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

Percentage Accurate: 84.7% → 99.0%

Time: 12.4s

Alternatives: 13

Speedup: 0.6×

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: 84.7% 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: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z - t}{z - a} + \frac{x}{y}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-56}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- z a))))
   (if (<= t_1 (- INFINITY))
     (* y (+ (/ (- z t) (- z a)) (/ x y)))
     (if (<= t_1 2e-56) (+ x t_1) (+ x (/ (- z t) (/ (- z a) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (((z - t) / (z - a)) + (x / y));
	} else if (t_1 <= 2e-56) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (((z - t) / (z - a)) + (x / y));
	} else if (t_1 <= 2e-56) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (z - a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (((z - t) / (z - a)) + (x / y))
	elif t_1 <= 2e-56:
		tmp = x + t_1
	else:
		tmp = x + ((z - t) / ((z - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(Float64(z - t) / Float64(z - a)) + Float64(x / y)));
	elseif (t_1 <= 2e-56)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (z - a);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (((z - t) / (z - a)) + (x / y));
	elseif (t_1 <= 2e-56)
		tmp = x + t_1;
	else
		tmp = x + ((z - t) / ((z - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-56], N[(x + t$95$1), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 28.5%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. div-sub 99.9%

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

   5. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.0000000000000001e-56

   1. Initial program 99.2%

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

   if 2.0000000000000001e-56 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-/l* 94.6%

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

      3. fma-define 94.6%

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

   3. Simplified 94.6%

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

      1. fma-undefine 94.6%

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

      2. associate-/l* 83.7%

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

      3. div-inv 83.6%

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

      4. *-commutative 83.6%

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

      5. associate-*r* 99.6%

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

      6. div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{z - t}{z - a} + \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq 2 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-147}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.45e-147)
   (+ x (/ (- z t) (/ (- z a) y)))
   (fma y (/ (- z t) (- z a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.45e-147) {
		tmp = x + ((z - t) / ((z - a) / y));
	} else {
		tmp = fma(y, ((z - t) / (z - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.45e-147)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	else
		tmp = fma(y, Float64(Float64(z - t) / Float64(z - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.45e-147], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4500000000000001e-147

