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

Percentage Accurate: 68.3% → 91.0%

Time: 16.7s

Alternatives: 18

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.3% 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: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-285}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_1 -1e-285)
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (if (<= t_1 0.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (- x (/ (- x t) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_1 <= -1e-285) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if (t_1 <= (-1d-285)) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else if (t_1 <= 0.0d0) then
        tmp = t + (((t - x) * (a - y)) / z)
    else
        tmp = x - ((x - t) / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_1 <= -1e-285) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if t_1 <= -1e-285:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	elif t_1 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x - ((x - t) / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e-285)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -1e-285)
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-285], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000007e-285

   1. Initial program 75.8%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   if -1.00000000000000007e-285 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.9%

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

      1. associate-*l/ 4.9%

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

   3. Simplified 4.9%

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

   4. Taylor expanded in z around -inf 99.9%

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

      1. +-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. mul-1-neg 99.9%

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

      6. unsub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. mul-1-neg 99.9%

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

      9. sub-neg 99.9%

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

      10. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 77.8%

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

      1. *-commutative 94.4%

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

      2. clear-num 94.3%

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

      3. un-div-inv 94.5%

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

   5. Applied egg-rr 94.5%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -1 \cdot 10^{-285}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 2: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-285} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -1e-285) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-285) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if ((t_1 <= (-1d-285)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) * ((y - z) / (a - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-285) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - z) * (x - t)) / (a - z))
	tmp = 0
	if (t_1 <= -1e-285) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-285) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if ((t_1 <= -1e-285) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	else
		tmp = t + (((t - x) * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-285], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -1.00000000000000007e-285 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 76.8%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   if -1.00000000000000007e-285 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.9%

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

      1. associate-*l/ 4.9%

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

   3. Simplified 4.9%

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

   4. Taylor expanded in z around -inf 99.9%

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

      1. +-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. mul-1-neg 99.9%

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

      6. unsub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. mul-1-neg 99.9%

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

      9. sub-neg 99.9%

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

      10. distribute-rgt-out-- 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -1 \cdot 10^{-285} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 3: 40.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-257}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-157}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-137}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= y -1.05e+79)
     (* t (/ y (- a z)))
     (if (<= y -1.9e-294)
       t_1
       (if (<= y 1.5e-257)
         t
         (if (<= y 6.7e-205)
           t_1
           (if (<= y 2.1e-157)
             t
             (if (<= y 1.2e-137)
               (/ (* x y) z)
               (if (<= y 1.35e-22)
                 t_1
                 (if (<= y 5.2e+80) t (* y (/ (- t x) a))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (y <= -1.05e+79) {
		tmp = t * (y / (a - z));
	} else if (y <= -1.9e-294) {
		tmp = t_1;
	} else if (y <= 1.5e-257) {
		tmp = t;
	} else if (y <= 6.7e-205) {
		tmp = t_1;
	} else if (y <= 2.1e-157) {
		tmp = t;
	} else if (y <= 1.2e-137) {
		tmp = (x * y) / z;
	} else if (y <= 1.35e-22) {
		tmp = t_1;
	} else if (y <= 5.2e+80) {
		tmp = t;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (y <= (-1.05d+79)) then
        tmp = t * (y / (a - z))
    else if (y <= (-1.9d-294)) then
        tmp = t_1
    else if (y <= 1.5d-257) then
        tmp = t
    else if (y <= 6.7d-205) then
        tmp = t_1
    else if (y <= 2.1d-157) then
        tmp = t
    else if (y <= 1.2d-137) then
        tmp = (x * y) / z
    else if (y <= 1.35d-22) then
        tmp = t_1
    else if (y <= 5.2d+80) then
        tmp = t
    else
        tmp = y * ((t - x) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (y <= -1.05e+79) {
		tmp = t * (y / (a - z));
	} else if (y <= -1.9e-294) {
		tmp = t_1;
	} else if (y <= 1.5e-257) {
		tmp = t;
	} else if (y <= 6.7e-205) {
		tmp = t_1;
	} else if (y <= 2.1e-157) {
		tmp = t;
	} else if (y <= 1.2e-137) {
		tmp = (x * y) / z;
	} else if (y <= 1.35e-22) {
		tmp = t_1;
	} else if (y <= 5.2e+80) {
		tmp = t;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if y <= -1.05e+79:
		tmp = t * (y / (a - z))
	elif y <= -1.9e-294:
		tmp = t_1
	elif y <= 1.5e-257:
		tmp = t
	elif y <= 6.7e-205:
		tmp = t_1
	elif y <= 2.1e-157:
		tmp = t
	elif y <= 1.2e-137:
		tmp = (x * y) / z
	elif y <= 1.35e-22:
		tmp = t_1
	elif y <= 5.2e+80:
		tmp = t
	else:
		tmp = y * ((t - x) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (y <= -1.05e+79)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (y <= -1.9e-294)
		tmp = t_1;
	elseif (y <= 1.5e-257)
		tmp = t;
	elseif (y <= 6.7e-205)
		tmp = t_1;
	elseif (y <= 2.1e-157)
		tmp = t;
	elseif (y <= 1.2e-137)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 1.35e-22)
		tmp = t_1;
	elseif (y <= 5.2e+80)
		tmp = t;
	else
		tmp = Float64(y * Float64(Float64(t - x) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (y <= -1.05e+79)
		tmp = t * (y / (a - z));
	elseif (y <= -1.9e-294)
		tmp = t_1;
	elseif (y <= 1.5e-257)
		tmp = t;
	elseif (y <= 6.7e-205)
		tmp = t_1;
	elseif (y <= 2.1e-157)
		tmp = t;
	elseif (y <= 1.2e-137)
		tmp = (x * y) / z;
	elseif (y <= 1.35e-22)
		tmp = t_1;
	elseif (y <= 5.2e+80)
		tmp = t;
	else
		tmp = y * ((t - x) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+79], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-294], t$95$1, If[LessEqual[y, 1.5e-257], t, If[LessEqual[y, 6.7e-205], t$95$1, If[LessEqual[y, 2.1e-157], t, If[LessEqual[y, 1.2e-137], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.35e-22], t$95$1, If[LessEqual[y, 5.2e+80], t, N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.05000000000000004e79

   1. Initial program 72.8%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

      1. clear-num 89.4%

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

      2. associate-/r/ 89.4%

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

   5. Applied egg-rr 89.4%

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

   6. Taylor expanded in y around -inf 66.3%

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

      1. associate-/l* 78.4%

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

      2. associate-/r/ 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in t around inf 42.9%

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

       1. associate-*l/ 57.4%

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

       2. *-commutative 57.4%

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

   11. Simplified 57.4%

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

   if -1.05000000000000004e79 < y < -1.9e-294 or 1.5e-257 < y < 6.7000000000000001e-205 or 1.2e-137 < y < 1.3500000000000001e-22

   1. Initial program 77.7%

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

      1. associate-*l/ 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in z around 0 54.4%

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

      1. +-commutative 54.4%

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

      2. associate-/l* 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in t around inf 52.3%

