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

Percentage Accurate: 68.5% → 90.5%

Time: 11.8s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-246) (not (<= t_1 0.0)))
     (fma (/ (- y z) (- a z)) (- t x) x)
     (+ t (/ (* (- t x) (- a y)) z)))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 71.3%

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

      1. +-commutative 71.3%

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

      2. associate-*l/ 89.4%

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

      3. fma-def 89.5%

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

   3. Simplified 89.5%

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

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

   1. Initial program 13.7%

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

      1. +-commutative 13.7%

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

      2. associate-*l/ 13.8%

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

      3. fma-def 13.8%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in z around -inf 99.8%

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

4. Final simplification 90.2%

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

Alternative 2: 90.5% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -5e-246) (not (<= t_1 0.0)))
     (+ x (* (- t x) (/ (- y z) (- a z))))
     (+ t (/ (* (- t x) (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-246) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -5e-246) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) * ((y - z) / (a - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if (t_1 <= -5e-246) or not (t_1 <= 0.0):
		tmp = x + ((t - x) * ((y - z) / (a - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / z)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 71.3%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

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

   1. Initial program 13.7%

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

      1. +-commutative 13.7%

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

      2. associate-*l/ 13.8%

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

      3. fma-def 13.8%

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

   3. Simplified 13.8%

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

   4. Taylor expanded in z around -inf 99.8%

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

4. Final simplification 90.2%

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

Alternative 3: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -5500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-116}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{+85} \lor \neg \left(a \leq 3.8 \cdot 10^{+153}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- t x) (/ a (- y z))))))
   (if (<= a -5500000.0)
     t_1
     (if (<= a 1.75e-116)
       (+ t (/ (- x t) (/ z y)))
       (if (or (<= a 5.9e+85) (not (<= a 3.8e+153)))
         t_1
         (+ t (* x (/ (- y a) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -5500000.0) {
		tmp = t_1;
	} else if (a <= 1.75e-116) {
		tmp = t + ((x - t) / (z / y));
	} else if ((a <= 5.9e+85) || !(a <= 3.8e+153)) {
		tmp = t_1;
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t - x) / (a / (y - z)))
    if (a <= (-5500000.0d0)) then
        tmp = t_1
    else if (a <= 1.75d-116) then
        tmp = t + ((x - t) / (z / y))
    else if ((a <= 5.9d+85) .or. (.not. (a <= 3.8d+153))) then
        tmp = t_1
    else
        tmp = t + (x * ((y - a) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) / (a / (y - z)));
	double tmp;
	if (a <= -5500000.0) {
		tmp = t_1;
	} else if (a <= 1.75e-116) {
		tmp = t + ((x - t) / (z / y));
	} else if ((a <= 5.9e+85) || !(a <= 3.8e+153)) {
		tmp = t_1;
	} else {
		tmp = t + (x * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) / (a / (y - z)))
	tmp = 0
	if a <= -5500000.0:
		tmp = t_1
	elif a <= 1.75e-116:
		tmp = t + ((x - t) / (z / y))
	elif (a <= 5.9e+85) or not (a <= 3.8e+153):
		tmp = t_1
	else:
		tmp = t + (x * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -5500000.0)
		tmp = t_1;
	elseif (a <= 1.75e-116)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	elseif ((a <= 5.9e+85) || !(a <= 3.8e+153))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -5500000.0)
		tmp = t_1;
	elseif (a <= 1.75e-116)
		tmp = t + ((x - t) / (z / y));
	elseif ((a <= 5.9e+85) || ~((a <= 3.8e+153)))
		tmp = t_1;
	else
		tmp = t + (x * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5500000.0], t$95$1, If[LessEqual[a, 1.75e-116], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 5.9e+85], N[Not[LessEqual[a, 3.8e+153]], $MachinePrecision]], t$95$1, N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.5e6 or 1.74999999999999992e-116 < a < 5.9e85 or 3.79999999999999966e153 < a

   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/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in a around inf 61.5%

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

      1. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

   if -5.5e6 < a < 1.74999999999999992e-116

   1. Initial program 64.0%

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

      1. associate-*l/ 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in z around inf 79.0%