   1. Initial program 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-/l* 94.7%

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

      3. fma-define 94.7%

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

   3. Simplified 94.7%

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

      1. fma-undefine 94.7%

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

      2. associate-/l* 85.9%

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

      3. div-inv 85.9%

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

      4. *-commutative 85.9%

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

      5. associate-*r* 98.9%

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

      6. div-inv 98.9%

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

   6. Applied egg-rr 98.9%

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

      1. clear-num 98.9%

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

      2. un-div-inv 99.0%

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

   8. Applied egg-rr 99.0%

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

   if -1.4500000000000001e-147 < x

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. associate-/l* 99.2%

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

      3. fma-define 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-147}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+99}:\\ \;\;\;\;x - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- z a)))))
   (if (<= z -3.2e+132)
     (+ x y)
     (if (<= z -1.95e+66)
       t_1
       (if (<= z -1.22e+28)
         (+ x y)
         (if (<= z 2.85e+23)
           (+ x (/ (* t y) a))
           (if (<= z 5e+99)
             (- x (/ (* t y) z))
             (if (<= z 1.12e+154) t_1 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (z <= -3.2e+132) {
		tmp = x + y;
	} else if (z <= -1.95e+66) {
		tmp = t_1;
	} else if (z <= -1.22e+28) {
		tmp = x + y;
	} else if (z <= 2.85e+23) {
		tmp = x + ((t * y) / a);
	} else if (z <= 5e+99) {
		tmp = x - ((t * y) / z);
	} else if (z <= 1.12e+154) {
		tmp = t_1;
	} else {
		tmp = x + 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (z - a))
    if (z <= (-3.2d+132)) then
        tmp = x + y
    else if (z <= (-1.95d+66)) then
        tmp = t_1
    else if (z <= (-1.22d+28)) then
        tmp = x + y
    else if (z <= 2.85d+23) then
        tmp = x + ((t * y) / a)
    else if (z <= 5d+99) then
        tmp = x - ((t * y) / z)
    else if (z <= 1.12d+154) then
        tmp = t_1
    else
        tmp = x + y
    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 * ((z - t) / (z - a));
	double tmp;
	if (z <= -3.2e+132) {
		tmp = x + y;
	} else if (z <= -1.95e+66) {
		tmp = t_1;
	} else if (z <= -1.22e+28) {
		tmp = x + y;
	} else if (z <= 2.85e+23) {
		tmp = x + ((t * y) / a);
	} else if (z <= 5e+99) {
		tmp = x - ((t * y) / z);
	} else if (z <= 1.12e+154) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (z - a))
	tmp = 0
	if z <= -3.2e+132:
		tmp = x + y
	elif z <= -1.95e+66:
		tmp = t_1
	elif z <= -1.22e+28:
		tmp = x + y
	elif z <= 2.85e+23:
		tmp = x + ((t * y) / a)
	elif z <= 5e+99:
		tmp = x - ((t * y) / z)
	elif z <= 1.12e+154:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if (z <= -3.2e+132)
		tmp = Float64(x + y);
	elseif (z <= -1.95e+66)
		tmp = t_1;
	elseif (z <= -1.22e+28)
		tmp = Float64(x + y);
	elseif (z <= 2.85e+23)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (z <= 5e+99)
		tmp = Float64(x - Float64(Float64(t * y) / z));
	elseif (z <= 1.12e+154)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	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 (z <= -3.2e+132)
		tmp = x + y;
	elseif (z <= -1.95e+66)
		tmp = t_1;
	elseif (z <= -1.22e+28)
		tmp = x + y;
	elseif (z <= 2.85e+23)
		tmp = x + ((t * y) / a);
	elseif (z <= 5e+99)
		tmp = x - ((t * y) / z);
	elseif (z <= 1.12e+154)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+132], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.95e+66], t$95$1, If[LessEqual[z, -1.22e+28], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.85e+23], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+99], N[(x - N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+154], t$95$1, N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1999999999999997e132 or -1.9500000000000002e66 < z < -1.2199999999999999e28 or 1.11999999999999994e154 < z

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 85.3%

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

      1. +-commutative 85.3%

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

   5. Simplified 85.3%

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

   if -3.1999999999999997e132 < z < -1.9500000000000002e66 or 5.00000000000000008e99 < z < 1.11999999999999994e154

   1. Initial program 63.8%

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

   3. Taylor expanded in x around 0 42.6%

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

      1. associate-*r/ 78.6%

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

   5. Simplified 78.6%

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

   if -1.2199999999999999e28 < z < 2.85e23

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 85.3%

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

   if 2.85e23 < z < 5.00000000000000008e99

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

      1. fma-undefine 99.8%

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

      2. associate-/l* 89.4%

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

      3. div-inv 89.5%

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

      4. *-commutative 89.5%

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

      5. associate-*r* 89.8%

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

      6. div-inv 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in a around 0 84.4%

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

   8. Taylor expanded in z around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. distribute-lft-neg-out 73.3%

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

      3. *-commutative 73.3%

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

   10. Simplified 73.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+132}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+28}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+99}:\\ \;\;\;\;x - \frac{t \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+154}:\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+261}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+261)))
     (* y (/ (- z t) (- z a)))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+261)) {
		tmp = y * ((z - t) / (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 = ((z - t) * y) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+261)) {
		tmp = y * ((z - t) / (z - a));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+261):
		tmp = y * ((z - t) / (z - a))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+261))
		tmp = Float64(y * Float64(Float64(z - t) / 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 = ((z - t) * y) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+261)))
		tmp = y * ((z - t) / (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[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+261]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / 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 9.9999999999999993e260 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 33.1%

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

   3. Taylor expanded in x around 0 33.1%

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

      1. associate-*r/ 87.8%

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

   5. Simplified 87.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 9.9999999999999993e260

   1. Initial program 99.3%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -\infty \lor \neg \left(\frac{\left(z - t\right) \cdot y}{z - a} \leq 10^{+261}\right):\\ \;\;\;\;y \cdot \frac{z - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{-56}\right):\\ \;\;\;\;x + \frac{y}{a - z} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- z a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e-56)))
     (+ x (* (/ y (- a z)) (- t z)))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e-56)) {
		tmp = x + ((y / (a - z)) * (t - z));
	} 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 = ((z - t) * y) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e-56)) {
		tmp = x + ((y / (a - z)) * (t - z));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (z - a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e-56):
		tmp = x + ((y / (a - z)) * (t - z))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e-56))
		tmp = Float64(x + Float64(Float64(y / Float64(a - z)) * Float64(t - z)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e-56)))
		tmp = x + ((y / (a - z)) * (t - z));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e-56]], $MachinePrecision]], N[(x + N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - z), $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 2.0000000000000001e-56 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 67.7%