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

   if -1.9e-294 < y < 1.5e-257 or 6.7000000000000001e-205 < y < 2.1e-157 or 1.3500000000000001e-22 < y < 5.19999999999999963e80

   1. Initial program 61.8%

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

      1. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in z around inf 58.2%

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

   if 2.1e-157 < y < 1.2e-137

   1. Initial program 61.1%

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

      1. associate-*l/ 60.7%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in y around -inf 62.7%

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

   5. Taylor expanded in a around 0 60.9%

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

      1. associate-*r/ 60.9%

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

      2. mul-1-neg 60.9%

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

      3. *-commutative 60.9%

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

      4. distribute-rgt-neg-in 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in t around 0 61.2%

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

   if 5.19999999999999963e80 < y

   1. Initial program 68.4%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around 0 42.6%

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

      1. +-commutative 42.6%

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

      2. associate-/l* 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in y around inf 60.8%

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

      1. div-sub 60.8%

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

      2. *-commutative 60.8%

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

   9. Simplified 60.8%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-294}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-257}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-205}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-157}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-137}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+80}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \]

Alternative 4: 58.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+154}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -3.1e+212)
     t_2
     (if (<= x -5.5e+154)
       (/ (- y a) (/ z x))
       (if (<= x -2.1e+81)
         (/ (- y) (/ (- a z) x))
         (if (<= x 9e-114)
           t_1
           (if (<= x 2.1e-82)
             (- x (/ y (/ a x)))
             (if (<= x 3.8e+51) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -3.1e+212) {
		tmp = t_2;
	} else if (x <= -5.5e+154) {
		tmp = (y - a) / (z / x);
	} else if (x <= -2.1e+81) {
		tmp = -y / ((a - z) / x);
	} else if (x <= 9e-114) {
		tmp = t_1;
	} else if (x <= 2.1e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 3.8e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-3.1d+212)) then
        tmp = t_2
    else if (x <= (-5.5d+154)) then
        tmp = (y - a) / (z / x)
    else if (x <= (-2.1d+81)) then
        tmp = -y / ((a - z) / x)
    else if (x <= 9d-114) then
        tmp = t_1
    else if (x <= 2.1d-82) then
        tmp = x - (y / (a / x))
    else if (x <= 3.8d+51) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -3.1e+212) {
		tmp = t_2;
	} else if (x <= -5.5e+154) {
		tmp = (y - a) / (z / x);
	} else if (x <= -2.1e+81) {
		tmp = -y / ((a - z) / x);
	} else if (x <= 9e-114) {
		tmp = t_1;
	} else if (x <= 2.1e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 3.8e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -3.1e+212:
		tmp = t_2
	elif x <= -5.5e+154:
		tmp = (y - a) / (z / x)
	elif x <= -2.1e+81:
		tmp = -y / ((a - z) / x)
	elif x <= 9e-114:
		tmp = t_1
	elif x <= 2.1e-82:
		tmp = x - (y / (a / x))
	elif x <= 3.8e+51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -3.1e+212)
		tmp = t_2;
	elseif (x <= -5.5e+154)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	elseif (x <= -2.1e+81)
		tmp = Float64(Float64(-y) / Float64(Float64(a - z) / x));
	elseif (x <= 9e-114)
		tmp = t_1;
	elseif (x <= 2.1e-82)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (x <= 3.8e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -3.1e+212)
		tmp = t_2;
	elseif (x <= -5.5e+154)
		tmp = (y - a) / (z / x);
	elseif (x <= -2.1e+81)
		tmp = -y / ((a - z) / x);
	elseif (x <= 9e-114)
		tmp = t_1;
	elseif (x <= 2.1e-82)
		tmp = x - (y / (a / x));
	elseif (x <= 3.8e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e+212], t$95$2, If[LessEqual[x, -5.5e+154], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e+81], N[((-y) / N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-114], t$95$1, If[LessEqual[x, 2.1e-82], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+51], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.09999999999999998e212 or 3.7999999999999997e51 < x

   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/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around 0 57.2%

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

      1. +-commutative 57.2%

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

      2. associate-/l* 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

   9. Simplified 67.6%

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

   if -3.09999999999999998e212 < x < -5.5000000000000006e154

   1. Initial program 55.1%

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

      1. associate-*l/ 55.2%

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

   3. Simplified 55.2%

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

   4. Taylor expanded in z around -inf 85.2%

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

      1. +-commutative 85.2%

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

      2. sub-neg 85.2%

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

      3. mul-1-neg 85.2%

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

      4. +-commutative 85.2%

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

      5. mul-1-neg 85.2%

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

      6. unsub-neg 85.2%

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

      7. +-commutative 85.2%

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

      8. mul-1-neg 85.2%

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

      9. sub-neg 85.2%

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

      10. distribute-rgt-out-- 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in t around 0 85.2%

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

      1. associate-/l* 85.4%

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

   9. Simplified 85.4%

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

   if -5.5000000000000006e154 < x < -2.0999999999999999e81

   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* 84.8%

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

   3. Simplified 84.8%

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

      1. clear-num 84.9%

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

      2. associate-/r/ 85.1%

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

   5. Applied egg-rr 85.1%

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

   6. Taylor expanded in y around -inf 55.7%

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

      1. associate-/l* 62.7%

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

      2. associate-/r/ 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in t around 0 55.2%

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

       1. mul-1-neg 55.2%

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

       2. associate-/l* 62.2%

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

   11. Simplified 62.2%

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

   if -2.0999999999999999e81 < x < 8.99999999999999937e-114 or 2.1e-82 < x < 3.7999999999999997e51

   1. Initial program 72.9%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 56.1%

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

      1. associate-*r/ 74.3%

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

   6. Simplified 74.3%

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

   if 8.99999999999999937e-114 < x < 2.1e-82

   1. Initial program 99.8%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-/l* 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. associate-/l* 83.6%