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

      1. associate--l+ 79.0%

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

      2. associate-*r/ 79.0%

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

      3. associate-*r/ 79.0%

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

      4. div-sub 79.0%

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

      5. distribute-lft-out-- 79.0%

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

      6. mul-1-neg 79.0%

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

      7. distribute-neg-frac 79.0%

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

      8. distribute-rgt-out-- 79.0%

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

      9. unsub-neg 79.0%

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

      10. associate-/l* 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in y around inf 89.6%

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

   if 5.9e85 < a < 3.79999999999999966e153

   1. Initial program 59.0%

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

      1. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in z around inf 59.4%

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

      1. associate--l+ 59.4%

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

      2. associate-*r/ 59.4%

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

      3. associate-*r/ 59.4%

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

      4. div-sub 59.4%

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

      5. distribute-lft-out-- 59.4%

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

      6. mul-1-neg 59.4%

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

      7. distribute-neg-frac 59.4%

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

      8. distribute-rgt-out-- 59.4%

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

      9. unsub-neg 59.4%

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

      10. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   7. Taylor expanded in t around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. associate-*r/ 73.2%

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

      3. *-commutative 73.2%

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

      4. distribute-rgt-neg-in 73.2%

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

   9. Simplified 73.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5500000:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-116}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{+85} \lor \neg \left(a \leq 3.8 \cdot 10^{+153}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 4: 57.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+172}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))))
   (if (<= a -4.2e-8)
     t_1
     (if (<= a 6.5e-50)
       (+ t (* x (/ y z)))
       (if (<= a 9e+52) (- x (/ x (/ a y))) (if (<= a 8e+172) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (a <= -4.2e-8) {
		tmp = t_1;
	} else if (a <= 6.5e-50) {
		tmp = t + (x * (y / z));
	} else if (a <= 9e+52) {
		tmp = x - (x / (a / y));
	} else if (a <= 8e+172) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / y))
    if (a <= (-4.2d-8)) then
        tmp = t_1
    else if (a <= 6.5d-50) then
        tmp = t + (x * (y / z))
    else if (a <= 9d+52) then
        tmp = x - (x / (a / y))
    else if (a <= 8d+172) then
        tmp = x + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (a <= -4.2e-8) {
		tmp = t_1;
	} else if (a <= 6.5e-50) {
		tmp = t + (x * (y / z));
	} else if (a <= 9e+52) {
		tmp = x - (x / (a / y));
	} else if (a <= 8e+172) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	tmp = 0
	if a <= -4.2e-8:
		tmp = t_1
	elif a <= 6.5e-50:
		tmp = t + (x * (y / z))
	elif a <= 9e+52:
		tmp = x - (x / (a / y))
	elif a <= 8e+172:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -4.2e-8)
		tmp = t_1;
	elseif (a <= 6.5e-50)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 9e+52)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (a <= 8e+172)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -4.2e-8)
		tmp = t_1;
	elseif (a <= 6.5e-50)
		tmp = t + (x * (y / z));
	elseif (a <= 9e+52)
		tmp = x - (x / (a / y));
	elseif (a <= 8e+172)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e-8], t$95$1, If[LessEqual[a, 6.5e-50], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+52], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+172], N[(x + t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.19999999999999989e-8 or 8.0000000000000007e172 < a

   1. Initial program 68.5%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in t around inf 82.9%

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

   5. Taylor expanded in z around 0 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-/l* 64.4%

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

   7. Simplified 64.4%

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

   if -4.19999999999999989e-8 < a < 6.49999999999999987e-50

   1. Initial program 65.2%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in z around inf 75.5%

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

      1. associate--l+ 75.5%

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

      2. associate-*r/ 75.5%

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

      3. associate-*r/ 75.5%

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

      4. div-sub 75.5%

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

      5. distribute-lft-out-- 75.5%

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

      6. mul-1-neg 75.5%

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

      7. distribute-neg-frac 75.5%

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

      8. distribute-rgt-out-- 75.5%

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

      9. unsub-neg 75.5%

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

      10. associate-/l* 86.6%

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

   6. Simplified 86.6%

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

   7. Taylor expanded in y around inf 85.8%

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

   8. Taylor expanded in t around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-*r/ 75.7%

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

      3. distribute-rgt-neg-in 75.7%

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

      4. distribute-neg-frac 75.7%

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

   10. Simplified 75.7%

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

   if 6.49999999999999987e-50 < a < 8.9999999999999999e52

   1. Initial program 73.7%

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

      1. associate-*l/ 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in z around 0 68.7%

