Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.8% → 98.0%

Time: 9.6s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2e+90)
   (fma y (/ (- z t) (- z a)) x)
   (+ x (/ (- t z) (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2e+90) {
		tmp = fma(y, ((z - t) / (z - a)), x);
	} else {
		tmp = x + ((t - z) / ((a - z) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2e+90)
		tmp = fma(y, Float64(Float64(z - t) / Float64(z - a)), x);
	else
		tmp = Float64(x + Float64(Float64(t - z) / Float64(Float64(a - z) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2e+90], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.99999999999999993e90

   1. Initial program 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-/l* 98.6%

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

      3. fma-define 98.6%

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

   3. Simplified 98.6%

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

   if 1.99999999999999993e90 < t

   1. Initial program 84.4%

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

      1. clear-num 84.3%

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

      2. inv-pow 84.3%

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

   4. Applied egg-rr 84.3%

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

      1. unpow-1 84.3%

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

      2. associate-/r* 99.7%

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

   6. Simplified 99.7%

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

      1. clear-num 99.9%

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

      2. add-cube-cbrt 99.1%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\frac{z - a}{y}} \]

      3. *-un-lft-identity 99.1%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 99.1%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 99.1%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 99.1%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 99.1%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 99.1%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 99.9%

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

      4. *-lft-identity 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+285}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 9.9999999999999998e284 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 35.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 35.8%

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

      1. associate-*l/ 88.3%

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

   5. Simplified 88.3%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 9.9999999999999998e284

   1. Initial program 99.8%

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

4. Final simplification 96.9%

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

Alternative 3: 61.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;y \leq -3800000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- 1.0 (/ t z)))))
   (if (<= y -3800000000.0)
     t_1
     (if (<= y 1.55e+76) (+ y x) (if (<= y 8.4e+152) (* y (/ t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (1.0 - (t / z));
	double tmp;
	if (y <= -3800000000.0) {
		tmp = t_1;
	} else if (y <= 1.55e+76) {
		tmp = y + x;
	} else if (y <= 8.4e+152) {
		tmp = y * (t / a);
	} 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 = y * (1.0d0 - (t / z))
    if (y <= (-3800000000.0d0)) then
        tmp = t_1
    else if (y <= 1.55d+76) then
        tmp = y + x
    else if (y <= 8.4d+152) then
        tmp = y * (t / a)
    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 = y * (1.0 - (t / z));
	double tmp;
	if (y <= -3800000000.0) {
		tmp = t_1;
	} else if (y <= 1.55e+76) {
		tmp = y + x;
	} else if (y <= 8.4e+152) {
		tmp = y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (1.0 - (t / z))
	tmp = 0
	if y <= -3800000000.0:
		tmp = t_1
	elif y <= 1.55e+76:
		tmp = y + x
	elif y <= 8.4e+152:
		tmp = y * (t / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(1.0 - Float64(t / z)))
	tmp = 0.0
	if (y <= -3800000000.0)
		tmp = t_1;
	elseif (y <= 1.55e+76)
		tmp = Float64(y + x);
	elseif (y <= 8.4e+152)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (1.0 - (t / z));
	tmp = 0.0;
	if (y <= -3800000000.0)
		tmp = t_1;
	elseif (y <= 1.55e+76)
		tmp = y + x;
	elseif (y <= 8.4e+152)
		tmp = y * (t / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3800000000.0], t$95$1, If[LessEqual[y, 1.55e+76], N[(y + x), $MachinePrecision], If[LessEqual[y, 8.4e+152], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8e9 or 8.4000000000000007e152 < y

   1. Initial program 60.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 48.9%

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

   4. Taylor expanded in a around 0 30.6%

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

      1. associate-/l* 56.5%

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

      2. div-sub 56.5%

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

      3. *-inverses 56.5%

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

   6. Simplified 56.5%

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

   if -3.8e9 < y < 1.55000000000000006e76

   1. Initial program 99.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 76.7%

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

      1. +-commutative 76.7%

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

   5. Simplified 76.7%

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

   if 1.55000000000000006e76 < y < 8.4000000000000007e152

   1. Initial program 75.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 53.3%

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

      1. +-commutative 53.3%

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

      2. associate-/l* 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in y around inf 73.1%

