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

Percentage Accurate: 68.8% → 90.9%

Time: 17.6s

Alternatives: 21

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: 68.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-279}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_1 -4e-279)
     (fma (/ (- y z) (- a z)) (- t x) x)
     (if (<= t_1 0.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_1 <= -4e-279) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -4e-279)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-279], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $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[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.00000000000000022e-279

   1. Initial program 70.3%

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

      1. +-commutative 70.3%

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

      2. associate-*l/ 91.2%

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

      3. fma-def 91.3%

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

   3. Simplified 91.3%

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

   if -4.00000000000000022e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.3%

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

      1. +-commutative 4.3%

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

      2. associate-*l/ 4.3%

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

      3. fma-def 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in z around -inf 99.8%

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

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

   1. Initial program 76.5%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

      1. *-commutative 89.9%

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

      2. clear-num 89.9%

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

      3. un-div-inv 90.0%

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

   5. Applied egg-rr 90.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -4 \cdot 10^{-279}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-279} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (or (<= t_1 -4e-279) (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 <= -4e-279) || !(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 <= (-4d-279)) .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 <= -4e-279) || !(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 <= -4e-279) 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 <= -4e-279) || !(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 <= -4e-279) || ~((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, -4e-279], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.00000000000000022e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.6%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   if -4.00000000000000022e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.3%

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

      1. +-commutative 4.3%

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

      2. associate-*l/ 4.3%

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

      3. fma-def 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in z around -inf 99.8%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -4 \cdot 10^{-279} \lor \neg \left(x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 3: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-279}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y z) (- x t)) (- a z)))))
   (if (<= t_1 -4e-279)
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (if (<= t_1 0.0)
       (+ t (/ (* (- t x) (- a y)) z))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_1 <= -4e-279) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((y - z) * (x - t)) / (a - z))
    if (t_1 <= (-4d-279)) 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 + ((t - x) / ((a - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - z) * (x - t)) / (a - z));
	double tmp;
	if (t_1 <= -4e-279) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else {
		tmp = x + ((t - x) / ((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 <= -4e-279:
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	elif t_1 <= 0.0:
		tmp = t + (((t - x) * (a - y)) / z)
	else:
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -4e-279)
		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(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - z) * (x - t)) / (a - z));
	tmp = 0.0;
	if (t_1 <= -4e-279)
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	elseif (t_1 <= 0.0)
		tmp = t + (((t - x) * (a - y)) / z);
	else
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-279], 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[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.00000000000000022e-279

   1. Initial program 70.3%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   if -4.00000000000000022e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.3%

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

      1. +-commutative 4.3%

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

      2. associate-*l/ 4.3%

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

      3. fma-def 4.3%

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

   3. Simplified 4.3%

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

   4. Taylor expanded in z around -inf 99.8%

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

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

   1. Initial program 76.5%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

      1. *-commutative 89.9%

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

      2. clear-num 89.9%

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

      3. un-div-inv 90.0%

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

   5. Applied egg-rr 90.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq -4 \cdot 10^{-279}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x - \frac{\left(y - z\right) \cdot \left(x - t\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 4: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := \frac{-t}{\frac{a - z}{z}}\\ t_3 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.004:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-194}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t))))
        (t_2 (/ (- t) (/ (- a z) z)))
        (t_3 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.05e+42)
     t_2
     (if (<= z -1.25e+21)
       t_1
       (if (<= z -0.004)
         (* y (/ (- x) (- a z)))
         (if (<= z -2.5e-67)
           (/ (* t (- z y)) z)
           (if (<= z -1.2e-177)
             t_1
             (if (<= z -1.5e-236)
               t_3
               (if (<= z 1.15e-194)
                 (+ x (/ (* y t) a))
                 (if (<= z 1.65e+18) t_3 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = -t / ((a - z) / z);
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.05e+42) {
		tmp = t_2;
	} else if (z <= -1.25e+21) {
		tmp = t_1;
	} else if (z <= -0.004) {
		tmp = y * (-x / (a - z));
	} else if (z <= -2.5e-67) {
		tmp = (t * (z - y)) / z;
	} else if (z <= -1.2e-177) {
		tmp = t_1;
	} else if (z <= -1.5e-236) {
		tmp = t_3;
	} else if (z <= 1.15e-194) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.65e+18) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    t_2 = -t / ((a - z) / z)
    t_3 = x * (1.0d0 - (y / a))
    if (z <= (-1.05d+42)) then
        tmp = t_2
    else if (z <= (-1.25d+21)) then
        tmp = t_1
    else if (z <= (-0.004d0)) then
        tmp = y * (-x / (a - z))
    else if (z <= (-2.5d-67)) then
        tmp = (t * (z - y)) / z
    else if (z <= (-1.2d-177)) then
        tmp = t_1
    else if (z <= (-1.5d-236)) then
        tmp = t_3
    else if (z <= 1.15d-194) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.65d+18) then
        tmp = t_3
    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 / (a / t));
	double t_2 = -t / ((a - z) / z);
	double t_3 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.05e+42) {
		tmp = t_2;
	} else if (z <= -1.25e+21) {
		tmp = t_1;
	} else if (z <= -0.004) {
		tmp = y * (-x / (a - z));
	} else if (z <= -2.5e-67) {
		tmp = (t * (z - y)) / z;
	} else if (z <= -1.2e-177) {
		tmp = t_1;
	} else if (z <= -1.5e-236) {
		tmp = t_3;
	} else if (z <= 1.15e-194) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.65e+18) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = -t / ((a - z) / z)
	t_3 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.05e+42:
		tmp = t_2
	elif z <= -1.25e+21:
		tmp = t_1
	elif z <= -0.004:
		tmp = y * (-x / (a - z))
	elif z <= -2.5e-67:
		tmp = (t * (z - y)) / z
	elif z <= -1.2e-177:
		tmp = t_1
	elif z <= -1.5e-236:
		tmp = t_3
	elif z <= 1.15e-194:
		tmp = x + ((y * t) / a)
	elif z <= 1.65e+18:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(Float64(-t) / Float64(Float64(a - z) / z))
	t_3 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.05e+42)
		tmp = t_2;
	elseif (z <= -1.25e+21)
		tmp = t_1;
	elseif (z <= -0.004)
		tmp = Float64(y * Float64(Float64(-x) / Float64(a - z)));
	elseif (z <= -2.5e-67)
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	elseif (z <= -1.2e-177)
		tmp = t_1;
	elseif (z <= -1.5e-236)
		tmp = t_3;
	elseif (z <= 1.15e-194)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.65e+18)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = -t / ((a - z) / z);
	t_3 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.05e+42)
		tmp = t_2;
	elseif (z <= -1.25e+21)
		tmp = t_1;
	elseif (z <= -0.004)
		tmp = y * (-x / (a - z));
	elseif (z <= -2.5e-67)
		tmp = (t * (z - y)) / z;
	elseif (z <= -1.2e-177)
		tmp = t_1;
	elseif (z <= -1.5e-236)
		tmp = t_3;
	elseif (z <= 1.15e-194)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.65e+18)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+42], t$95$2, If[LessEqual[z, -1.25e+21], t$95$1, If[LessEqual[z, -0.004], N[(y * N[((-x) / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-67], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.2e-177], t$95$1, If[LessEqual[z, -1.5e-236], t$95$3, If[LessEqual[z, 1.15e-194], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+18], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.04999999999999998e42 or 1.65e18 < z