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

   9. Simplified 83.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+154}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+81}:\\ \;\;\;\;\frac{-y}{\frac{a - z}{x}}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 5: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -4.2e+212)
     t_2
     (if (<= x -4.2e+152)
       (/ (- y a) (/ z x))
       (if (<= x -5e+79)
         (* y (/ (- t x) (- a z)))
         (if (<= x 1.05e-113)
           t_1
           (if (<= x 2.2e-82)
             (- x (/ y (/ a x)))
             (if (<= x 1.35e+51) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.2e+212) {
		tmp = t_2;
	} else if (x <= -4.2e+152) {
		tmp = (y - a) / (z / x);
	} else if (x <= -5e+79) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 1.05e-113) {
		tmp = t_1;
	} else if (x <= 2.2e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 1.35e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-4.2d+212)) then
        tmp = t_2
    else if (x <= (-4.2d+152)) then
        tmp = (y - a) / (z / x)
    else if (x <= (-5d+79)) then
        tmp = y * ((t - x) / (a - z))
    else if (x <= 1.05d-113) then
        tmp = t_1
    else if (x <= 2.2d-82) then
        tmp = x - (y / (a / x))
    else if (x <= 1.35d+51) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -4.2e+212) {
		tmp = t_2;
	} else if (x <= -4.2e+152) {
		tmp = (y - a) / (z / x);
	} else if (x <= -5e+79) {
		tmp = y * ((t - x) / (a - z));
	} else if (x <= 1.05e-113) {
		tmp = t_1;
	} else if (x <= 2.2e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 1.35e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -4.2e+212:
		tmp = t_2
	elif x <= -4.2e+152:
		tmp = (y - a) / (z / x)
	elif x <= -5e+79:
		tmp = y * ((t - x) / (a - z))
	elif x <= 1.05e-113:
		tmp = t_1
	elif x <= 2.2e-82:
		tmp = x - (y / (a / x))
	elif x <= 1.35e+51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -4.2e+212)
		tmp = t_2;
	elseif (x <= -4.2e+152)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	elseif (x <= -5e+79)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (x <= 1.05e-113)
		tmp = t_1;
	elseif (x <= 2.2e-82)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (x <= 1.35e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -4.2e+212)
		tmp = t_2;
	elseif (x <= -4.2e+152)
		tmp = (y - a) / (z / x);
	elseif (x <= -5e+79)
		tmp = y * ((t - x) / (a - z));
	elseif (x <= 1.05e-113)
		tmp = t_1;
	elseif (x <= 2.2e-82)
		tmp = x - (y / (a / x));
	elseif (x <= 1.35e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+212], t$95$2, If[LessEqual[x, -4.2e+152], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5e+79], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-113], t$95$1, If[LessEqual[x, 2.2e-82], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+51], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.2e212 or 1.34999999999999996e51 < x

   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/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around 0 57.2%

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

      1. +-commutative 57.2%

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

      2. associate-/l* 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

   9. Simplified 67.6%

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

   if -4.2e212 < x < -4.2000000000000003e152

   1. Initial program 55.1%

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

      1. associate-*l/ 55.2%

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

   3. Simplified 55.2%

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

   4. Taylor expanded in z around -inf 85.2%

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

      1. +-commutative 85.2%

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

      2. sub-neg 85.2%

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

      3. mul-1-neg 85.2%

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

      4. +-commutative 85.2%

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

      5. mul-1-neg 85.2%

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

      6. unsub-neg 85.2%

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

      7. +-commutative 85.2%

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

      8. mul-1-neg 85.2%

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

      9. sub-neg 85.2%

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

      10. distribute-rgt-out-- 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in t around 0 85.2%

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

      1. associate-/l* 85.4%

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

   9. Simplified 85.4%

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

   if -4.2000000000000003e152 < x < -5e79

   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/ 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in y around inf 62.7%

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

      1. div-sub 62.7%

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

      2. *-commutative 62.7%

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

   6. Simplified 62.7%

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

   if -5e79 < x < 1.05e-113 or 2.19999999999999986e-82 < x < 1.34999999999999996e51

   1. Initial program 72.9%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 56.1%

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

      1. associate-*r/ 74.3%

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

   6. Simplified 74.3%

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

   if 1.05e-113 < x < 2.19999999999999986e-82

   1. Initial program 99.8%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-/l* 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. associate-/l* 83.6%

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

   9. Simplified 83.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 6: 59.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -3.25 \cdot 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+80}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -3.25e+212)
     t_2
     (if (<= x -2.2e+154)
       (/ (- y a) (/ z x))
       (if (<= x -1.9e+80)
         (* (- t x) (/ y (- a z)))
         (if (<= x 1.05e-113)
           t_1
           (if (<= x 2.1e-82)
             (- x (/ y (/ a x)))
             (if (<= x 7e+51) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -3.25e+212) {
		tmp = t_2;
	} else if (x <= -2.2e+154) {
		tmp = (y - a) / (z / x);
	} else if (x <= -1.9e+80) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 1.05e-113) {
		tmp = t_1;
	} else if (x <= 2.1e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 7e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-3.25d+212)) then
        tmp = t_2
    else if (x <= (-2.2d+154)) then
        tmp = (y - a) / (z / x)
    else if (x <= (-1.9d+80)) then
        tmp = (t - x) * (y / (a - z))
    else if (x <= 1.05d-113) then
        tmp = t_1
    else if (x <= 2.1d-82) then
        tmp = x - (y / (a / x))
    else if (x <= 7d+51) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -3.25e+212) {
		tmp = t_2;
	} else if (x <= -2.2e+154) {
		tmp = (y - a) / (z / x);
	} else if (x <= -1.9e+80) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 1.05e-113) {
		tmp = t_1;
	} else if (x <= 2.1e-82) {
		tmp = x - (y / (a / x));
	} else if (x <= 7e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -3.25e+212:
		tmp = t_2
	elif x <= -2.2e+154:
		tmp = (y - a) / (z / x)
	elif x <= -1.9e+80:
		tmp = (t - x) * (y / (a - z))
	elif x <= 1.05e-113:
		tmp = t_1
	elif x <= 2.1e-82:
		tmp = x - (y / (a / x))
	elif x <= 7e+51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -3.25e+212)
		tmp = t_2;
	elseif (x <= -2.2e+154)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	elseif (x <= -1.9e+80)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (x <= 1.05e-113)
		tmp = t_1;
	elseif (x <= 2.1e-82)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (x <= 7e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -3.25e+212)
		tmp = t_2;
	elseif (x <= -2.2e+154)
		tmp = (y - a) / (z / x);
	elseif (x <= -1.9e+80)
		tmp = (t - x) * (y / (a - z));
	elseif (x <= 1.05e-113)
		tmp = t_1;
	elseif (x <= 2.1e-82)
		tmp = x - (y / (a / x));
	elseif (x <= 7e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.25e+212], t$95$2, If[LessEqual[x, -2.2e+154], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e+80], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-113], t$95$1, If[LessEqual[x, 2.1e-82], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+51], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.24999999999999999e212 or 7e51 < x

   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/ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around 0 57.2%

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

      1. +-commutative 57.2%

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

      2. associate-/l* 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

   9. Simplified 67.6%

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

   if -3.24999999999999999e212 < x < -2.2000000000000001e154

   1. Initial program 55.1%

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

      1. associate-*l/ 55.2%

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

   3. Simplified 55.2%

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

   4. Taylor expanded in z around -inf 85.2%

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

      1. +-commutative 85.2%

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

      2. sub-neg 85.2%

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

      3. mul-1-neg 85.2%

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

      4. +-commutative 85.2%

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

      5. mul-1-neg 85.2%

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

      6. unsub-neg 85.2%

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

      7. +-commutative 85.2%

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

      8. mul-1-neg 85.2%

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

      9. sub-neg 85.2%

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

      10. distribute-rgt-out-- 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in t around 0 85.2%