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

      1. +-commutative 73.1%

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

   8. Simplified 73.1%

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

   9. Taylor expanded in x around 0 52.4%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3800000000:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1950 \lor \neg \left(y \leq 4.7 \cdot 10^{+48}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1950.0) (not (<= y 4.7e+48)))
   (* (- z t) (/ y (- z a)))
   (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1950.0) || !(y <= 4.7e+48)) {
		tmp = (z - t) * (y / (z - a));
	} else {
		tmp = y + 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 ((y <= (-1950.0d0)) .or. (.not. (y <= 4.7d+48))) then
        tmp = (z - t) * (y / (z - a))
    else
        tmp = y + 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 ((y <= -1950.0) || !(y <= 4.7e+48)) {
		tmp = (z - t) * (y / (z - a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1950.0) or not (y <= 4.7e+48):
		tmp = (z - t) * (y / (z - a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1950.0) || !(y <= 4.7e+48))
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1950.0) || ~((y <= 4.7e+48)))
		tmp = (z - t) * (y / (z - a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1950.0], N[Not[LessEqual[y, 4.7e+48]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1950 or 4.70000000000000012e48 < y

   1. Initial program 64.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 51.4%

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

      1. associate-*l/ 77.1%

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

   5. Simplified 77.1%

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

   if -1950 < y < 4.70000000000000012e48

   1. Initial program 100.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.3%

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

      1. +-commutative 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1950 \lor \neg \left(y \leq 4.7 \cdot 10^{+48}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+46} \lor \neg \left(z \leq 5.5 \cdot 10^{-46}\right):\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e+46) (not (<= z 5.5e-46)))
   (- x (* y (+ (/ t z) -1.0)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+46) || !(z <= 5.5e-46)) {
		tmp = x - (y * ((t / z) + -1.0));
	} else {
		tmp = x + (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 ((z <= (-5.8d+46)) .or. (.not. (z <= 5.5d-46))) then
        tmp = x - (y * ((t / z) + (-1.0d0)))
    else
        tmp = x + (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 ((z <= -5.8e+46) || !(z <= 5.5e-46)) {
		tmp = x - (y * ((t / z) + -1.0));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e+46) or not (z <= 5.5e-46):
		tmp = x - (y * ((t / z) + -1.0))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e+46) || !(z <= 5.5e-46))
		tmp = Float64(x - Float64(y * Float64(Float64(t / z) + -1.0)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.8e+46) || ~((z <= 5.5e-46)))
		tmp = x - (y * ((t / z) + -1.0));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e+46], N[Not[LessEqual[z, 5.5e-46]], $MachinePrecision]], N[(x - N[(y * N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000004e46 or 5.49999999999999983e-46 < z

   1. Initial program 73.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 67.8%

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

      1. associate-/l* 39.6%

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

      2. div-sub 39.6%

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

      3. *-inverses 39.6%

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

   5. Simplified 88.2%

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

   if -5.8000000000000004e46 < z < 5.49999999999999983e-46

   1. Initial program 93.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 70.6%

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

      1. +-commutative 70.6%

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

      2. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+46} \lor \neg \left(z \leq 5.5 \cdot 10^{-46}\right):\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{+44} \lor \neg \left(a \leq 0.0145\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.26e+44) (not (<= a 0.0145)))
   (+ x (* y (/ (- t z) a)))
   (+ x (/ (- z t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.26e+44) || !(a <= 0.0145)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((z - 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 <= (-1.26d+44)) .or. (.not. (a <= 0.0145d0))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((z - 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 <= -1.26e+44) || !(a <= 0.0145)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((z - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.26e+44) or not (a <= 0.0145):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((z - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.26e+44) || !(a <= 0.0145))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.26e+44) || ~((a <= 0.0145)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((z - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.26e+44], N[Not[LessEqual[a, 0.0145]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.25999999999999996e44 or 0.0145000000000000007 < a

   1. Initial program 81.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

      3. associate-/l* 87.5%

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

   5. Simplified 87.5%

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

   if -1.25999999999999996e44 < a < 0.0145000000000000007

   1. Initial program 85.3%

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

      1. clear-num 85.2%

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

      2. inv-pow 85.2%

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

   4. Applied egg-rr 85.2%

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

      1. unpow-1 85.2%

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

      2. associate-/r* 97.7%

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

   6. Simplified 97.7%

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

      1. clear-num 97.8%

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

      2. add-cube-cbrt 97.0%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\frac{z - a}{y}} \]