   1. Initial program 45.7%

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

      1. associate-*l/ 73.2%

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

   3. Simplified 73.2%

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

      1. clear-num 73.2%

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

      2. associate-/r/ 73.0%

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

   5. Applied egg-rr 73.0%

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

   6. Taylor expanded in x around 0 48.2%

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

      1. associate-/l* 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in y around 0 42.4%

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

       1. mul-1-neg 42.4%

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

       2. associate-/l* 59.9%

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

       3. distribute-neg-frac 59.9%

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

   11. Simplified 59.9%

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

   if -1.04999999999999998e42 < z < -1.25e21 or -2.4999999999999999e-67 < z < -1.1999999999999999e-177

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

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

      2. associate-*l/ 89.1%

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

      3. fma-def 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in z around 0 52.4%

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

      1. +-commutative 52.4%

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

      2. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

   7. Taylor expanded in t around inf 52.6%

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

      1. associate-/l* 70.9%

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

   9. Simplified 70.9%

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

   if -1.25e21 < z < -0.0040000000000000001

   1. Initial program 51.1%

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

      1. +-commutative 51.1%

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

      2. associate-*l/ 51.1%

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

      3. fma-def 51.1%

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

   3. Simplified 51.1%

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

   4. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in y around inf 52.4%

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

      1. associate-*r/ 52.4%

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

      2. associate-*r* 52.4%

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

      3. mul-1-neg 52.4%

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

   9. Simplified 52.4%

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

   10. Taylor expanded in y around 0 52.4%

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

       1. mul-1-neg 52.4%

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

       2. associate-*r/ 52.4%

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

       3. distribute-rgt-neg-in 52.4%

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

       4. distribute-neg-frac 52.4%

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

   12. Simplified 52.4%

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

   if -0.0040000000000000001 < z < -2.4999999999999999e-67

   1. Initial program 93.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 58.1%

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

      1. associate-/l* 58.2%

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

   8. Simplified 58.2%

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

   9. Taylor expanded in a around 0 51.6%

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

       1. associate-*r/ 51.6%

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

       2. associate-*r* 51.6%

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

       3. mul-1-neg 51.6%

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

   11. Simplified 51.6%

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

   if -1.1999999999999999e-177 < z < -1.50000000000000007e-236 or 1.15000000000000001e-194 < z < 1.65e18

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-*l/ 97.2%

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

      3. fma-def 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 76.8%

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

      1. *-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. unsub-neg 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in z around 0 68.6%

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

   if -1.50000000000000007e-236 < z < 1.15000000000000001e-194

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-*l/ 92.1%

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

      3. fma-def 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 82.6%

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

      1. +-commutative 82.6%

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

      2. associate-/l* 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in t around inf 76.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -0.004:\\ \;\;\;\;y \cdot \frac{-x}{a - z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-177}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-194}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \end{array} \]

Alternative 5: 46.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -2.4 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-218}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-89}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (+ x (/ y (/ a t)))))
   (if (<= a -2.4e-11)
     t_2
     (if (<= a -1.08e-125)
       t_1
       (if (<= a -4e-218)
         t
         (if (<= a 3.8e-273)
           t_1
           (if (<= a 2.5e-89)
             t
             (if (<= a 5.2e+90)
               (* x (- 1.0 (/ y a)))
               (if (<= a 9.5e+94) t t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -2.4e-11) {
		tmp = t_2;
	} else if (a <= -1.08e-125) {
		tmp = t_1;
	} else if (a <= -4e-218) {
		tmp = t;
	} else if (a <= 3.8e-273) {
		tmp = t_1;
	} else if (a <= 2.5e-89) {
		tmp = t;
	} else if (a <= 5.2e+90) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 9.5e+94) {
		tmp = t;
	} 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 - a) / z)
    t_2 = x + (y / (a / t))
    if (a <= (-2.4d-11)) then
        tmp = t_2
    else if (a <= (-1.08d-125)) then
        tmp = t_1
    else if (a <= (-4d-218)) then
        tmp = t
    else if (a <= 3.8d-273) then
        tmp = t_1
    else if (a <= 2.5d-89) then
        tmp = t
    else if (a <= 5.2d+90) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 9.5d+94) then
        tmp = t
    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 - a) / z);
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -2.4e-11) {
		tmp = t_2;
	} else if (a <= -1.08e-125) {
		tmp = t_1;
	} else if (a <= -4e-218) {
		tmp = t;
	} else if (a <= 3.8e-273) {
		tmp = t_1;
	} else if (a <= 2.5e-89) {
		tmp = t;
	} else if (a <= 5.2e+90) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 9.5e+94) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x + (y / (a / t))
	tmp = 0
	if a <= -2.4e-11:
		tmp = t_2
	elif a <= -1.08e-125:
		tmp = t_1
	elif a <= -4e-218:
		tmp = t
	elif a <= 3.8e-273:
		tmp = t_1
	elif a <= 2.5e-89:
		tmp = t
	elif a <= 5.2e+90:
		tmp = x * (1.0 - (y / a))
	elif a <= 9.5e+94:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -2.4e-11)
		tmp = t_2;
	elseif (a <= -1.08e-125)
		tmp = t_1;
	elseif (a <= -4e-218)
		tmp = t;
	elseif (a <= 3.8e-273)
		tmp = t_1;
	elseif (a <= 2.5e-89)
		tmp = t;
	elseif (a <= 5.2e+90)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 9.5e+94)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -2.4e-11)
		tmp = t_2;
	elseif (a <= -1.08e-125)
		tmp = t_1;
	elseif (a <= -4e-218)
		tmp = t;
	elseif (a <= 3.8e-273)
		tmp = t_1;
	elseif (a <= 2.5e-89)
		tmp = t;
	elseif (a <= 5.2e+90)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 9.5e+94)
		tmp = t;
	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 - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.4e-11], t$95$2, If[LessEqual[a, -1.08e-125], t$95$1, If[LessEqual[a, -4e-218], t, If[LessEqual[a, 3.8e-273], t$95$1, If[LessEqual[a, 2.5e-89], t, If[LessEqual[a, 5.2e+90], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+94], t, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.4000000000000001e-11 or 9.4999999999999998e94 < 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. +-commutative 71.8%