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

   5. Taylor expanded in t around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. sub-neg 55.6%

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

      3. associate-/l* 55.6%

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

   7. Simplified 55.6%

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

   if 8.9999999999999999e52 < a < 8.0000000000000007e172

   1. Initial program 66.2%

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

      1. associate-/l* 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in t around inf 67.4%

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

   5. Taylor expanded in z around inf 56.8%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+172}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -0.00012:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-229}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))))
   (if (<= a -0.00012)
     t_1
     (if (<= a 1.15e-229)
       (+ t (* x (/ y z)))
       (if (<= a 7.8e+177) (* t (/ (- y z) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (a <= -0.00012) {
		tmp = t_1;
	} else if (a <= 1.15e-229) {
		tmp = t + (x * (y / z));
	} else if (a <= 7.8e+177) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / y))
    if (a <= (-0.00012d0)) then
        tmp = t_1
    else if (a <= 1.15d-229) then
        tmp = t + (x * (y / z))
    else if (a <= 7.8d+177) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (a <= -0.00012) {
		tmp = t_1;
	} else if (a <= 1.15e-229) {
		tmp = t + (x * (y / z));
	} else if (a <= 7.8e+177) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	tmp = 0
	if a <= -0.00012:
		tmp = t_1
	elif a <= 1.15e-229:
		tmp = t + (x * (y / z))
	elif a <= 7.8e+177:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -0.00012)
		tmp = t_1;
	elseif (a <= 1.15e-229)
		tmp = Float64(t + Float64(x * Float64(y / z)));
	elseif (a <= 7.8e+177)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -0.00012)
		tmp = t_1;
	elseif (a <= 1.15e-229)
		tmp = t + (x * (y / z));
	elseif (a <= 7.8e+177)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00012], t$95$1, If[LessEqual[a, 1.15e-229], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e+177], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.20000000000000003e-4 or 7.7999999999999998e177 < a

   1. Initial program 67.8%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around inf 83.6%

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

   5. Taylor expanded in z around 0 59.3%

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

      1. +-commutative 59.3%

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

      2. associate-/l* 64.7%

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

   7. Simplified 64.7%

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

   if -1.20000000000000003e-4 < a < 1.14999999999999998e-229

   1. Initial program 65.5%

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

      1. associate-*l/ 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in z around inf 81.0%

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

      1. associate--l+ 81.0%

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

      2. associate-*r/ 81.0%

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

      3. associate-*r/ 81.0%

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

      4. div-sub 81.0%

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

      5. distribute-lft-out-- 81.0%

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

      6. mul-1-neg 81.0%

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

      7. distribute-neg-frac 81.0%

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

      8. distribute-rgt-out-- 81.0%

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

      9. unsub-neg 81.0%

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

      10. associate-/l* 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in y around inf 90.6%

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

   8. Taylor expanded in t around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-*r/ 78.9%

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

      3. distribute-rgt-neg-in 78.9%

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

      4. distribute-neg-frac 78.9%

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

   10. Simplified 78.9%

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

   if 1.14999999999999998e-229 < a < 7.7999999999999998e177

   1. Initial program 67.9%

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

      1. associate-*l/ 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in x around 0 39.4%

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

      1. associate-*r/ 59.2%

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

   6. Simplified 59.2%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00012:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-229}:\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{-15} \lor \neg \left(a \leq 1.25 \cdot 10^{-109}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.6e-15) (not (<= a 1.25e-109)))
   (+ x (/ (- y z) (/ (- a z) t)))
   (+ t (/ (- x t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.6e-15) || !(a <= 1.25e-109)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6.6d-15)) .or. (.not. (a <= 1.25d-109))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.6e-15) || !(a <= 1.25e-109)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.6e-15) or not (a <= 1.25e-109):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.6e-15) || !(a <= 1.25e-109))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.6e-15) || ~((a <= 1.25e-109)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.6e-15], N[Not[LessEqual[a, 1.25e-109]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.6e-15 or 1.25000000000000005e-109 < a

   1. Initial program 69.3%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in t around inf 77.2%

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

   if -6.6e-15 < a < 1.25000000000000005e-109

   1. Initial program 64.0%

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

      1. associate-*l/ 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in z around inf 79.1%