      3. *-un-lft-identity 97.0%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 96.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 96.9%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 96.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 97.0%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 97.0%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 97.8%

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

      4. *-lft-identity 97.8%

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

   10. Simplified 97.8%

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

   11. Taylor expanded in z around inf 84.3%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.26 \cdot 10^{+44} \lor \neg \left(a \leq 0.0145\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+43} \lor \neg \left(a \leq 0.00185\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.4e+43) (not (<= a 0.00185)))
   (+ x (/ y (/ a (- t z))))
   (+ x (/ (- z t) (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.4e+43) || !(a <= 0.00185)) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = x + ((z - 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 <= (-2.4d+43)) .or. (.not. (a <= 0.00185d0))) then
        tmp = x + (y / (a / (t - z)))
    else
        tmp = x + ((z - 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 <= -2.4e+43) || !(a <= 0.00185)) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = x + ((z - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.4e+43) or not (a <= 0.00185):
		tmp = x + (y / (a / (t - z)))
	else:
		tmp = x + ((z - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.4e+43) || !(a <= 0.00185))
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - z))));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.4e+43) || ~((a <= 0.00185)))
		tmp = x + (y / (a / (t - z)));
	else
		tmp = x + ((z - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.4e+43], N[Not[LessEqual[a, 0.00185]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.40000000000000023e43 or 0.0018500000000000001 < a

   1. Initial program 81.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

      3. associate-/l* 87.5%

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

   5. Simplified 87.5%

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

      1. clear-num 87.4%

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

      2. un-div-inv 87.5%

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

   7. Applied egg-rr 87.5%

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

   if -2.40000000000000023e43 < a < 0.0018500000000000001

   1. Initial program 85.3%

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

      1. clear-num 85.2%

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

      2. inv-pow 85.2%

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

   4. Applied egg-rr 85.2%

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

      1. unpow-1 85.2%

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

      2. associate-/r* 97.7%

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

   6. Simplified 97.7%

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

      1. clear-num 97.8%

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

      2. add-cube-cbrt 97.0%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\frac{z - a}{y}} \]

      3. *-un-lft-identity 97.0%

         \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

      4. times-frac 96.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

      5. pow2 96.9%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

   8. Applied egg-rr 96.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
   9. Step-by-step derivation

      1. times-frac 97.0%

         \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

      2. unpow2 97.0%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

      3. rem-3cbrt-lft 97.8%

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

      4. *-lft-identity 97.8%

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

   10. Simplified 97.8%

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

   11. Taylor expanded in z around inf 84.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+43} \lor \neg \left(a \leq 0.00185\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+46} \lor \neg \left(z \leq 8.5 \cdot 10^{+79}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+46) (not (<= z 8.5e+79))) (+ y x) (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+46) || !(z <= 8.5e+79)) {
		tmp = y + x;
	} else {
		tmp = x + ((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 ((z <= (-6.5d+46)) .or. (.not. (z <= 8.5d+79))) then
        tmp = y + x
    else
        tmp = x + ((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 ((z <= -6.5e+46) || !(z <= 8.5e+79)) {
		tmp = y + x;
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+46) or not (z <= 8.5e+79):
		tmp = y + x
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+46) || !(z <= 8.5e+79))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e+46) || ~((z <= 8.5e+79)))
		tmp = y + x;
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+46], N[Not[LessEqual[z, 8.5e+79]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000008e46 or 8.4999999999999998e79 < z

   1. Initial program 70.3%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 82.5%

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

      1. +-commutative 82.5%

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

   5. Simplified 82.5%

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

   if -6.50000000000000008e46 < z < 8.4999999999999998e79

   1. Initial program 93.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 71.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+46} \lor \neg \left(z \leq 8.5 \cdot 10^{+79}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46} \lor \neg \left(z \leq 3.2 \cdot 10^{-44}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+46) (not (<= z 3.2e-44))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+46) || !(z <= 3.2e-44)) {
		tmp = y + x;
	} else {
		tmp = x + (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 ((z <= (-5.2d+46)) .or. (.not. (z <= 3.2d-44))) then
        tmp = y + x
    else
        tmp = x + (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 ((z <= -5.2e+46) || !(z <= 3.2e-44)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+46) or not (z <= 3.2e-44):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+46) || !(z <= 3.2e-44))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e+46) || ~((z <= 3.2e-44)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+46], N[Not[LessEqual[z, 3.2e-44]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000027e46 or 3.19999999999999995e-44 < z