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

      2. associate-*l/ 93.1%

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

      3. fma-def 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-/l* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in t around inf 58.6%

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

      1. associate-/l* 63.7%

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

   9. Simplified 63.7%

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

   if -2.4000000000000001e-11 < a < -1.07999999999999998e-125 or -4.0000000000000001e-218 < a < 3.8000000000000004e-273

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. associate-*l/ 77.6%

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

      3. fma-def 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in z around inf 56.4%

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

      1. associate-*r/ 56.4%

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

      2. +-commutative 56.4%

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

      3. distribute-lft-in 56.4%

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

      4. neg-mul-1 56.4%

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

      5. mul-1-neg 56.4%

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

      6. remove-double-neg 56.4%

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

      7. mul-1-neg 56.4%

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

      8. sub-neg 56.4%

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

   9. Simplified 56.4%

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

   if -1.07999999999999998e-125 < a < -4.0000000000000001e-218 or 3.8000000000000004e-273 < a < 2.49999999999999983e-89 or 5.1999999999999997e90 < a < 9.4999999999999998e94

   1. Initial program 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-*l/ 74.1%

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

      3. fma-def 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in z around inf 56.6%

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

   if 2.49999999999999983e-89 < a < 5.1999999999999997e90

   1. Initial program 73.9%

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

      1. +-commutative 73.9%

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

      2. associate-*l/ 83.6%

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

      3. fma-def 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 44.8%

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

      1. *-commutative 44.8%

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

      2. mul-1-neg 44.8%

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

      3. unsub-neg 44.8%

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

   6. Simplified 44.8%

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

   7. Taylor expanded in z around 0 42.0%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-218}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-89}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6: 46.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.46 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-219}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-88}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+91}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (+ x (/ y (/ a t)))))
   (if (<= a -2.1e-14)
     t_2
     (if (<= a -1.46e-130)
       t_1
       (if (<= a -6e-219)
         t
         (if (<= a 6.5e-273)
           t_1
           (if (<= a 1.45e-88)
             t
             (if (<= a 6e+91)
               (- x (/ y (/ a x)))
               (if (<= a 9.5e+94) t t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -2.1e-14) {
		tmp = t_2;
	} else if (a <= -1.46e-130) {
		tmp = t_1;
	} else if (a <= -6e-219) {
		tmp = t;
	} else if (a <= 6.5e-273) {
		tmp = t_1;
	} else if (a <= 1.45e-88) {
		tmp = t;
	} else if (a <= 6e+91) {
		tmp = x - (y / (a / x));
	} else if (a <= 9.5e+94) {
		tmp = t;
	} 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 - a) / z)
    t_2 = x + (y / (a / t))
    if (a <= (-2.1d-14)) then
        tmp = t_2
    else if (a <= (-1.46d-130)) then
        tmp = t_1
    else if (a <= (-6d-219)) then
        tmp = t
    else if (a <= 6.5d-273) then
        tmp = t_1
    else if (a <= 1.45d-88) then
        tmp = t
    else if (a <= 6d+91) then
        tmp = x - (y / (a / x))
    else if (a <= 9.5d+94) then
        tmp = t
    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 - a) / z);
	double t_2 = x + (y / (a / t));
	double tmp;
	if (a <= -2.1e-14) {
		tmp = t_2;
	} else if (a <= -1.46e-130) {
		tmp = t_1;
	} else if (a <= -6e-219) {
		tmp = t;
	} else if (a <= 6.5e-273) {
		tmp = t_1;
	} else if (a <= 1.45e-88) {
		tmp = t;
	} else if (a <= 6e+91) {
		tmp = x - (y / (a / x));
	} else if (a <= 9.5e+94) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x + (y / (a / t))
	tmp = 0
	if a <= -2.1e-14:
		tmp = t_2
	elif a <= -1.46e-130:
		tmp = t_1
	elif a <= -6e-219:
		tmp = t
	elif a <= 6.5e-273:
		tmp = t_1
	elif a <= 1.45e-88:
		tmp = t
	elif a <= 6e+91:
		tmp = x - (y / (a / x))
	elif a <= 9.5e+94:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (a <= -2.1e-14)
		tmp = t_2;
	elseif (a <= -1.46e-130)
		tmp = t_1;
	elseif (a <= -6e-219)
		tmp = t;
	elseif (a <= 6.5e-273)
		tmp = t_1;
	elseif (a <= 1.45e-88)
		tmp = t;
	elseif (a <= 6e+91)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (a <= 9.5e+94)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	t_2 = x + (y / (a / t));
	tmp = 0.0;
	if (a <= -2.1e-14)
		tmp = t_2;
	elseif (a <= -1.46e-130)
		tmp = t_1;
	elseif (a <= -6e-219)
		tmp = t;
	elseif (a <= 6.5e-273)
		tmp = t_1;
	elseif (a <= 1.45e-88)
		tmp = t;
	elseif (a <= 6e+91)
		tmp = x - (y / (a / x));
	elseif (a <= 9.5e+94)
		tmp = t;
	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 - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e-14], t$95$2, If[LessEqual[a, -1.46e-130], t$95$1, If[LessEqual[a, -6e-219], t, If[LessEqual[a, 6.5e-273], t$95$1, If[LessEqual[a, 1.45e-88], t, If[LessEqual[a, 6e+91], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+94], t, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.0999999999999999e-14 or 9.4999999999999998e94 < 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. +-commutative 71.8%

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

      2. associate-*l/ 93.1%

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

      3. fma-def 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-/l* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in t around inf 58.6%

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

      1. associate-/l* 63.7%

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

   9. Simplified 63.7%

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

   if -2.0999999999999999e-14 < a < -1.46e-130 or -6.0000000000000002e-219 < a < 6.49999999999999979e-273

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. associate-*l/ 77.6%

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

      3. fma-def 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in z around inf 56.4%

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

      1. associate-*r/ 56.4%

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

      2. +-commutative 56.4%

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

      3. distribute-lft-in 56.4%

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

      4. neg-mul-1 56.4%

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

      5. mul-1-neg 56.4%

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

      6. remove-double-neg 56.4%

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

      7. mul-1-neg 56.4%

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

      8. sub-neg 56.4%

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

   9. Simplified 56.4%

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

   if -1.46e-130 < a < -6.0000000000000002e-219 or 6.49999999999999979e-273 < a < 1.4500000000000001e-88 or 6.00000000000000012e91 < a < 9.4999999999999998e94

   1. Initial program 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-*l/ 74.1%

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

      3. fma-def 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in z around inf 56.6%

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

   if 1.4500000000000001e-88 < a < 6.00000000000000012e91

   1. Initial program 73.9%

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

      1. +-commutative 73.9%

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

      2. associate-*l/ 83.6%

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

      3. fma-def 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in z around 0 48.7%