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

      1. associate-/l* 85.4%

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

   9. Simplified 85.4%

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

   if -2.2000000000000001e154 < x < -1.89999999999999999e80

   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* 84.8%

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

   3. Simplified 84.8%

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

      1. clear-num 84.9%

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

      2. associate-/r/ 85.1%

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

   5. Applied egg-rr 85.1%

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

   6. Taylor expanded in y around -inf 55.7%

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

      1. associate-/l* 62.7%

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

      2. associate-/r/ 62.8%

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

   8. Simplified 62.8%

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

   if -1.89999999999999999e80 < x < 1.05e-113 or 2.1e-82 < x < 7e51

   1. Initial program 72.9%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 56.1%

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

      1. associate-*r/ 74.3%

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

   6. Simplified 74.3%

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

   if 1.05e-113 < x < 2.1e-82

   1. Initial program 99.8%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-/l* 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. associate-/l* 83.6%

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

   9. Simplified 83.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+80}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-82}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 7: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-271}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-136}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-91}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= a -1.7e+184)
     x
     (if (<= a -3.5e+93)
       t_1
       (if (<= a -1.65e-271)
         t
         (if (<= a 2.5e-136)
           (/ y (/ z x))
           (if (<= a 6.5e-91) t (if (<= a 1.75e+68) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (a <= -1.7e+184) {
		tmp = x;
	} else if (a <= -3.5e+93) {
		tmp = t_1;
	} else if (a <= -1.65e-271) {
		tmp = t;
	} else if (a <= 2.5e-136) {
		tmp = y / (z / x);
	} else if (a <= 6.5e-91) {
		tmp = t;
	} else if (a <= 1.75e+68) {
		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 / (a - z))
    if (a <= (-1.7d+184)) then
        tmp = x
    else if (a <= (-3.5d+93)) then
        tmp = t_1
    else if (a <= (-1.65d-271)) then
        tmp = t
    else if (a <= 2.5d-136) then
        tmp = y / (z / x)
    else if (a <= 6.5d-91) then
        tmp = t
    else if (a <= 1.75d+68) 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 / (a - z));
	double tmp;
	if (a <= -1.7e+184) {
		tmp = x;
	} else if (a <= -3.5e+93) {
		tmp = t_1;
	} else if (a <= -1.65e-271) {
		tmp = t;
	} else if (a <= 2.5e-136) {
		tmp = y / (z / x);
	} else if (a <= 6.5e-91) {
		tmp = t;
	} else if (a <= 1.75e+68) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if a <= -1.7e+184:
		tmp = x
	elif a <= -3.5e+93:
		tmp = t_1
	elif a <= -1.65e-271:
		tmp = t
	elif a <= 2.5e-136:
		tmp = y / (z / x)
	elif a <= 6.5e-91:
		tmp = t
	elif a <= 1.75e+68:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (a <= -1.7e+184)
		tmp = x;
	elseif (a <= -3.5e+93)
		tmp = t_1;
	elseif (a <= -1.65e-271)
		tmp = t;
	elseif (a <= 2.5e-136)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 6.5e-91)
		tmp = t;
	elseif (a <= 1.75e+68)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (a <= -1.7e+184)
		tmp = x;
	elseif (a <= -3.5e+93)
		tmp = t_1;
	elseif (a <= -1.65e-271)
		tmp = t;
	elseif (a <= 2.5e-136)
		tmp = y / (z / x);
	elseif (a <= 6.5e-91)
		tmp = t;
	elseif (a <= 1.75e+68)
		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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+184], x, If[LessEqual[a, -3.5e+93], t$95$1, If[LessEqual[a, -1.65e-271], t, If[LessEqual[a, 2.5e-136], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-91], t, If[LessEqual[a, 1.75e+68], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.7000000000000001e184 or 1.74999999999999989e68 < a

   1. Initial program 64.3%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in a around inf 58.3%

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

   if -1.7000000000000001e184 < a < -3.49999999999999998e93 or 6.5000000000000001e-91 < a < 1.74999999999999989e68

   1. Initial program 73.9%

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

      1. associate-/l* 83.2%

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

   3. Simplified 83.2%

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

      1. clear-num 83.1%

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

      2. associate-/r/ 83.1%

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

   5. Applied egg-rr 83.1%

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

   6. Taylor expanded in y around -inf 47.9%

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

      1. associate-/l* 55.3%

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

      2. associate-/r/ 55.7%

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

   8. Simplified 55.7%

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

   9. Taylor expanded in t around inf 29.6%

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

       1. associate-*l/ 38.6%

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

       2. *-commutative 38.6%

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

   11. Simplified 38.6%

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

   if -3.49999999999999998e93 < a < -1.6500000000000001e-271 or 2.5000000000000001e-136 < a < 6.5000000000000001e-91

   1. Initial program 76.1%

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

      1. associate-*l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in z around inf 40.2%

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

   if -1.6500000000000001e-271 < a < 2.5000000000000001e-136

   1. Initial program 77.6%

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

      1. associate-*l/ 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in y around -inf 77.2%

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

   5. Taylor expanded in a around 0 72.5%

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

      1. associate-*r/ 72.5%

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

      2. mul-1-neg 72.5%

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

      3. *-commutative 72.5%

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

      4. distribute-rgt-neg-in 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in t around 0 50.8%

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

      1. associate-/l* 50.9%

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

   10. Simplified 50.9%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+184}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-271}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-136}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-91}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := t - \frac{y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (- t (/ y (/ z t)))))
   (if (<= z -9e+151)
     t_2
     (if (<= z -3.1e-267)
       t_1
       (if (<= z 2.8e-252)
         (* y (/ (- t x) a))
         (if (<= z 7.5e-196)
           t_1
           (if (<= z 3.4e-152)
             (* x (- 1.0 (/ y a)))
             (if (<= z 9.6e-70) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -9e+151) {
		tmp = t_2;
	} else if (z <= -3.1e-267) {
		tmp = t_1;
	} else if (z <= 2.8e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 7.5e-196) {
		tmp = t_1;
	} else if (z <= 3.4e-152) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9.6e-70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    t_2 = t - (y / (z / t))
    if (z <= (-9d+151)) then
        tmp = t_2
    else if (z <= (-3.1d-267)) then
        tmp = t_1
    else if (z <= 2.8d-252) then
        tmp = y * ((t - x) / a)
    else if (z <= 7.5d-196) then
        tmp = t_1
    else if (z <= 3.4d-152) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 9.6d-70) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t - (y / (z / t));
	double tmp;
	if (z <= -9e+151) {
		tmp = t_2;
	} else if (z <= -3.1e-267) {
		tmp = t_1;
	} else if (z <= 2.8e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 7.5e-196) {
		tmp = t_1;
	} else if (z <= 3.4e-152) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 9.6e-70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = t - (y / (z / t))
	tmp = 0
	if z <= -9e+151:
		tmp = t_2
	elif z <= -3.1e-267:
		tmp = t_1
	elif z <= 2.8e-252:
		tmp = y * ((t - x) / a)
	elif z <= 7.5e-196:
		tmp = t_1
	elif z <= 3.4e-152:
		tmp = x * (1.0 - (y / a))
	elif z <= 9.6e-70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(t - Float64(y / Float64(z / t)))
	tmp = 0.0
	if (z <= -9e+151)
		tmp = t_2;
	elseif (z <= -3.1e-267)
		tmp = t_1;
	elseif (z <= 2.8e-252)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 7.5e-196)
		tmp = t_1;
	elseif (z <= 3.4e-152)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 9.6e-70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = t - (y / (z / t));
	tmp = 0.0;
	if (z <= -9e+151)
		tmp = t_2;
	elseif (z <= -3.1e-267)
		tmp = t_1;
	elseif (z <= 2.8e-252)
		tmp = y * ((t - x) / a);
	elseif (z <= 7.5e-196)
		tmp = t_1;
	elseif (z <= 3.4e-152)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 9.6e-70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+151], t$95$2, If[LessEqual[z, -3.1e-267], t$95$1, If[LessEqual[z, 2.8e-252], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-196], t$95$1, If[LessEqual[z, 3.4e-152], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-70], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999997e151 or 9.6000000000000005e-70 < z