   1. Initial program 73.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 80.3%

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

      1. +-commutative 80.3%

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

   5. Simplified 80.3%

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

   if -5.20000000000000027e46 < z < 3.19999999999999995e-44

   1. Initial program 93.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 70.6%

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

      1. +-commutative 70.6%

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

      2. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+46} \lor \neg \left(z \leq 3.2 \cdot 10^{-44}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+172}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.22e+172) y (if (<= y 1.2e+131) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.22e+172) {
		tmp = y;
	} else if (y <= 1.2e+131) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-1.22d+172)) then
        tmp = y
    else if (y <= 1.2d+131) then
        tmp = x
    else
        tmp = 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 (y <= -1.22e+172) {
		tmp = y;
	} else if (y <= 1.2e+131) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.22e+172:
		tmp = y
	elif y <= 1.2e+131:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.22e+172)
		tmp = y;
	elseif (y <= 1.2e+131)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.22e+172)
		tmp = y;
	elseif (y <= 1.2e+131)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.22e+172], y, If[LessEqual[y, 1.2e+131], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.21999999999999999e172 or 1.2e131 < y

   1. Initial program 49.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 47.8%

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

   4. Taylor expanded in z around inf 40.6%

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

   if -1.21999999999999999e172 < y < 1.2e131

   1. Initial program 95.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 61.9%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+172}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{t - z}{\frac{a - z}{y}} \end{array} \]

FPCore

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

C

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

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 + ((t - z) / ((a - z) / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.6%

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

   1. clear-num 83.5%

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

   2. inv-pow 83.5%

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

4. Applied egg-rr 83.5%

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

   1. unpow-1 83.5%

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

   2. associate-/r* 96.8%

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

6. Simplified 96.8%

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

   1. clear-num 96.9%

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

   2. add-cube-cbrt 96.2%

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{\frac{z - a}{y}} \]

   3. *-un-lft-identity 96.2%

      \[\leadsto x + \frac{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}{\color{blue}{1 \cdot \frac{z - a}{y}}} \]

   4. times-frac 96.2%

      \[\leadsto x + \color{blue}{\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]

   5. pow2 96.2%

      \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{z - t}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}} \]

8. Applied egg-rr 96.2%

   \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{z - t}}{\frac{z - a}{y}}} \]
9. Step-by-step derivation

   1. times-frac 96.2%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{z - t}\right)}^{2} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}}} \]

   2. unpow2 96.2%

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \sqrt[3]{z - t}}{1 \cdot \frac{z - a}{y}} \]

   3. rem-3cbrt-lft 96.9%

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

   4. *-lft-identity 96.9%

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

10. Simplified 96.9%

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

11. Final simplification 96.9%

    \[\leadsto x + \frac{t - z}{\frac{a - z}{y}} \]
12. Add Preprocessing

Alternative 12: 60.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.2 \cdot 10^{+259}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 6.2e+259) (+ y x) (* t (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 6.2e+259) {
		tmp = y + x;
	} 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 (t <= 6.2d+259) then
        tmp = y + x
    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 (t <= 6.2e+259) {
		tmp = y + x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 6.2e+259:
		tmp = y + x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 6.2e+259)
		tmp = Float64(y + x);
	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 (t <= 6.2e+259)
		tmp = y + x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 6.2e+259], N[(y + x), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.2000000000000007e259

   1. Initial program 84.2%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 63.0%

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

      1. +-commutative 63.0%

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

   5. Simplified 63.0%

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

   if 6.2000000000000007e259 < t

   1. Initial program 65.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.5%

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

   4. Taylor expanded in z around 0 65.5%

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

      1. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.2 \cdot 10^{+259}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ y + x \end{array} \]

FPCore

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

C

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

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 = y + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 83.6%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 61.2%

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

   1. +-commutative 61.2%

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

5. Simplified 61.2%

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

6. Final simplification 61.2%

   \[\leadsto y + x \]
7. Add Preprocessing

Alternative 14: 51.5% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.6%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 49.4%

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

4. Final simplification 49.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z - a}{z - t}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((z - a) / (z - 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 = x + (y / ((z - a) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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