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

      1. associate--l+ 79.1%

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

      2. associate-*r/ 79.1%

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

      3. associate-*r/ 79.1%

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

      4. div-sub 79.1%

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

      5. distribute-lft-out-- 79.1%

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

      6. mul-1-neg 79.1%

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

      7. distribute-neg-frac 79.1%

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

      8. distribute-rgt-out-- 79.1%

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

      9. unsub-neg 79.1%

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

      10. associate-/l* 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in y around inf 89.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{-15} \lor \neg \left(a \leq 1.25 \cdot 10^{-109}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 7: 76.7% accurate, 0.9× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e-9) (not (<= a 1.3e-109)))
   (+ x (/ (- y z) (/ (- a z) t)))
   (- t (/ (- t x) (/ z (- y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-9) || !(a <= 1.3e-109)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.8d-9)) .or. (.not. (a <= 1.3d-109))) then
        tmp = x + ((y - z) / ((a - z) / t))
    else
        tmp = t - ((t - x) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-9) || !(a <= 1.3e-109)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else {
		tmp = t - ((t - x) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e-9) or not (a <= 1.3e-109):
		tmp = x + ((y - z) / ((a - z) / t))
	else:
		tmp = t - ((t - x) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e-9) || !(a <= 1.3e-109))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e-9) || ~((a <= 1.3e-109)))
		tmp = x + ((y - z) / ((a - z) / t));
	else
		tmp = t - ((t - x) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e-9], N[Not[LessEqual[a, 1.3e-109]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 69.3%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in t around inf 77.2%

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

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

   1. Initial program 64.0%

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

      1. associate-*l/ 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in z around inf 79.1%

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

      1. associate--l+ 79.1%

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

      2. associate-*r/ 79.1%

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

      3. associate-*r/ 79.1%

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

      4. div-sub 79.1%

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

      5. distribute-lft-out-- 79.1%

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

      6. mul-1-neg 79.1%

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

      7. distribute-neg-frac 79.1%

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

      8. distribute-rgt-out-- 79.1%

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

      9. unsub-neg 79.1%

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

      10. associate-/l* 89.7%

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

   6. Simplified 89.7%

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

4. Final simplification 82.4%

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

Alternative 8: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+26} \lor \neg \left(z \leq 9.2 \cdot 10^{+58}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.35e+26) (not (<= z 9.2e+58)))
   (+ t (* x (/ y z)))
   (- x (* (/ y a) (- x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.35e+26) || !(z <= 9.2e+58)) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.35d+26)) .or. (.not. (z <= 9.2d+58))) then
        tmp = t + (x * (y / z))
    else
        tmp = x - ((y / a) * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.35e+26) || !(z <= 9.2e+58)) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x - ((y / a) * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.35e+26) or not (z <= 9.2e+58):
		tmp = t + (x * (y / z))
	else:
		tmp = x - ((y / a) * (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.35e+26) || !(z <= 9.2e+58))
		tmp = Float64(t + Float64(x * Float64(y / z)));
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.35e+26) || ~((z <= 9.2e+58)))
		tmp = t + (x * (y / z));
	else
		tmp = x - ((y / a) * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.35e+26], N[Not[LessEqual[z, 9.2e+58]], $MachinePrecision]], N[(t + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3499999999999999e26 or 9.2000000000000001e58 < z

   1. Initial program 44.0%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. associate--l+ 61.0%

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

      2. associate-*r/ 61.0%

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

      3. associate-*r/ 61.0%

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

      4. div-sub 61.0%

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

      5. distribute-lft-out-- 61.0%

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

      6. mul-1-neg 61.0%

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

      7. distribute-neg-frac 61.0%

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

      8. distribute-rgt-out-- 61.9%

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

      9. unsub-neg 61.9%

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

      10. associate-/l* 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in y around inf 75.3%

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

   8. Taylor expanded in t around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. associate-*r/ 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