   1. Initial program 54.4%

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

      1. associate-*l/ 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in z around -inf 72.4%

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

      1. +-commutative 72.4%

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

      2. sub-neg 72.4%

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

      3. mul-1-neg 72.4%

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

      4. +-commutative 72.4%

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

      5. mul-1-neg 72.4%

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

      6. unsub-neg 72.4%

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

      7. +-commutative 72.4%

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

      8. mul-1-neg 72.4%

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

      9. sub-neg 72.4%

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

      10. distribute-rgt-out-- 72.6%

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

   6. Simplified 72.6%

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

   7. Taylor expanded in y around inf 68.2%

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

   8. Taylor expanded in t around inf 55.3%

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

      1. associate-/l* 60.3%

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

   10. Simplified 60.3%

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

   if -8.9999999999999997e151 < z < -3.1000000000000001e-267 or 2.80000000000000018e-252 < z < 7.5e-196 or 3.39999999999999984e-152 < z < 9.6000000000000005e-70

   1. Initial program 83.0%

      \[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \]
   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 z around 0 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in t around inf 55.9%

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

   if -3.1000000000000001e-267 < z < 2.80000000000000018e-252

   1. Initial program 85.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 94.8%

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

   6. Simplified 94.8%

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

   7. Taylor expanded in y around inf 79.6%

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

      1. div-sub 79.6%

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

      2. *-commutative 79.6%

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

   9. Simplified 79.6%

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

   if 7.5e-196 < z < 3.39999999999999984e-152

   1. Initial program 82.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 62.6%

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

      1. +-commutative 62.6%

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

      2. associate-/l* 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

   9. Simplified 68.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+151}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-267}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-70}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]

Alternative 9: 53.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := t + \frac{x \cdot y}{z}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (+ t (/ (* x y) z))))
   (if (<= z -3e+46)
     t_2
     (if (<= z -2.95e-270)
       t_1
       (if (<= z 4.4e-252)
         (* y (/ (- t x) a))
         (if (<= z 1.06e-193)
           t_1
           (if (<= z 4.6e-149)
             (* x (- 1.0 (/ y a)))
             (if (<= z 1.8e-69) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t + ((x * y) / z);
	double tmp;
	if (z <= -3e+46) {
		tmp = t_2;
	} else if (z <= -2.95e-270) {
		tmp = t_1;
	} else if (z <= 4.4e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.06e-193) {
		tmp = t_1;
	} else if (z <= 4.6e-149) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.8e-69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    t_2 = t + ((x * y) / z)
    if (z <= (-3d+46)) then
        tmp = t_2
    else if (z <= (-2.95d-270)) then
        tmp = t_1
    else if (z <= 4.4d-252) then
        tmp = y * ((t - x) / a)
    else if (z <= 1.06d-193) then
        tmp = t_1
    else if (z <= 4.6d-149) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.8d-69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t + ((x * y) / z);
	double tmp;
	if (z <= -3e+46) {
		tmp = t_2;
	} else if (z <= -2.95e-270) {
		tmp = t_1;
	} else if (z <= 4.4e-252) {
		tmp = y * ((t - x) / a);
	} else if (z <= 1.06e-193) {
		tmp = t_1;
	} else if (z <= 4.6e-149) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.8e-69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = t + ((x * y) / z)
	tmp = 0
	if z <= -3e+46:
		tmp = t_2
	elif z <= -2.95e-270:
		tmp = t_1
	elif z <= 4.4e-252:
		tmp = y * ((t - x) / a)
	elif z <= 1.06e-193:
		tmp = t_1
	elif z <= 4.6e-149:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.8e-69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(t + Float64(Float64(x * y) / z))
	tmp = 0.0
	if (z <= -3e+46)
		tmp = t_2;
	elseif (z <= -2.95e-270)
		tmp = t_1;
	elseif (z <= 4.4e-252)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 1.06e-193)
		tmp = t_1;
	elseif (z <= 4.6e-149)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.8e-69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = t + ((x * y) / z);
	tmp = 0.0;
	if (z <= -3e+46)
		tmp = t_2;
	elseif (z <= -2.95e-270)
		tmp = t_1;
	elseif (z <= 4.4e-252)
		tmp = y * ((t - x) / a);
	elseif (z <= 1.06e-193)
		tmp = t_1;
	elseif (z <= 4.6e-149)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.8e-69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+46], t$95$2, If[LessEqual[z, -2.95e-270], t$95$1, If[LessEqual[z, 4.4e-252], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-193], t$95$1, If[LessEqual[z, 4.6e-149], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-69], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.00000000000000023e46 or 1.80000000000000009e-69 < z

   1. Initial program 54.3%

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

      1. associate-*l/ 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in z around -inf 69.0%

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

      1. +-commutative 69.0%

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

      2. sub-neg 69.0%

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

      3. mul-1-neg 69.0%

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

      4. +-commutative 69.0%

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

      5. mul-1-neg 69.0%

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

      6. unsub-neg 69.0%

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

      7. +-commutative 69.0%

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

      8. mul-1-neg 69.0%

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

      9. sub-neg 69.0%

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

      10. distribute-rgt-out-- 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in y around inf 64.7%

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

   8. Taylor expanded in t around 0 59.6%

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

      1. associate-*r* 59.6%

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

      2. mul-1-neg 59.6%

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

   10. Simplified 59.6%

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

   if -3.00000000000000023e46 < z < -2.95e-270 or 4.3999999999999998e-252 < z < 1.06e-193 or 4.5999999999999999e-149 < z < 1.80000000000000009e-69

   1. Initial program 87.1%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 62.5%

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

      1. +-commutative 62.5%

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

      2. associate-/l* 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in t around inf 60.0%