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

      1. +-commutative 48.7%

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

      2. associate-/l* 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in t around 0 38.9%

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

      1. +-commutative 38.9%

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

      2. mul-1-neg 38.9%

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

      3. unsub-neg 38.9%

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

      4. associate-/l* 42.1%

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

   9. Simplified 42.1%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;a \leq -1.46 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-219}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-88}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+91}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 7: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y - a}{\frac{z}{t - x}}\\ t_2 := x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{if}\;a \leq -50000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 25000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (- y a) (/ z (- t x)))))
        (t_2 (+ x (/ (- y z) (/ (- a z) t)))))
   (if (<= a -50000000.0)
     t_2
     (if (<= a 1e-88)
       t_1
       (if (<= a 25000000000000.0)
         t_2
         (if (<= a 7e+43)
           t_1
           (if (<= a 2.2e+78) (+ x (/ y (/ a (- t x)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y - a) / (z / (t - x)));
	double t_2 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -50000000.0) {
		tmp = t_2;
	} else if (a <= 1e-88) {
		tmp = t_1;
	} else if (a <= 25000000000000.0) {
		tmp = t_2;
	} else if (a <= 7e+43) {
		tmp = t_1;
	} else if (a <= 2.2e+78) {
		tmp = x + (y / (a / (t - x)));
	} 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 - a) / (z / (t - x)))
    t_2 = x + ((y - z) / ((a - z) / t))
    if (a <= (-50000000.0d0)) then
        tmp = t_2
    else if (a <= 1d-88) then
        tmp = t_1
    else if (a <= 25000000000000.0d0) then
        tmp = t_2
    else if (a <= 7d+43) then
        tmp = t_1
    else if (a <= 2.2d+78) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y - a) / (z / (t - x)));
	double t_2 = x + ((y - z) / ((a - z) / t));
	double tmp;
	if (a <= -50000000.0) {
		tmp = t_2;
	} else if (a <= 1e-88) {
		tmp = t_1;
	} else if (a <= 25000000000000.0) {
		tmp = t_2;
	} else if (a <= 7e+43) {
		tmp = t_1;
	} else if (a <= 2.2e+78) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y - a) / (z / (t - x)))
	t_2 = x + ((y - z) / ((a - z) / t))
	tmp = 0
	if a <= -50000000.0:
		tmp = t_2
	elif a <= 1e-88:
		tmp = t_1
	elif a <= 25000000000000.0:
		tmp = t_2
	elif a <= 7e+43:
		tmp = t_1
	elif a <= 2.2e+78:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y - a) / Float64(z / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (a <= -50000000.0)
		tmp = t_2;
	elseif (a <= 1e-88)
		tmp = t_1;
	elseif (a <= 25000000000000.0)
		tmp = t_2;
	elseif (a <= 7e+43)
		tmp = t_1;
	elseif (a <= 2.2e+78)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y - a) / (z / (t - x)));
	t_2 = x + ((y - z) / ((a - z) / t));
	tmp = 0.0;
	if (a <= -50000000.0)
		tmp = t_2;
	elseif (a <= 1e-88)
		tmp = t_1;
	elseif (a <= 25000000000000.0)
		tmp = t_2;
	elseif (a <= 7e+43)
		tmp = t_1;
	elseif (a <= 2.2e+78)
		tmp = x + (y / (a / (t - x)));
	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 - a), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -50000000.0], t$95$2, If[LessEqual[a, 1e-88], t$95$1, If[LessEqual[a, 25000000000000.0], t$95$2, If[LessEqual[a, 7e+43], t$95$1, If[LessEqual[a, 2.2e+78], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5e7 or 9.99999999999999934e-89 < a < 2.5e13 or 2.20000000000000014e78 < a

   1. Initial program 72.5%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 82.6%

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

   if -5e7 < a < 9.99999999999999934e-89 or 2.5e13 < a < 7.0000000000000002e43

   1. Initial program 63.8%

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

      1. +-commutative 63.8%

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

      2. associate-*l/ 75.1%

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

      3. fma-def 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in z around inf 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 84.0%

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

      3. distribute-lft-out-- 84.0%

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

      4. mul-1-neg 84.0%

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

      5. distribute-neg-frac 84.0%

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

      6. associate-/l* 82.4%

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

      7. *-commutative 82.4%

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

      8. distribute-rgt-out-- 82.4%

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

      9. unsub-neg 82.4%

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

      10. distribute-rgt-out-- 82.4%

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

      11. *-commutative 82.4%

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

      12. associate-/l* 84.0%

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

   6. Simplified 84.0%

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

   if 7.0000000000000002e43 < a < 2.20000000000000014e78

   1. Initial program 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-*l/ 99.7%

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

      3. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -50000000:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 10^{-88}:\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 25000000000000:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+43}:\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 8: 54.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a - z}{z}}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-175}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ (- a z) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= z -2.1e+43)
     t_1
     (if (<= z -3.8e-175)
       (+ x (/ y (/ a t)))
       (if (<= z -3.4e-236)
         t_2
         (if (<= z 2.4e-196)
           (+ x (/ (* y t) a))
           (if (<= z 1.4e+18) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / ((a - z) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.1e+43) {
		tmp = t_1;
	} else if (z <= -3.8e-175) {
		tmp = x + (y / (a / t));
	} else if (z <= -3.4e-236) {
		tmp = t_2;
	} else if (z <= 2.4e-196) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.4e+18) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = -t / ((a - z) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (z <= (-2.1d+43)) then
        tmp = t_1
    else if (z <= (-3.8d-175)) then
        tmp = x + (y / (a / t))
    else if (z <= (-3.4d-236)) then
        tmp = t_2
    else if (z <= 2.4d-196) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.4d+18) then
        tmp = t_2
    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 / ((a - z) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -2.1e+43) {
		tmp = t_1;
	} else if (z <= -3.8e-175) {
		tmp = x + (y / (a / t));
	} else if (z <= -3.4e-236) {
		tmp = t_2;
	} else if (z <= 2.4e-196) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.4e+18) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / ((a - z) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -2.1e+43:
		tmp = t_1
	elif z <= -3.8e-175:
		tmp = x + (y / (a / t))
	elif z <= -3.4e-236:
		tmp = t_2
	elif z <= 2.4e-196:
		tmp = x + ((y * t) / a)
	elif z <= 1.4e+18:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(Float64(a - z) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -2.1e+43)
		tmp = t_1;
	elseif (z <= -3.8e-175)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= -3.4e-236)
		tmp = t_2;
	elseif (z <= 2.4e-196)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.4e+18)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / ((a - z) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -2.1e+43)
		tmp = t_1;
	elseif (z <= -3.8e-175)
		tmp = x + (y / (a / t));
	elseif (z <= -3.4e-236)
		tmp = t_2;
	elseif (z <= 2.4e-196)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.4e+18)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+43], t$95$1, If[LessEqual[z, -3.8e-175], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e-236], t$95$2, If[LessEqual[z, 2.4e-196], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+18], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.10000000000000002e43 or 1.4e18 < z