      4. distribute-neg-frac 68.8%

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

   10. Simplified 68.8%

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

   if -2.3499999999999999e26 < z < 9.2000000000000001e58

   1. Initial program 89.4%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 74.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+26} \lor \neg \left(z \leq 9.2 \cdot 10^{+58}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+26} \lor \neg \left(z \leq 2.3 \cdot 10^{+58}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+26) (not (<= z 2.3e+58)))
   (+ t (* x (/ y z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+26) || !(z <= 2.3e+58)) {
		tmp = t + (x * (y / 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 <= (-1.5d+26)) .or. (.not. (z <= 2.3d+58))) then
        tmp = t + (x * (y / 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 <= -1.5e+26) || !(z <= 2.3e+58)) {
		tmp = t + (x * (y / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+26) or not (z <= 2.3e+58):
		tmp = t + (x * (y / z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+26) || !(z <= 2.3e+58))
		tmp = Float64(t + Float64(x * Float64(y / 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 <= -1.5e+26) || ~((z <= 2.3e+58)))
		tmp = t + (x * (y / z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+26], N[Not[LessEqual[z, 2.3e+58]], $MachinePrecision]], N[(t + N[(x * N[(y / 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 < -1.49999999999999999e26 or 2.30000000000000002e58 < z

   1. Initial program 44.0%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 61.0%

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

      1. associate--l+ 61.0%

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

      2. associate-*r/ 61.0%

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

      3. associate-*r/ 61.0%

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

      4. div-sub 61.0%

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

      5. distribute-lft-out-- 61.0%

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

      6. mul-1-neg 61.0%

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

      7. distribute-neg-frac 61.0%

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

      8. distribute-rgt-out-- 61.9%

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

      9. unsub-neg 61.9%

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

      10. associate-/l* 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in y around inf 75.3%

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

   8. Taylor expanded in t around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. associate-*r/ 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

      4. distribute-neg-frac 68.8%

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

   10. Simplified 68.8%

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

   if -1.49999999999999999e26 < z < 2.30000000000000002e58

   1. Initial program 89.4%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 70.6%

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

      1. associate-/l* 75.6%

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

   6. Simplified 75.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+26} \lor \neg \left(z \leq 2.3 \cdot 10^{+58}\right):\\ \;\;\;\;t + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 10: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+25} \lor \neg \left(z \leq 8.5 \cdot 10^{+36}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e+25) (not (<= z 8.5e+36)))
   (+ t (/ (- x t) (/ z y)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+25) || !(z <= 8.5e+36)) {
		tmp = t + ((x - t) / (z / y));
	} 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 <= (-1.25d+25)) .or. (.not. (z <= 8.5d+36))) then
        tmp = t + ((x - t) / (z / y))
    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 <= -1.25e+25) || !(z <= 8.5e+36)) {
		tmp = t + ((x - t) / (z / y));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e+25) or not (z <= 8.5e+36):
		tmp = t + ((x - t) / (z / y))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e+25) || !(z <= 8.5e+36))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	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 <= -1.25e+25) || ~((z <= 8.5e+36)))
		tmp = t + ((x - t) / (z / y));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e+25], N[Not[LessEqual[z, 8.5e+36]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $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 < -1.25000000000000006e25 or 8.50000000000000014e36 < z

   1. Initial program 44.9%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 61.4%

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

      1. associate--l+ 61.4%

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

      2. associate-*r/ 61.4%

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

      3. associate-*r/ 61.4%

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

      4. div-sub 61.4%

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

      5. distribute-lft-out-- 61.4%

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

      6. mul-1-neg 61.4%

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

      7. distribute-neg-frac 61.4%

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

      8. distribute-rgt-out-- 62.3%

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

      9. unsub-neg 62.3%

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

      10. associate-/l* 81.6%

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

   6. Simplified 81.6%

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

   7. Taylor expanded in y around inf 75.3%

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

   if -1.25000000000000006e25 < z < 8.50000000000000014e36

   1. Initial program 89.9%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 71.2%

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

      1. associate-/l* 76.3%

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

   6. Simplified 76.3%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+25} \lor \neg \left(z \leq 8.5 \cdot 10^{+36}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 11: 70.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+25}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+25)
   (+ t (* x (/ (- y a) z)))
   (if (<= z 8e+36) (+ x (/ y (/ a (- t x)))) (+ t (/ (- x t) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+25) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= 8e+36) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x - t) / (z / 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 <= (-8.5d+25)) then
        tmp = t + (x * ((y - a) / z))
    else if (z <= 8d+36) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + ((x - t) / (z / 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 <= -8.5e+25) {
		tmp = t + (x * ((y - a) / z));
	} else if (z <= 8e+36) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+25:
		tmp = t + (x * ((y - a) / z))
	elif z <= 8e+36:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+25)
		tmp = Float64(t + Float64(x * Float64(Float64(y - a) / z)));
	elseif (z <= 8e+36)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+25)
		tmp = t + (x * ((y - a) / z));
	elseif (z <= 8e+36)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+25], N[(t + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+36], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000007e25