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

   if -2.95e-270 < z < 4.3999999999999998e-252

   1. Initial program 85.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 94.8%

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

   6. Simplified 94.8%

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

   7. Taylor expanded in y around inf 79.6%

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

      1. div-sub 79.6%

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

      2. *-commutative 79.6%

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

   9. Simplified 79.6%

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

   if 1.06e-193 < z < 4.5999999999999999e-149

   1. Initial program 82.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 62.6%

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

      1. +-commutative 62.6%

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

      2. associate-/l* 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

   9. Simplified 68.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+46}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-270}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-193}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \]

Alternative 10: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-125}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+70} \lor \neg \left(a \leq 2.8 \cdot 10^{+105}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -4.5e-40)
     t_1
     (if (<= a 6.4e-125)
       (+ t (/ (* y (- x t)) z))
       (if (or (<= a 1.15e+70) (not (<= a 2.8e+105)))
         t_1
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -4.5e-40) {
		tmp = t_1;
	} else if (a <= 6.4e-125) {
		tmp = t + ((y * (x - t)) / z);
	} else if ((a <= 1.15e+70) || !(a <= 2.8e+105)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / t))
    if (a <= (-4.5d-40)) then
        tmp = t_1
    else if (a <= 6.4d-125) then
        tmp = t + ((y * (x - t)) / z)
    else if ((a <= 1.15d+70) .or. (.not. (a <= 2.8d+105))) then
        tmp = t_1
    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 t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -4.5e-40) {
		tmp = t_1;
	} else if (a <= 6.4e-125) {
		tmp = t + ((y * (x - t)) / z);
	} else if ((a <= 1.15e+70) || !(a <= 2.8e+105)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if a <= -4.5e-40:
		tmp = t_1
	elif a <= 6.4e-125:
		tmp = t + ((y * (x - t)) / z)
	elif (a <= 1.15e+70) or not (a <= 2.8e+105):
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -4.5e-40)
		tmp = t_1;
	elseif (a <= 6.4e-125)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif ((a <= 1.15e+70) || !(a <= 2.8e+105))
		tmp = t_1;
	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)
	t_1 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (a <= -4.5e-40)
		tmp = t_1;
	elseif (a <= 6.4e-125)
		tmp = t + ((y * (x - t)) / z);
	elseif ((a <= 1.15e+70) || ~((a <= 2.8e+105)))
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e-40], t$95$1, If[LessEqual[a, 6.4e-125], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.15e+70], N[Not[LessEqual[a, 2.8e+105]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.5000000000000001e-40 or 6.3999999999999997e-125 < a < 1.14999999999999997e70 or 2.8000000000000001e105 < a

   1. Initial program 71.8%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in t around inf 77.6%

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

   if -4.5000000000000001e-40 < a < 6.3999999999999997e-125

   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/ 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in z around -inf 84.7%

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

      1. +-commutative 84.7%

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

      2. sub-neg 84.7%

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

      3. mul-1-neg 84.7%

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

      4. +-commutative 84.7%

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

      5. mul-1-neg 84.7%

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

      6. unsub-neg 84.7%

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

      7. +-commutative 84.7%

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

      8. mul-1-neg 84.7%

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

      9. sub-neg 84.7%

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

      10. distribute-rgt-out-- 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in y around inf 80.2%

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

   if 1.14999999999999997e70 < a < 2.8000000000000001e105

   1. Initial program 60.9%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-125}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+70} \lor \neg \left(a \leq 2.8 \cdot 10^{+105}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 11: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-126}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+69} \lor \neg \left(a \leq 7 \cdot 10^{+105}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -8.2e-37)
     t_1
     (if (<= a 3e-126)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (or (<= a 9.2e+69) (not (<= a 7e+105)))
         t_1
         (+ x (/ y (/ a (- t x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -8.2e-37) {
		tmp = t_1;
	} else if (a <= 3e-126) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if ((a <= 9.2e+69) || !(a <= 7e+105)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / t))
    if (a <= (-8.2d-37)) then
        tmp = t_1
    else if (a <= 3d-126) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if ((a <= 9.2d+69) .or. (.not. (a <= 7d+105))) then
        tmp = t_1
    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 t_1 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -8.2e-37) {
		tmp = t_1;
	} else if (a <= 3e-126) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if ((a <= 9.2e+69) || !(a <= 7e+105)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if a <= -8.2e-37:
		tmp = t_1
	elif a <= 3e-126:
		tmp = t + (((t - x) * (a - y)) / z)
	elif (a <= 9.2e+69) or not (a <= 7e+105):
		tmp = t_1
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -8.2e-37)
		tmp = t_1;
	elseif (a <= 3e-126)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif ((a <= 9.2e+69) || !(a <= 7e+105))
		tmp = t_1;
	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)
	t_1 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (a <= -8.2e-37)
		tmp = t_1;
	elseif (a <= 3e-126)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif ((a <= 9.2e+69) || ~((a <= 7e+105)))
		tmp = t_1;
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e-37], t$95$1, If[LessEqual[a, 3e-126], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 9.2e+69], N[Not[LessEqual[a, 7e+105]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.1999999999999996e-37 or 3.0000000000000002e-126 < a < 9.20000000000000067e69 or 6.99999999999999982e105 < a

   1. Initial program 71.8%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in t around inf 77.6%

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

   if -8.1999999999999996e-37 < a < 3.0000000000000002e-126

   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/ 83.0%

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

   3. Simplified 83.0%

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

   4. Taylor expanded in z around -inf 84.7%

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

      1. +-commutative 84.7%

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

      2. sub-neg 84.7%

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

      3. mul-1-neg 84.7%

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

      4. +-commutative 84.7%

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

      5. mul-1-neg 84.7%

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

      6. unsub-neg 84.7%

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

      7. +-commutative 84.7%

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

      8. mul-1-neg 84.7%

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

      9. sub-neg 84.7%

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

      10. distribute-rgt-out-- 84.7%

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

   6. Simplified 84.7%

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

   if 9.20000000000000067e69 < a < 6.99999999999999982e105

   1. Initial program 60.9%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-126}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+69} \lor \neg \left(a \leq 7 \cdot 10^{+105}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 12: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -56 \lor \neg \left(z \leq -8 \cdot 10^{-74}\right) \land \left(z \leq -1.1 \cdot 10^{-92} \lor \neg \left(z \leq 7 \cdot 10^{-37}\right)\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -56.0)
         (and (not (<= z -8e-74)) (or (<= z -1.1e-92) (not (<= z 7e-37)))))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -56.0) || (!(z <= -8e-74) && ((z <= -1.1e-92) || !(z <= 7e-37)))) {
		tmp = t * ((y - z) / (a - z));
	} 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 <= (-56.0d0)) .or. (.not. (z <= (-8d-74))) .and. (z <= (-1.1d-92)) .or. (.not. (z <= 7d-37))) then
        tmp = t * ((y - z) / (a - z))
    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 <= -56.0) || (!(z <= -8e-74) && ((z <= -1.1e-92) || !(z <= 7e-37)))) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -56.0) or (not (z <= -8e-74) and ((z <= -1.1e-92) or not (z <= 7e-37))):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -56.0) || (!(z <= -8e-74) && ((z <= -1.1e-92) || !(z <= 7e-37))))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	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 <= -56.0) || (~((z <= -8e-74)) && ((z <= -1.1e-92) || ~((z <= 7e-37)))))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -56.0], And[N[Not[LessEqual[z, -8e-74]], $MachinePrecision], Or[LessEqual[z, -1.1e-92], N[Not[LessEqual[z, 7e-37]], $MachinePrecision]]]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $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 < -56 or -7.99999999999999966e-74 < z < -1.09999999999999994e-92 or 7.0000000000000003e-37 < z