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

      1. +-commutative 67.7%

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

      2. associate-/l* 96.1%

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

      3. fma-define 96.1%

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

   3. Simplified 96.1%

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

      1. fma-undefine 96.1%

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

      2. associate-/l* 67.7%

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

      3. div-inv 67.6%

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

      4. *-commutative 67.6%

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

      5. associate-*r* 99.7%

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

      6. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.0000000000000001e-56

   1. Initial program 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -\infty \lor \neg \left(\frac{\left(z - t\right) \cdot y}{z - a} \leq 2 \cdot 10^{-56}\right):\\ \;\;\;\;x + \frac{y}{a - z} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{a - z} \cdot \left(t - z\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-56}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) (- z a))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (/ y (- a z)) (- t z)))
     (if (<= t_1 2e-56) (+ x t_1) (+ x (/ (- z t) (/ (- z a) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((y / (a - z)) * (t - z));
	} else if (t_1 <= 2e-56) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((y / (a - z)) * (t - z));
	} else if (t_1 <= 2e-56) {
		tmp = x + t_1;
	} else {
		tmp = x + ((z - t) / ((z - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / (z - a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((y / (a - z)) * (t - z))
	elif t_1 <= 2e-56:
		tmp = x + t_1
	else:
		tmp = x + ((z - t) / ((z - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y / Float64(a - z)) * Float64(t - z)));
	elseif (t_1 <= 2e-56)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(z - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / (z - a);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((y / (a - z)) * (t - z));
	elseif (t_1 <= 2e-56)
		tmp = x + t_1;
	else
		tmp = x + ((z - t) / ((z - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-56], N[(x + t$95$1), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 28.5%

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

      1. +-commutative 28.5%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. associate-/l* 28.5%

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

      3. div-inv 28.5%

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

      4. *-commutative 28.5%

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

      5. associate-*r* 99.7%

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

      6. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2.0000000000000001e-56

   1. Initial program 99.2%

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

   if 2.0000000000000001e-56 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-/l* 94.6%

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

      3. fma-define 94.6%

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

   3. Simplified 94.6%

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

      1. fma-undefine 94.6%

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

      2. associate-/l* 83.7%

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

      3. div-inv 83.6%

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

      4. *-commutative 83.6%

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

      5. associate-*r* 99.6%

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

      6. div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -\infty:\\ \;\;\;\;x + \frac{y}{a - z} \cdot \left(t - z\right)\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq 2 \cdot 10^{-56}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{z - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+22} \lor \neg \left(z \leq 6.8 \cdot 10^{+22}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e+22) (not (<= z 6.8e+22)))
   (+ x (* y (/ (- z t) z)))
   (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+22) || !(z <= 6.8e+22)) {
		tmp = x + (y * ((z - t) / z));
	} 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 <= (-6.8d+22)) .or. (.not. (z <= 6.8d+22))) then
        tmp = x + (y * ((z - t) / z))
    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 <= -6.8e+22) || !(z <= 6.8e+22)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e+22) or not (z <= 6.8e+22):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e+22) || !(z <= 6.8e+22))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	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 <= -6.8e+22) || ~((z <= 6.8e+22)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e+22], N[Not[LessEqual[z, 6.8e+22]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8e22 or 6.8e22 < z

   1. Initial program 73.9%

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

   3. Taylor expanded in a around 0 66.1%

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

      1. +-commutative 66.1%

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

      2. associate-/l* 86.2%

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

   5. Simplified 86.2%

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

   if -6.8e22 < z < 6.8e22

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 85.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+22} \lor \neg \left(z \leq 6.8 \cdot 10^{+22}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-22} \lor \neg \left(a \leq 1350000\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.35e-22) (not (<= a 1350000.0)))
   (+ x (* y (/ (- t z) a)))
   (+ x (* y (/ (- z t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e-22) || !(a <= 1350000.0)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.35d-22)) .or. (.not. (a <= 1350000.0d0))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + (y * ((z - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.35e-22) || !(a <= 1350000.0)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.35e-22) or not (a <= 1350000.0):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.35e-22) || !(a <= 1350000.0))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.35e-22) || ~((a <= 1350000.0)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.35e-22], N[Not[LessEqual[a, 1350000.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3500000000000001e-22 or 1.35e6 < a