   1. Initial program 54.7%

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

      1. associate-*l/ 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in z around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. associate-*r/ 68.9%

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

      3. associate-*r/ 68.9%

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

      4. div-sub 68.9%

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

      5. distribute-lft-out-- 68.9%

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

      6. mul-1-neg 68.9%

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

      7. distribute-neg-frac 68.9%

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

      8. distribute-rgt-out-- 70.8%

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

      9. unsub-neg 70.8%

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

      10. associate-/l* 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in t around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. associate-*r/ 76.4%

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

      3. *-commutative 76.4%

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

      4. distribute-rgt-neg-in 76.4%

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

   9. Simplified 76.4%

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

   if -8.5000000000000007e25 < z < 8.00000000000000034e36

   1. Initial program 89.9%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 71.2%

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

      1. associate-/l* 76.3%

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

   6. Simplified 76.3%

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

   if 8.00000000000000034e36 < z

   1. Initial program 36.6%

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

      1. associate-*l/ 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in z around inf 55.0%

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

      1. associate--l+ 55.0%

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

      2. associate-*r/ 55.0%

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

      3. associate-*r/ 55.0%

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

      4. div-sub 55.0%

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

      5. distribute-lft-out-- 55.0%

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

      6. mul-1-neg 55.0%

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

      7. distribute-neg-frac 55.0%

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

      8. distribute-rgt-out-- 55.0%

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

      9. unsub-neg 55.0%

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

      10. associate-/l* 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in y around inf 76.1%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+25}:\\ \;\;\;\;t + x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 12: 57.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26} \lor \neg \left(z \leq 1.3 \cdot 10^{+54}\right):\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+26) (not (<= z 1.3e+54)))
   (- t (* t (/ y z)))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+26) || !(z <= 1.3e+54)) {
		tmp = t - (t * (y / z));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.2d+26)) .or. (.not. (z <= 1.3d+54))) then
        tmp = t - (t * (y / z))
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+26) || !(z <= 1.3e+54)) {
		tmp = t - (t * (y / z));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+26) or not (z <= 1.3e+54):
		tmp = t - (t * (y / z))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+26) || !(z <= 1.3e+54))
		tmp = Float64(t - Float64(t * Float64(y / z)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+26) || ~((z <= 1.3e+54)))
		tmp = t - (t * (y / z));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+26], N[Not[LessEqual[z, 1.3e+54]], $MachinePrecision]], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e26 or 1.30000000000000003e54 < z

   1. Initial program 44.4%

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

      1. associate-*l/ 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in z around inf 61.3%

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

      1. associate--l+ 61.3%

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

      2. associate-*r/ 61.3%

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

      3. associate-*r/ 61.3%

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

      4. div-sub 61.3%

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

      5. distribute-lft-out-- 61.3%

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

      6. mul-1-neg 61.3%

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

      7. distribute-neg-frac 61.3%

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

      8. distribute-rgt-out-- 62.2%

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

      9. unsub-neg 62.2%

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

      10. associate-/l* 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in y around inf 75.5%