   1. Initial program 57.4%

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

      1. associate-*l/ 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in x around 0 48.1%

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

      1. associate-*r/ 66.6%

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

   6. Simplified 66.6%

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

   if -56 < z < -7.99999999999999966e-74 or -1.09999999999999994e-92 < z < 7.0000000000000003e-37

   1. Initial program 86.9%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   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* 78.2%

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

   6. Simplified 78.2%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -56 \lor \neg \left(z \leq -8 \cdot 10^{-74}\right) \land \left(z \leq -1.1 \cdot 10^{-92} \lor \neg \left(z \leq 7 \cdot 10^{-37}\right)\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 13: 42.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-102} \lor \neg \left(x \leq 2.5 \cdot 10^{-116} \lor \neg \left(x \leq 4.7 \cdot 10^{-82}\right) \land x \leq 1.9 \cdot 10^{-44}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.75e-102)
         (not (or (<= x 2.5e-116) (and (not (<= x 4.7e-82)) (<= x 1.9e-44)))))
   (* x (- 1.0 (/ y a)))
   (* t (/ y (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.75e-102) || !((x <= 2.5e-116) || (!(x <= 4.7e-82) && (x <= 1.9e-44)))) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.75d-102)) .or. (.not. (x <= 2.5d-116) .or. (.not. (x <= 4.7d-82)) .and. (x <= 1.9d-44))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t * (y / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.75e-102) || !((x <= 2.5e-116) || (!(x <= 4.7e-82) && (x <= 1.9e-44)))) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t * (y / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.75e-102) or not ((x <= 2.5e-116) or (not (x <= 4.7e-82) and (x <= 1.9e-44))):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t * (y / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.75e-102) || !((x <= 2.5e-116) || (!(x <= 4.7e-82) && (x <= 1.9e-44))))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t * Float64(y / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.75e-102) || ~(((x <= 2.5e-116) || (~((x <= 4.7e-82)) && (x <= 1.9e-44)))))
		tmp = x * (1.0 - (y / a));
	else
		tmp = t * (y / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.75e-102], N[Not[Or[LessEqual[x, 2.5e-116], And[N[Not[LessEqual[x, 4.7e-82]], $MachinePrecision], LessEqual[x, 1.9e-44]]]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.74999999999999993e-102 or 2.5000000000000001e-116 < x < 4.7000000000000001e-82 or 1.9e-44 < x

   1. Initial program 71.0%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in z around 0 49.7%

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

      1. +-commutative 49.7%

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

      2. associate-/l* 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

   9. Simplified 53.6%

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

   if -1.74999999999999993e-102 < x < 2.5000000000000001e-116 or 4.7000000000000001e-82 < x < 1.9e-44

   1. Initial program 73.9%

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

      1. associate-/l* 87.2%

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

   3. Simplified 87.2%

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

      1. clear-num 87.1%

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

      2. associate-/r/ 87.1%

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

   5. Applied egg-rr 87.1%

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

   6. Taylor expanded in y around -inf 39.9%

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

      1. associate-/l* 47.8%

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

      2. associate-/r/ 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in t around inf 36.3%

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

       1. associate-*l/ 45.2%

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

       2. *-commutative 45.2%

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

   11. Simplified 45.2%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-102} \lor \neg \left(x \leq 2.5 \cdot 10^{-116} \lor \neg \left(x \leq 4.7 \cdot 10^{-82}\right) \land x \leq 1.9 \cdot 10^{-44}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 14: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{if}\;a \leq -9 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-136}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))))
   (if (<= a -9e-37)
     t_1
     (if (<= a 5.8e-136)
       (+ t (/ (* y (- x t)) z))
       (if (<= a 2.6e+69) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -9e-37) {
		tmp = t_1;
	} else if (a <= 5.8e-136) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 2.6e+69) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / (t - x)))
    if (a <= (-9d-37)) then
        tmp = t_1
    else if (a <= 5.8d-136) then
        tmp = t + ((y * (x - t)) / z)
    else if (a <= 2.6d+69) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double tmp;
	if (a <= -9e-37) {
		tmp = t_1;
	} else if (a <= 5.8e-136) {
		tmp = t + ((y * (x - t)) / z);
	} else if (a <= 2.6e+69) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	tmp = 0
	if a <= -9e-37:
		tmp = t_1
	elif a <= 5.8e-136:
		tmp = t + ((y * (x - t)) / z)
	elif a <= 2.6e+69:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	tmp = 0.0
	if (a <= -9e-37)
		tmp = t_1;
	elseif (a <= 5.8e-136)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	elseif (a <= 2.6e+69)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	tmp = 0.0;
	if (a <= -9e-37)
		tmp = t_1;
	elseif (a <= 5.8e-136)
		tmp = t + ((y * (x - t)) / z);
	elseif (a <= 2.6e+69)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e-37], t$95$1, If[LessEqual[a, 5.8e-136], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+69], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.00000000000000081e-37 or 2.6000000000000002e69 < a

   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/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 58.2%

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

      1. +-commutative 58.2%

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

      2. associate-/l* 77.1%

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

   6. Simplified 77.1%

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

   if -9.00000000000000081e-37 < a < 5.79999999999999989e-136

   1. Initial program 75.1%

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

      1. associate-*l/ 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in z around -inf 84.5%

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

      1. +-commutative 84.5%

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

      2. sub-neg 84.5%

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

      3. mul-1-neg 84.5%

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

      4. +-commutative 84.5%

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

      5. mul-1-neg 84.5%

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

      6. unsub-neg 84.5%

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

      7. +-commutative 84.5%

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

      8. mul-1-neg 84.5%

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

      9. sub-neg 84.5%

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

      10. distribute-rgt-out-- 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in y around inf 80.0%

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

   if 5.79999999999999989e-136 < a < 2.6000000000000002e69

   1. Initial program 77.4%

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

      1. associate-*l/ 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in x around 0 55.3%