   1. Initial program 45.7%

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

      1. associate-*l/ 73.2%

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

   3. Simplified 73.2%

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

      1. clear-num 73.2%

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

      2. associate-/r/ 73.0%

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

   5. Applied egg-rr 73.0%

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

   6. Taylor expanded in x around 0 48.2%

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

      1. associate-/l* 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in y around 0 42.4%

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

       1. mul-1-neg 42.4%

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

       2. associate-/l* 59.9%

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

       3. distribute-neg-frac 59.9%

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

   11. Simplified 59.9%

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

   if -2.10000000000000002e43 < z < -3.8e-175

   1. Initial program 73.9%

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

      1. +-commutative 73.9%

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

      2. associate-*l/ 89.1%

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

      3. fma-def 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in z around 0 47.3%

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

      1. +-commutative 47.3%

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

      2. associate-/l* 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in t around inf 42.8%

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

      1. associate-/l* 53.5%

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

   9. Simplified 53.5%

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

   if -3.8e-175 < z < -3.3999999999999998e-236 or 2.40000000000000021e-196 < z < 1.4e18

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-*l/ 97.2%

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

      3. fma-def 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 76.8%

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

      1. *-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. unsub-neg 76.8%

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

   6. Simplified 76.8%

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

   7. Taylor expanded in z around 0 68.6%

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

   if -3.3999999999999998e-236 < z < 2.40000000000000021e-196

   1. Initial program 94.2%

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

      1. +-commutative 94.2%

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

      2. associate-*l/ 92.1%

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

      3. fma-def 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 82.6%

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

      1. +-commutative 82.6%

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

      2. associate-/l* 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in t around inf 76.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+43}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-175}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-196}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a - z}{z}}\\ \end{array} \]

Alternative 9: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ t_2 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+103}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))) (t_2 (* x (- 1.0 (/ y a)))))
   (if (<= x -1.15e+277)
     t_2
     (if (<= x -8e+173)
       t_1
       (if (<= x -1.45e+103)
         (- x (/ y (/ a x)))
         (if (<= x 5.6e+30)
           (* t (/ (- y z) (- a z)))
           (if (<= x 4.6e+194) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.15e+277) {
		tmp = t_2;
	} else if (x <= -8e+173) {
		tmp = t_1;
	} else if (x <= -1.45e+103) {
		tmp = x - (y / (a / x));
	} else if (x <= 5.6e+30) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 4.6e+194) {
		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 - a) / z)
    t_2 = x * (1.0d0 - (y / a))
    if (x <= (-1.15d+277)) then
        tmp = t_2
    else if (x <= (-8d+173)) then
        tmp = t_1
    else if (x <= (-1.45d+103)) then
        tmp = x - (y / (a / x))
    else if (x <= 5.6d+30) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 4.6d+194) 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 - a) / z);
	double t_2 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -1.15e+277) {
		tmp = t_2;
	} else if (x <= -8e+173) {
		tmp = t_1;
	} else if (x <= -1.45e+103) {
		tmp = x - (y / (a / x));
	} else if (x <= 5.6e+30) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 4.6e+194) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	t_2 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -1.15e+277:
		tmp = t_2
	elif x <= -8e+173:
		tmp = t_1
	elif x <= -1.45e+103:
		tmp = x - (y / (a / x))
	elif x <= 5.6e+30:
		tmp = t * ((y - z) / (a - z))
	elif x <= 4.6e+194:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	t_2 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -1.15e+277)
		tmp = t_2;
	elseif (x <= -8e+173)
		tmp = t_1;
	elseif (x <= -1.45e+103)
		tmp = Float64(x - Float64(y / Float64(a / x)));
	elseif (x <= 5.6e+30)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 4.6e+194)
		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 - a) / z);
	t_2 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -1.15e+277)
		tmp = t_2;
	elseif (x <= -8e+173)
		tmp = t_1;
	elseif (x <= -1.45e+103)
		tmp = x - (y / (a / x));
	elseif (x <= 5.6e+30)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 4.6e+194)
		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 - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+277], t$95$2, If[LessEqual[x, -8e+173], t$95$1, If[LessEqual[x, -1.45e+103], N[(x - N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+30], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+194], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.14999999999999997e277 or 4.6000000000000001e194 < x

   1. Initial program 50.7%

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

      1. +-commutative 50.7%

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

      2. associate-*l/ 84.2%

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

      3. fma-def 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in x around inf 83.1%

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

      1. *-commutative 83.1%

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

      2. mul-1-neg 83.1%

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

      3. unsub-neg 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in z around 0 77.0%

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

   if -1.14999999999999997e277 < x < -8.0000000000000001e173 or 5.59999999999999966e30 < x < 4.6000000000000001e194

   1. Initial program 55.6%

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

      1. +-commutative 55.6%

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

      2. associate-*l/ 67.4%

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

      3. fma-def 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in x around inf 57.0%

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

      1. *-commutative 57.0%

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

      2. mul-1-neg 57.0%

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

      3. unsub-neg 57.0%

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

   6. Simplified 57.0%

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

   7. Taylor expanded in z around inf 58.1%

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

      1. associate-*r/ 58.1%

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

      2. +-commutative 58.1%

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

      3. distribute-lft-in 58.1%

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

      4. neg-mul-1 58.1%

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

      5. mul-1-neg 58.1%

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

      6. remove-double-neg 58.1%

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

      7. mul-1-neg 58.1%

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

      8. sub-neg 58.1%

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

   9. Simplified 58.1%

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

   if -8.0000000000000001e173 < x < -1.4499999999999999e103

   1. Initial program 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*l/ 93.0%

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

      3. fma-def 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in t around 0 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. associate-/l* 82.1%

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

   9. Simplified 82.1%

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

   if -1.4499999999999999e103 < x < 5.59999999999999966e30

   1. Initial program 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-*l/ 89.3%

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

      3. fma-def 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around inf 72.0%

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

      1. div-sub 72.0%

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

   6. Simplified 72.0%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+103}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+194}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