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

   8. Taylor expanded in t around inf 48.7%

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

      1. associate-*r/ 59.3%

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

   10. Simplified 59.3%

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

   if -4.2000000000000002e26 < z < 1.30000000000000003e54

   1. Initial program 89.3%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 75.6%

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

   5. Taylor expanded in z around 0 58.8%

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

      1. +-commutative 58.8%

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

      2. associate-/l* 63.9%

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

   7. Simplified 63.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26} \lor \neg \left(z \leq 1.3 \cdot 10^{+54}\right):\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 13: 39.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.6e-27)
   (+ x t)
   (if (<= z 4.7e-144) (* t (/ y (- a z))) (if (<= z 1.7e+220) (+ x t) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e-27) {
		tmp = x + t;
	} else if (z <= 4.7e-144) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.7e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.6d-27)) then
        tmp = x + t
    else if (z <= 4.7d-144) then
        tmp = t * (y / (a - z))
    else if (z <= 1.7d+220) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e-27) {
		tmp = x + t;
	} else if (z <= 4.7e-144) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.7e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.6e-27:
		tmp = x + t
	elif z <= 4.7e-144:
		tmp = t * (y / (a - z))
	elif z <= 1.7e+220:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.6e-27)
		tmp = Float64(x + t);
	elseif (z <= 4.7e-144)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.7e+220)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.6e-27)
		tmp = x + t;
	elseif (z <= 4.7e-144)
		tmp = t * (y / (a - z));
	elseif (z <= 1.7e+220)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.6e-27], N[(x + t), $MachinePrecision], If[LessEqual[z, 4.7e-144], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+220], N[(x + t), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5999999999999999e-27 or 4.7000000000000002e-144 < z < 1.7e220

   1. Initial program 60.2%

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

      1. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in t around inf 66.4%

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

   5. Taylor expanded in z around inf 46.2%

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

   if -5.5999999999999999e-27 < z < 4.7000000000000002e-144

   1. Initial program 94.9%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in x around 0 43.1%

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

      1. associate-*r/ 45.6%

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

   6. Simplified 45.6%

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

   7. Taylor expanded in y around inf 42.0%

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

   if 1.7e220 < z

   1. Initial program 18.4%

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

      1. associate-*l/ 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in z around inf 74.9%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 54.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+26) t (if (<= z 1.5e+59) (+ x (/ t (/ a y))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+26) {
		tmp = t;
	} else if (z <= 1.5e+59) {
		tmp = x + (t / (a / y));
	} 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 <= (-4.2d+26)) then
        tmp = t
    else if (z <= 1.5d+59) then
        tmp = x + (t / (a / y))
    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 <= -4.2e+26) {
		tmp = t;
	} else if (z <= 1.5e+59) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+26:
		tmp = t
	elif z <= 1.5e+59:
		tmp = x + (t / (a / y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+26)
		tmp = t;
	elseif (z <= 1.5e+59)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+26)
		tmp = t;
	elseif (z <= 1.5e+59)
		tmp = x + (t / (a / y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+26], t, If[LessEqual[z, 1.5e+59], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e26 or 1.5e59 < z

   1. Initial program 44.0%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 51.6%

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

   if -4.2000000000000002e26 < z < 1.5e59

   1. Initial program 89.4%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 75.8%

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

   5. Taylor expanded in z around 0 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-/l* 64.2%

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

   7. Simplified 64.2%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 39.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+26) t (if (<= z 9000000.0) x (if (<= z 1.7e+220) (+ x t) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+26) {
		tmp = t;
	} else if (z <= 9000000.0) {
		tmp = x;
	} else if (z <= 1.7e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+26)) then
        tmp = t
    else if (z <= 9000000.0d0) then
        tmp = x
    else if (z <= 1.7d+220) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+26) {
		tmp = t;
	} else if (z <= 9000000.0) {
		tmp = x;
	} else if (z <= 1.7e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+26:
		tmp = t
	elif z <= 9000000.0:
		tmp = x
	elif z <= 1.7e+220:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+26)
		tmp = t;
	elseif (z <= 9000000.0)
		tmp = x;
	elseif (z <= 1.7e+220)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+26)
		tmp = t;
	elseif (z <= 9000000.0)
		tmp = x;
	elseif (z <= 1.7e+220)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+26], t, If[LessEqual[z, 9000000.0], x, If[LessEqual[z, 1.7e+220], N[(x + t), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.30000000000000001e26 or 1.7e220 < z

   1. Initial program 44.6%

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

      1. associate-*l/ 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in z around inf 58.6%

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

   if -1.30000000000000001e26 < z < 9e6

   1. Initial program 90.8%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around inf 37.9%

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

   if 9e6 < z < 1.7e220

   1. Initial program 49.9%

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

      1. associate-/l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in t around inf 69.0%

