

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

   if 1.50000000000000006e-61 < x

   1. Initial program 62.3%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in a around inf 38.9%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-258}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-192}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 29.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-261}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.18e+83)
   (* x (/ y z))
   (if (<= x -4.4e-261)
     t
     (if (<= x 8.5e-197) (/ y (/ a t)) (if (<= x 1.25e-62) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.18e+83) {
		tmp = x * (y / z);
	} else if (x <= -4.4e-261) {
		tmp = t;
	} else if (x <= 8.5e-197) {
		tmp = y / (a / t);
	} else if (x <= 1.25e-62) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.18d+83)) then
        tmp = x * (y / z)
    else if (x <= (-4.4d-261)) then
        tmp = t
    else if (x <= 8.5d-197) then
        tmp = y / (a / t)
    else if (x <= 1.25d-62) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.18e+83) {
		tmp = x * (y / z);
	} else if (x <= -4.4e-261) {
		tmp = t;
	} else if (x <= 8.5e-197) {
		tmp = y / (a / t);
	} else if (x <= 1.25e-62) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.18e+83:
		tmp = x * (y / z)
	elif x <= -4.4e-261:
		tmp = t
	elif x <= 8.5e-197:
		tmp = y / (a / t)
	elif x <= 1.25e-62:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.18e+83)
		tmp = Float64(x * Float64(y / z));
	elseif (x <= -4.4e-261)
		tmp = t;
	elseif (x <= 8.5e-197)
		tmp = Float64(y / Float64(a / t));
	elseif (x <= 1.25e-62)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.18e+83)
		tmp = x * (y / z);
	elseif (x <= -4.4e-261)
		tmp = t;
	elseif (x <= 8.5e-197)
		tmp = y / (a / t);
	elseif (x <= 1.25e-62)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.18e+83], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.4e-261], t, If[LessEqual[x, 8.5e-197], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-62], t, x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.1799999999999999e83

   1. Initial program 52.5%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in z around inf 49.4%

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

   5. Taylor expanded in x around inf 55.1%

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

   6. Taylor expanded in y around inf 48.0%

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

   if -1.1799999999999999e83 < x < -4.4000000000000003e-261 or 8.5e-197 < x < 1.25e-62

   1. Initial program 74.9%

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

      1. associate-*l/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around inf 42.8%

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

   if -4.4000000000000003e-261 < x < 8.5e-197

   1. Initial program 79.7%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around 0 59.1%

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

   5. Taylor expanded in z around 0 33.4%

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

      1. associate-/l* 42.6%

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

   7. Simplified 42.6%

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

   if 1.25e-62 < x

   1. Initial program 62.3%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in a around inf 38.9%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-261}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-62}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 30.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2e+80) (* y (/ x z)) (if (<= x 1.2e-61) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2e+80) {
		tmp = y * (x / z);
	} else if (x <= 1.2e-61) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2d+80)) then
        tmp = y * (x / z)
    else if (x <= 1.2d-61) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2e+80) {
		tmp = y * (x / z);
	} else if (x <= 1.2e-61) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2e+80:
		tmp = y * (x / z)
	elif x <= 1.2e-61:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2e+80)
		tmp = Float64(y * Float64(x / z));
	elseif (x <= 1.2e-61)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2e+80)
		tmp = y * (x / z);
	elseif (x <= 1.2e-61)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2e+80], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-61], t, x]]

Derivation

1. Split input into 3 regimes

2. if x < -2e80

   1. Initial program 52.5%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in z around inf 49.4%

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

   5. Taylor expanded in x around inf 55.1%

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

   6. Taylor expanded in y around inf 42.4%

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

      1. *-rgt-identity 42.4%

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

      2. *-commutative 42.4%

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

      3. times-frac 42.7%

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

      4. /-rgt-identity 42.7%

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

   8. Simplified 42.7%

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

   if -2e80 < x < 1.2e-61

   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/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 38.8%

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

   if 1.2e-61 < x

   1. Initial program 62.3%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in a around inf 38.9%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-61}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 38.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e-12) x (if (<= a 1.04e+82) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e-12) {
		tmp = x;
	} else if (a <= 1.04e+82) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d-12)) then
        tmp = x
    else if (a <= 1.04d+82) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e-12) {
		tmp = x;
	} else if (a <= 1.04e+82) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e-12:
		tmp = x
	elif a <= 1.04e+82:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e-12)
		tmp = x;
	elseif (a <= 1.04e+82)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e-12)
		tmp = x;
	elseif (a <= 1.04e+82)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e-12], x, If[LessEqual[a, 1.04e+82], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.49999999999999985e-12 or 1.03999999999999997e82 < a

   1. Initial program 64.1%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in a around inf 49.2%

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

   if -2.49999999999999985e-12 < a < 1.03999999999999997e82

   1. Initial program 70.2%

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

      1. associate-*l/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in z around inf 35.2%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{+82}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 24.9% 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 67.6%

   \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
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 25.4%

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

5. Final simplification 25.4%

   \[\leadsto t \]

Developer target: 83.5% 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 2023279 
(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))))