Alternative 10: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+41} \lor \neg \left(z \leq 112\right):\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+41) (not (<= z 112.0)))
   (- t (/ (- y a) (/ z (- t x))))
   (+ x (* (- t x) (* (- y z) (/ 1.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+41) || !(z <= 112.0)) {
		tmp = t - ((y - a) / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * ((y - z) * (1.0 / a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+41)) .or. (.not. (z <= 112.0d0))) then
        tmp = t - ((y - a) / (z / (t - x)))
    else
        tmp = x + ((t - x) * ((y - z) * (1.0d0 / a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+41) || !(z <= 112.0)) {
		tmp = t - ((y - a) / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * ((y - z) * (1.0 / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+41) or not (z <= 112.0):
		tmp = t - ((y - a) / (z / (t - x)))
	else:
		tmp = x + ((t - x) * ((y - z) * (1.0 / a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+41) || !(z <= 112.0))
		tmp = Float64(t - Float64(Float64(y - a) / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) * Float64(1.0 / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+41) || ~((z <= 112.0)))
		tmp = t - ((y - a) / (z / (t - x)));
	else
		tmp = x + ((t - x) * ((y - z) * (1.0 / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+41], N[Not[LessEqual[z, 112.0]], $MachinePrecision]], N[(t - N[(N[(y - a), $MachinePrecision] / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999996e41 or 112 < z

   1. Initial program 47.9%

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

      1. +-commutative 47.9%

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

      2. associate-*l/ 74.3%

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

      3. fma-def 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. associate-/l* 79.3%

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

      3. distribute-lft-out-- 79.3%

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

      4. mul-1-neg 79.3%

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

      5. distribute-neg-frac 79.3%

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

      6. associate-/l* 70.3%

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

      7. *-commutative 70.3%

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

      8. distribute-rgt-out-- 70.1%

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

      9. unsub-neg 70.1%

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

      10. distribute-rgt-out-- 70.3%

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

      11. *-commutative 70.3%

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

      12. associate-/l* 79.3%

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

   6. Simplified 79.3%

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

   if -9.4999999999999996e41 < z < 112

   1. Initial program 87.4%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

      1. clear-num 93.0%

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

      2. associate-/r/ 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in a around inf 78.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+41} \lor \neg \left(z \leq 112\right):\\ \;\;\;\;t - \frac{y - a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a}\right)\\ \end{array} \]

Alternative 11: 33.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-14} \lor \neg \left(x \leq 4.8 \cdot 10^{+28}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (- y a) z))))
   (if (<= x -6.4e+139)
     t_1
     (if (<= x -3.5e+97)
       x
       (if (or (<= x -4.9e-14) (not (<= x 4.8e+28))) t_1 t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (x <= -6.4e+139) {
		tmp = t_1;
	} else if (x <= -3.5e+97) {
		tmp = x;
	} else if ((x <= -4.9e-14) || !(x <= 4.8e+28)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (x <= (-6.4d+139)) then
        tmp = t_1
    else if (x <= (-3.5d+97)) then
        tmp = x
    else if ((x <= (-4.9d-14)) .or. (.not. (x <= 4.8d+28))) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (x <= -6.4e+139) {
		tmp = t_1;
	} else if (x <= -3.5e+97) {
		tmp = x;
	} else if ((x <= -4.9e-14) || !(x <= 4.8e+28)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if x <= -6.4e+139:
		tmp = t_1
	elif x <= -3.5e+97:
		tmp = x
	elif (x <= -4.9e-14) or not (x <= 4.8e+28):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (x <= -6.4e+139)
		tmp = t_1;
	elseif (x <= -3.5e+97)
		tmp = x;
	elseif ((x <= -4.9e-14) || !(x <= 4.8e+28))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (x <= -6.4e+139)
		tmp = t_1;
	elseif (x <= -3.5e+97)
		tmp = x;
	elseif ((x <= -4.9e-14) || ~((x <= 4.8e+28)))
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+139], t$95$1, If[LessEqual[x, -3.5e+97], x, If[Or[LessEqual[x, -4.9e-14], N[Not[LessEqual[x, 4.8e+28]], $MachinePrecision]], t$95$1, t]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4000000000000002e139 or -3.5000000000000001e97 < x < -4.89999999999999995e-14 or 4.79999999999999962e28 < x

   1. Initial program 57.9%

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

      1. +-commutative 57.9%

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

      2. associate-*l/ 76.2%

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

      3. fma-def 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in x around inf 64.7%

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

      1. *-commutative 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in z around inf 49.9%

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

      1. associate-*r/ 49.9%

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

      2. +-commutative 49.9%

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

      3. distribute-lft-in 49.9%

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

      4. neg-mul-1 49.9%

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

      5. mul-1-neg 49.9%

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

      6. remove-double-neg 49.9%

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

      7. mul-1-neg 49.9%

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

      8. sub-neg 49.9%

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

   9. Simplified 49.9%

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

   if -6.4000000000000002e139 < x < -3.5000000000000001e97

   1. Initial program 75.3%

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

      1. +-commutative 75.3%

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

      2. associate-*l/ 83.8%

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

      3. fma-def 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in a around inf 61.0%

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

   if -4.89999999999999995e-14 < x < 4.79999999999999962e28

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-*l/ 90.1%

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

      3. fma-def 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in z around inf 43.8%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+97}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-14} \lor \neg \left(x \leq 4.8 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 48.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+197}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+197)
   t
   (if (<= z -6e+151)
     (* x (/ (- y a) z))
     (if (<= z -1.3e+43) t (if (<= z 1.66e+18) (* x (- 1.0 (/ y a))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+197) {
		tmp = t;
	} else if (z <= -6e+151) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.3e+43) {
		tmp = t;
	} else if (z <= 1.66e+18) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.5d+197)) then
        tmp = t
    else if (z <= (-6d+151)) then
        tmp = x * ((y - a) / z)
    else if (z <= (-1.3d+43)) then
        tmp = t
    else if (z <= 1.66d+18) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+197) {
		tmp = t;
	} else if (z <= -6e+151) {
		tmp = x * ((y - a) / z);
	} else if (z <= -1.3e+43) {
		tmp = t;
	} else if (z <= 1.66e+18) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+197:
		tmp = t
	elif z <= -6e+151:
		tmp = x * ((y - a) / z)
	elif z <= -1.3e+43:
		tmp = t
	elif z <= 1.66e+18:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+197)
		tmp = t;
	elseif (z <= -6e+151)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= -1.3e+43)
		tmp = t;
	elseif (z <= 1.66e+18)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+197)
		tmp = t;
	elseif (z <= -6e+151)
		tmp = x * ((y - a) / z);
	elseif (z <= -1.3e+43)
		tmp = t;
	elseif (z <= 1.66e+18)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+197], t, If[LessEqual[z, -6e+151], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e+43], t, If[LessEqual[z, 1.66e+18], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4999999999999997e197 or -5.9999999999999998e151 < z < -1.3000000000000001e43 or 1.66e18 < z

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-*l/ 74.3%

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

      3. fma-def 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in z around inf 56.3%

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

   if -9.4999999999999997e197 < z < -5.9999999999999998e151

   1. Initial program 32.6%

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

      1. +-commutative 32.6%

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

      2. associate-*l/ 61.3%

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

      3. fma-def 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in x around inf 32.4%