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

   5. Taylor expanded in z around inf 45.2%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 37.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-93}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e-93)
   (+ x t)
   (if (<= z 2e-139) (* t (/ y a)) (if (<= z 1.75e+220) (+ x t) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e-93) {
		tmp = x + t;
	} else if (z <= 2e-139) {
		tmp = t * (y / a);
	} else if (z <= 1.75e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.9d-93)) then
        tmp = x + t
    else if (z <= 2d-139) then
        tmp = t * (y / a)
    else if (z <= 1.75d+220) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e-93) {
		tmp = x + t;
	} else if (z <= 2e-139) {
		tmp = t * (y / a);
	} else if (z <= 1.75e+220) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e-93:
		tmp = x + t
	elif z <= 2e-139:
		tmp = t * (y / a)
	elif z <= 1.75e+220:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e-93)
		tmp = Float64(x + t);
	elseif (z <= 2e-139)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 1.75e+220)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.9e-93)
		tmp = x + t;
	elseif (z <= 2e-139)
		tmp = t * (y / a);
	elseif (z <= 1.75e+220)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e-93], N[(x + t), $MachinePrecision], If[LessEqual[z, 2e-139], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+220], N[(x + t), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999998e-93 or 2.00000000000000006e-139 < z < 1.74999999999999993e220

   1. Initial program 61.0%

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

      1. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in t around inf 67.5%

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

   5. Taylor expanded in z around inf 45.3%

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

   if -2.8999999999999998e-93 < z < 2.00000000000000006e-139

   1. Initial program 97.0%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 46.2%

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

      1. associate-*r/ 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in z around 0 39.5%

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

   if 1.74999999999999993e220 < z

   1. Initial program 18.4%

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

      1. associate-*l/ 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in z around inf 74.9%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-93}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+220}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17: 39.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+101}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.9e+62) (* x (/ y z)) (if (<= y 2.6e+101) (+ x t) (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.9e+62) {
		tmp = x * (y / z);
	} else if (y <= 2.6e+101) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5.9d+62)) then
        tmp = x * (y / z)
    else if (y <= 2.6d+101) then
        tmp = x + t
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.9e+62) {
		tmp = x * (y / z);
	} else if (y <= 2.6e+101) {
		tmp = x + t;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.9e+62:
		tmp = x * (y / z)
	elif y <= 2.6e+101:
		tmp = x + t
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.9e+62)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 2.6e+101)
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.9e+62)
		tmp = x * (y / z);
	elseif (y <= 2.6e+101)
		tmp = x + t;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.9e+62], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+101], N[(x + t), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9000000000000003e62

   1. Initial program 57.1%

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

      1. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in z around inf 40.3%

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

      1. associate--l+ 40.3%

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

      2. associate-*r/ 40.3%

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

      3. associate-*r/ 40.3%

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

      4. div-sub 40.4%

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

      5. distribute-lft-out-- 40.4%

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

      6. mul-1-neg 40.4%

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

      7. distribute-neg-frac 40.4%

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

      8. distribute-rgt-out-- 43.0%

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

      9. unsub-neg 43.0%

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

      10. associate-/l* 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in y around inf 66.4%

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

   8. Taylor expanded in t around 0 25.6%

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

      1. associate-*r/ 40.7%

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

   10. Simplified 40.7%

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

   if -5.9000000000000003e62 < y < 2.6e101

   1. Initial program 69.5%

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

      1. associate-/l* 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in t around inf 69.9%

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

   5. Taylor expanded in z around inf 46.5%

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

   if 2.6e101 < y

   1. Initial program 67.8%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around 0 51.6%

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

      1. associate-*r/ 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in z around 0 44.8%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+101}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 18: 39.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e+26) t (if (<= z 6.4e+58) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+26) {
		tmp = t;
	} else if (z <= 6.4e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.6d+26)) then
        tmp = t
    else if (z <= 6.4d+58) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+26) {
		tmp = t;
	} else if (z <= 6.4e+58) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e+26:
		tmp = t
	elif z <= 6.4e+58:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e+26)
		tmp = t;
	elseif (z <= 6.4e+58)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e+26)
		tmp = t;
	elseif (z <= 6.4e+58)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e+26], t, If[LessEqual[z, 6.4e+58], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000014e26 or 6.40000000000000031e58 < z

   1. Initial program 44.0%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 51.6%

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

   if -1.60000000000000014e26 < z < 6.40000000000000031e58

   1. Initial program 89.4%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in a around inf 37.0%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 25.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return t;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 67.1%

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

   1. associate-*l/ 83.8%

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

3. Simplified 83.8%

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

4. Taylor expanded in z around inf 30.5%

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

5. Final simplification 30.5%

   \[\leadsto t \]

Developer target: 84.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

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

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