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

      1. associate-*r/ 62.9%

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

   6. Simplified 62.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-136}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 15: 37.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-85}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= a -4.8e+179)
     x
     (if (<= a -4.2e+91)
       t_1
       (if (<= a 8.8e-85)
         t
         (if (<= a 6.8e+36) t_1 (if (<= a 1.65e+68) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -4.8e+179) {
		tmp = x;
	} else if (a <= -4.2e+91) {
		tmp = t_1;
	} else if (a <= 8.8e-85) {
		tmp = t;
	} else if (a <= 6.8e+36) {
		tmp = t_1;
	} else if (a <= 1.65e+68) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (a <= (-4.8d+179)) then
        tmp = x
    else if (a <= (-4.2d+91)) then
        tmp = t_1
    else if (a <= 8.8d-85) then
        tmp = t
    else if (a <= 6.8d+36) then
        tmp = t_1
    else if (a <= 1.65d+68) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -4.8e+179) {
		tmp = x;
	} else if (a <= -4.2e+91) {
		tmp = t_1;
	} else if (a <= 8.8e-85) {
		tmp = t;
	} else if (a <= 6.8e+36) {
		tmp = t_1;
	} else if (a <= 1.65e+68) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if a <= -4.8e+179:
		tmp = x
	elif a <= -4.2e+91:
		tmp = t_1
	elif a <= 8.8e-85:
		tmp = t
	elif a <= 6.8e+36:
		tmp = t_1
	elif a <= 1.65e+68:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (a <= -4.8e+179)
		tmp = x;
	elseif (a <= -4.2e+91)
		tmp = t_1;
	elseif (a <= 8.8e-85)
		tmp = t;
	elseif (a <= 6.8e+36)
		tmp = t_1;
	elseif (a <= 1.65e+68)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (a <= -4.8e+179)
		tmp = x;
	elseif (a <= -4.2e+91)
		tmp = t_1;
	elseif (a <= 8.8e-85)
		tmp = t;
	elseif (a <= 6.8e+36)
		tmp = t_1;
	elseif (a <= 1.65e+68)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+179], x, If[LessEqual[a, -4.2e+91], t$95$1, If[LessEqual[a, 8.8e-85], t, If[LessEqual[a, 6.8e+36], t$95$1, If[LessEqual[a, 1.65e+68], t, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.80000000000000025e179 or 1.65e68 < a

   1. Initial program 64.0%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in a around inf 56.9%

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

   if -4.80000000000000025e179 < a < -4.20000000000000015e91 or 8.8e-85 < a < 6.7999999999999996e36

   1. Initial program 77.0%

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

      1. associate-*l/ 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in y around -inf 49.5%

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

   5. Taylor expanded in t around inf 31.1%

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

   6. Taylor expanded in a around inf 26.0%

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

      1. associate-/l* 34.1%

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

   8. Simplified 34.1%

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

      1. associate-/r/ 35.5%

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

   10. Applied egg-rr 35.5%

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

   if -4.20000000000000015e91 < a < 8.8e-85 or 6.7999999999999996e36 < a < 1.65e68

   1. Initial program 75.2%

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

      1. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in z around inf 36.9%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-85}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 36.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-273}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-139}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.3e+179)
   x
   (if (<= a -2.8e+91)
     (* t (/ y a))
     (if (<= a -6e-273)
       t
       (if (<= a 7.5e-139) (/ y (/ z x)) (if (<= a 1.65e+68) t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e+179) {
		tmp = x;
	} else if (a <= -2.8e+91) {
		tmp = t * (y / a);
	} else if (a <= -6e-273) {
		tmp = t;
	} else if (a <= 7.5e-139) {
		tmp = y / (z / x);
	} else if (a <= 1.65e+68) {
		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 <= (-4.3d+179)) then
        tmp = x
    else if (a <= (-2.8d+91)) then
        tmp = t * (y / a)
    else if (a <= (-6d-273)) then
        tmp = t
    else if (a <= 7.5d-139) then
        tmp = y / (z / x)
    else if (a <= 1.65d+68) 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 <= -4.3e+179) {
		tmp = x;
	} else if (a <= -2.8e+91) {
		tmp = t * (y / a);
	} else if (a <= -6e-273) {
		tmp = t;
	} else if (a <= 7.5e-139) {
		tmp = y / (z / x);
	} else if (a <= 1.65e+68) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.3e+179:
		tmp = x
	elif a <= -2.8e+91:
		tmp = t * (y / a)
	elif a <= -6e-273:
		tmp = t
	elif a <= 7.5e-139:
		tmp = y / (z / x)
	elif a <= 1.65e+68:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.3e+179)
		tmp = x;
	elseif (a <= -2.8e+91)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= -6e-273)
		tmp = t;
	elseif (a <= 7.5e-139)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 1.65e+68)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.3e+179)
		tmp = x;
	elseif (a <= -2.8e+91)
		tmp = t * (y / a);
	elseif (a <= -6e-273)
		tmp = t;
	elseif (a <= 7.5e-139)
		tmp = y / (z / x);
	elseif (a <= 1.65e+68)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.3e+179], x, If[LessEqual[a, -2.8e+91], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-273], t, If[LessEqual[a, 7.5e-139], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+68], t, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.2999999999999999e179 or 1.65e68 < a

   1. Initial program 64.0%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in a around inf 56.9%

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

   if -4.2999999999999999e179 < a < -2.7999999999999999e91

   1. Initial program 63.1%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around -inf 36.0%

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

   5. Taylor expanded in t around inf 25.0%

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

   6. Taylor expanded in a around inf 25.0%

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

      1. associate-/l* 50.9%

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

   8. Simplified 50.9%

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

      1. associate-/r/ 51.1%

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

   10. Applied egg-rr 51.1%

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

   if -2.7999999999999999e91 < a < -5.99999999999999975e-273 or 7.5000000000000001e-139 < a < 1.65e68

   1. Initial program 77.1%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in z around inf 33.2%

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

   if -5.99999999999999975e-273 < a < 7.5000000000000001e-139

   1. Initial program 77.6%

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

      1. associate-*l/ 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in y around -inf 77.2%

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

   5. Taylor expanded in a around 0 72.5%

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

      1. associate-*r/ 72.5%

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

      2. mul-1-neg 72.5%

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

      3. *-commutative 72.5%

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

      4. distribute-rgt-neg-in 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in t around 0 50.8%

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

      1. associate-/l* 50.9%

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

   10. Simplified 50.9%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-273}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-139}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 39.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+99) x (if (<= a 1.7e+68) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+99) {
		tmp = x;
	} else if (a <= 1.7e+68) {
		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+99)) then
        tmp = x
    else if (a <= 1.7d+68) 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+99) {
		tmp = x;
	} else if (a <= 1.7e+68) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+99:
		tmp = x
	elif a <= 1.7e+68:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+99)
		tmp = x;
	elseif (a <= 1.7e+68)
		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+99)
		tmp = x;
	elseif (a <= 1.7e+68)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+99], x, If[LessEqual[a, 1.7e+68], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.50000000000000004e99 or 1.70000000000000008e68 < a

   1. Initial program 63.2%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in a around inf 53.2%

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

   if -2.50000000000000004e99 < a < 1.70000000000000008e68

   1. Initial program 77.2%

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

      1. associate-*l/ 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in z around inf 31.0%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 25.6% 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 72.3%

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

   1. associate-*l/ 88.7%

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

3. Simplified 88.7%

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

4. Taylor expanded in z around inf 23.8%

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

5. Final simplification 23.8%

   \[\leadsto t \]

Developer target: 83.8% 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 2023238 
(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))))