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

      1. *-commutative 32.4%

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

      2. mul-1-neg 32.4%

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

      3. unsub-neg 32.4%

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

   6. Simplified 32.4%

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

   7. Taylor expanded in z around inf 60.9%

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

      1. associate-*r/ 60.9%

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

      2. +-commutative 60.9%

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

      3. distribute-lft-in 60.9%

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

      4. neg-mul-1 60.9%

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

      5. mul-1-neg 60.9%

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

      6. remove-double-neg 60.9%

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

      7. mul-1-neg 60.9%

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

      8. sub-neg 60.9%

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

   9. Simplified 60.9%

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

   if -1.3000000000000001e43 < z < 1.66e18

   1. Initial program 87.9%

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

      1. +-commutative 87.9%

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

      2. associate-*l/ 93.4%

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

      3. fma-def 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. mul-1-neg 64.4%

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

      3. unsub-neg 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 55.4%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+197}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 48.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+197}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+150}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.6e+197)
   t
   (if (<= z -7.8e+150)
     (* (- y a) (/ x z))
     (if (<= z -2.9e+43) t (if (<= z 1.45e+18) (* x (- 1.0 (/ y a))) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.6e+197) {
		tmp = t;
	} else if (z <= -7.8e+150) {
		tmp = (y - a) * (x / z);
	} else if (z <= -2.9e+43) {
		tmp = t;
	} else if (z <= 1.45e+18) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.6d+197)) then
        tmp = t
    else if (z <= (-7.8d+150)) then
        tmp = (y - a) * (x / z)
    else if (z <= (-2.9d+43)) then
        tmp = t
    else if (z <= 1.45d+18) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.6e+197) {
		tmp = t;
	} else if (z <= -7.8e+150) {
		tmp = (y - a) * (x / z);
	} else if (z <= -2.9e+43) {
		tmp = t;
	} else if (z <= 1.45e+18) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.6e+197:
		tmp = t
	elif z <= -7.8e+150:
		tmp = (y - a) * (x / z)
	elif z <= -2.9e+43:
		tmp = t
	elif z <= 1.45e+18:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.6e+197)
		tmp = t;
	elseif (z <= -7.8e+150)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (z <= -2.9e+43)
		tmp = t;
	elseif (z <= 1.45e+18)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.6e+197)
		tmp = t;
	elseif (z <= -7.8e+150)
		tmp = (y - a) * (x / z);
	elseif (z <= -2.9e+43)
		tmp = t;
	elseif (z <= 1.45e+18)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.6e+197], t, If[LessEqual[z, -7.8e+150], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e+43], t, If[LessEqual[z, 1.45e+18], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.6000000000000003e197 or -7.79999999999999981e150 < z < -2.9000000000000002e43 or 1.45e18 < z

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-*l/ 74.3%

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

      3. fma-def 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in z around inf 56.3%

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

   if -7.6000000000000003e197 < z < -7.79999999999999981e150

   1. Initial program 32.6%

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

      1. +-commutative 32.6%

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

      2. associate-*l/ 61.3%

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

      3. fma-def 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in x around inf 32.4%

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

      1. *-commutative 32.4%

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

      2. mul-1-neg 32.4%

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

      3. unsub-neg 32.4%

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

   6. Simplified 32.4%

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

   7. Taylor expanded in z around inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-/l* 61.1%

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

      3. mul-1-neg 61.1%

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

      4. sub-neg 61.1%

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

      5. distribute-neg-frac 61.1%

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

      6. mul-1-neg 61.1%

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

      7. sub-neg 61.1%

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

      8. mul-1-neg 61.1%

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

      9. +-commutative 61.1%

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

      10. distribute-lft-in 61.1%

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

      11. neg-mul-1 61.1%

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

      12. mul-1-neg 61.1%

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

      13. remove-double-neg 61.1%

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

      14. mul-1-neg 61.1%

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

      15. sub-neg 61.1%

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

   9. Simplified 61.1%

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

   10. Taylor expanded in y around 0 51.6%

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

       1. associate-/l* 61.1%

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

       2. mul-1-neg 61.1%

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

       3. associate-/l* 61.1%

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

       4. sub-neg 61.1%

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

       5. div-sub 61.1%

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

       6. *-rgt-identity 61.1%

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

       7. associate-*r/ 60.9%

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

       8. associate-/r/ 60.9%

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

       9. associate-*l/ 61.1%

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

       10. *-lft-identity 61.1%

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

   12. Simplified 61.1%

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

   if -2.9000000000000002e43 < z < 1.45e18

   1. Initial program 87.9%

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

      1. +-commutative 87.9%

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

      2. associate-*l/ 93.4%

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

      3. fma-def 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in x around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. mul-1-neg 64.4%

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

      3. unsub-neg 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 55.4%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+197}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+150}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+75} \lor \neg \left(x \leq 3 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.55e+75) (not (<= x 3e+48)))
   (* x (+ (/ (- z y) (- a z)) 1.0))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.55e+75) || !(x <= 3e+48)) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.55d+75)) .or. (.not. (x <= 3d+48))) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.55e+75) || !(x <= 3e+48)) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.55e+75) or not (x <= 3e+48):
		tmp = x * (((z - y) / (a - z)) + 1.0)
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.55e+75) || !(x <= 3e+48))
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.55e+75) || ~((x <= 3e+48)))
		tmp = x * (((z - y) / (a - z)) + 1.0);
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.55e+75], N[Not[LessEqual[x, 3e+48]], $MachinePrecision]], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5500000000000001e75 or 3e48 < x

   1. Initial program 59.5%

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

      1. +-commutative 59.5%

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

      2. associate-*l/ 77.1%

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

      3. fma-def 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in x around inf 70.2%

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

      1. *-commutative 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

   6. Simplified 70.2%

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

   if -1.5500000000000001e75 < x < 3e48

   1. Initial program 74.6%

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

      1. +-commutative 74.6%

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

      2. associate-*l/ 88.9%

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

      3. fma-def 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in t around inf 73.0%

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

      1. div-sub 73.0%

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

   6. Simplified 73.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+75} \lor \neg \left(x \leq 3 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 15: 70.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.9 \cdot 10^{+118} \lor \neg \left(x \leq 8 \cdot 10^{+49}\right):\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -6.9e+118) (not (<= x 8e+49)))
   (* x (+ (/ (- z y) (- a z)) 1.0))
   (+ x (/ (- y z) (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.9e+118) || !(x <= 8e+49)) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-6.9d+118)) .or. (.not. (x <= 8d+49))) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    else
        tmp = x + ((y - z) / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.9e+118) || !(x <= 8e+49)) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -6.9e+118) or not (x <= 8e+49):
		tmp = x * (((z - y) / (a - z)) + 1.0)
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -6.9e+118) || !(x <= 8e+49))
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -6.9e+118) || ~((x <= 8e+49)))
		tmp = x * (((z - y) / (a - z)) + 1.0);
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -6.9e+118], N[Not[LessEqual[x, 8e+49]], $MachinePrecision]], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.90000000000000003e118 or 7.99999999999999957e49 < x

   1. Initial program 58.3%

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

      1. +-commutative 58.3%

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

      2. associate-*l/ 76.7%

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

      3. fma-def 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in x around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. mul-1-neg 71.1%

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

      3. unsub-neg 71.1%

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

   6. Simplified 71.1%

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

   if -6.90000000000000003e118 < x < 7.99999999999999957e49

   1. Initial program 74.3%

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

      1. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in t around inf 79.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.9 \cdot 10^{+118} \lor \neg \left(x \leq 8 \cdot 10^{+49}\right):\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 16: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+42} \lor \neg \left(z \leq 1.42 \cdot 10^{+18}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.3e+42) (not (<= z 1.42e+18)))
   (* 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 <= -4.3e+42) || !(z <= 1.42e+18)) {
		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 <= (-4.3d+42)) .or. (.not. (z <= 1.42d+18))) 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 <= -4.3e+42) || !(z <= 1.42e+18)) {
		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 <= -4.3e+42) or not (z <= 1.42e+18):
		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 <= -4.3e+42) || !(z <= 1.42e+18))
		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 <= -4.3e+42) || ~((z <= 1.42e+18)))
		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, -4.3e+42], N[Not[LessEqual[z, 1.42e+18]], $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 < -4.2999999999999998e42 or 1.42e18 < z

   1. Initial program 45.7%

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

      1. +-commutative 45.7%

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

      2. associate-*l/ 73.2%

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

      3. fma-def 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in t around inf 65.6%

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

      1. div-sub 65.6%

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

   6. Simplified 65.6%

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

   if -4.2999999999999998e42 < z < 1.42e18

   1. Initial program 87.9%

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

      1. +-commutative 87.9%

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

      2. associate-*l/ 93.4%

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

      3. fma-def 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-/l* 71.7%

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

   6. Simplified 71.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+42} \lor \neg \left(z \leq 1.42 \cdot 10^{+18}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 17: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+42} \lor \neg \left(z \leq 1.45 \cdot 10^{+18}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e+42) (not (<= z 1.45e+18)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ (- t x) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+42) || !(z <= 1.45e+18)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.3d+42)) .or. (.not. (z <= 1.45d+18))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+42) || !(z <= 1.45e+18)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e+42) or not (z <= 1.45e+18):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e+42) || !(z <= 1.45e+18))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e+42) || ~((z <= 1.45e+18)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e+42], N[Not[LessEqual[z, 1.45e+18]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e42 or 1.45e18 < z

   1. Initial program 45.7%

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

      1. +-commutative 45.7%

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

      2. associate-*l/ 73.2%

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

      3. fma-def 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in t around inf 65.6%

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

      1. div-sub 65.6%

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

   6. Simplified 65.6%

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

   if -2.3e42 < z < 1.45e18

   1. Initial program 87.9%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

      1. *-commutative 93.4%

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

      2. clear-num 93.2%

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

      3. un-div-inv 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in z around 0 73.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+42} \lor \neg \left(z \leq 1.45 \cdot 10^{+18}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]

Alternative 18: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e+43)
   (* t (/ (- y z) (- a z)))
   (if (<= z 1.4e+18) (+ x (/ (- t x) (/ a y))) (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+43) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.4e+18) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = 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) :: tmp
    if (z <= (-1.6d+43)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 1.4d+18) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = 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 tmp;
	if (z <= -1.6e+43) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.4e+18) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e+43:
		tmp = t * ((y - z) / (a - z))
	elif z <= 1.4e+18:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e+43)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 1.4e+18)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e+43)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 1.4e+18)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e+43], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+18], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000007e43

   1. Initial program 44.5%

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

      1. +-commutative 44.5%

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

      2. associate-*l/ 72.1%

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

      3. fma-def 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in t around inf 63.9%

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

      1. div-sub 63.9%

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

   6. Simplified 63.9%

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

   if -1.60000000000000007e43 < z < 1.4e18

   1. Initial program 87.9%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

      1. *-commutative 93.4%

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

      2. clear-num 93.2%

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

      3. un-div-inv 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in z around 0 73.3%

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

   if 1.4e18 < z

   1. Initial program 46.6%

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

      1. associate-*l/ 74.1%

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

   3. Simplified 74.1%

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

      1. clear-num 74.1%

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

      2. associate-/r/ 73.8%

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

   5. Applied egg-rr 73.8%

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

   6. Taylor expanded in x around 0 51.4%

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

      1. associate-/l* 66.9%

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

   8. Simplified 66.9%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 19: 39.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+43) t (if (<= z 1.6e+18) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+43) {
		tmp = t;
	} else if (z <= 1.6e+18) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+43)) then
        tmp = t
    else if (z <= 1.6d+18) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+43) {
		tmp = t;
	} else if (z <= 1.6e+18) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+43:
		tmp = t
	elif z <= 1.6e+18:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+43)
		tmp = t;
	elseif (z <= 1.6e+18)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+43)
		tmp = t;
	elseif (z <= 1.6e+18)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+43], t, If[LessEqual[z, 1.6e+18], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999998e43 or 1.6e18 < z

   1. Initial program 45.7%

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

      1. +-commutative 45.7%

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

      2. associate-*l/ 73.2%

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

      3. fma-def 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in z around inf 52.6%

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

   if -6.4999999999999998e43 < z < 1.6e18

   1. Initial program 87.9%

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

      1. +-commutative 87.9%

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

      2. associate-*l/ 93.4%

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

      3. fma-def 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in a around inf 37.1%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 68.4%

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

2. Taylor expanded in t around 0 38.2%

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

   1. mul-1-neg 38.2%

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

   2. distribute-rgt-neg-out 38.2%

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

4. Simplified 38.2%

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

5. Taylor expanded in z around inf 2.9%

   \[\leadsto \color{blue}{-1 \cdot x + x} \]
6. Step-by-step derivation

   1. distribute-lft1-in 2.9%

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

   2. metadata-eval 2.9%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.9%

      \[\leadsto \color{blue}{0} \]

7. Simplified 2.9%

   \[\leadsto \color{blue}{0} \]

8. Final simplification 2.9%

   \[\leadsto 0 \]

Alternative 21: 25.1% 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 68.4%

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

   1. +-commutative 68.4%

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

   2. associate-*l/ 84.1%

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

   3. fma-def 84.1%

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

3. Simplified 84.1%

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

4. Taylor expanded in z around inf 28.9%

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

5. Final simplification 28.9%

   \[\leadsto t \]

Developer target: 84.9% 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 2023200 
(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))))