   1. Initial program 87.4%

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

   3. Taylor expanded in a around inf 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

      3. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

   if -1.3500000000000001e-22 < a < 1.35e6

   1. Initial program 86.3%

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

   3. Taylor expanded in a around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-/l* 86.1%

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

   5. Simplified 86.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-22} \lor \neg \left(a \leq 1350000\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-22} \lor \neg \left(a \leq 41000000\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.7e-22) (not (<= a 41000000.0)))
   (+ x (/ y (/ a (- t z))))
   (+ x (* y (/ (- z t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e-22) || !(a <= 41000000.0)) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.7d-22)) .or. (.not. (a <= 41000000.0d0))) then
        tmp = x + (y / (a / (t - z)))
    else
        tmp = x + (y * ((z - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e-22) || !(a <= 41000000.0)) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.7e-22) or not (a <= 41000000.0):
		tmp = x + (y / (a / (t - z)))
	else:
		tmp = x + (y * ((z - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.7e-22) || !(a <= 41000000.0))
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - z))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.7e-22) || ~((a <= 41000000.0)))
		tmp = x + (y / (a / (t - z)));
	else
		tmp = x + (y * ((z - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.7e-22], N[Not[LessEqual[a, 41000000.0]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6999999999999999e-22 or 4.1e7 < a

   1. Initial program 87.4%

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

   3. Taylor expanded in a around inf 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

      3. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

      1. clear-num 86.5%

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

      2. un-div-inv 86.6%

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

   7. Applied egg-rr 86.6%

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

   if -1.6999999999999999e-22 < a < 4.1e7

   1. Initial program 86.3%

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

   3. Taylor expanded in a around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-/l* 86.1%

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

   5. Simplified 86.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-22} \lor \neg \left(a \leq 41000000\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+27} \lor \neg \left(z \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+27) (not (<= z 5e+49)))
   (+ x (* y (/ (- z t) z)))
   (- x (* t (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+27) || !(z <= 5e+49)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x - (t * (y / (z - 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 <= (-4d+27)) .or. (.not. (z <= 5d+49))) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x - (t * (y / (z - 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 <= -4e+27) || !(z <= 5e+49)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+27) or not (z <= 5e+49):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x - (t * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+27) || !(z <= 5e+49))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+27) || ~((z <= 5e+49)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x - (t * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+27], N[Not[LessEqual[z, 5e+49]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0000000000000001e27 or 5.0000000000000004e49 < z

   1. Initial program 73.2%

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

   3. Taylor expanded in a around 0 65.7%

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

      1. +-commutative 65.7%

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

      2. associate-/l* 87.0%

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

   5. Simplified 87.0%

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

   if -4.0000000000000001e27 < z < 5.0000000000000004e49

   1. Initial program 98.4%

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

   3. Taylor expanded in t around inf 92.8%

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

      1. mul-1-neg 92.8%

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

      2. associate-/l* 92.5%

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

      3. distribute-rgt-neg-in 92.5%

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

      4. distribute-frac-neg2 92.5%

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

      5. sub-neg 92.5%

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

      6. distribute-neg-in 92.5%

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

      7. remove-double-neg 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+27} \lor \neg \left(z \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+21} \lor \neg \left(z \leq 3.5 \cdot 10^{+49}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.25e+21) (not (<= z 3.5e+49))) (+ x y) (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.25e+21) || !(z <= 3.5e+49)) {
		tmp = x + y;
	} 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 <= (-2.25d+21)) .or. (.not. (z <= 3.5d+49))) then
        tmp = x + y
    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 <= -2.25e+21) || !(z <= 3.5e+49)) {
		tmp = x + y;
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.25e+21) or not (z <= 3.5e+49):
		tmp = x + y
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.25e+21) || !(z <= 3.5e+49))
		tmp = Float64(x + y);
	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 <= -2.25e+21) || ~((z <= 3.5e+49)))
		tmp = x + y;
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.25e+21], N[Not[LessEqual[z, 3.5e+49]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25e21 or 3.49999999999999975e49 < z

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 76.6%

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

      1. +-commutative 76.6%

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

   5. Simplified 76.6%

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

   if -2.25e21 < z < 3.49999999999999975e49

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 83.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+21} \lor \neg \left(z \leq 3.5 \cdot 10^{+49}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+20} \lor \neg \left(z \leq 10^{+43}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+20) (not (<= z 1e+43))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+20) || !(z <= 1e+43)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.3d+20)) .or. (.not. (z <= 1d+43))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+20) || !(z <= 1e+43)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+20) or not (z <= 1e+43):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+20) || !(z <= 1e+43))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e+20) || ~((z <= 1e+43)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+20], N[Not[LessEqual[z, 1e+43]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e20 or 1.00000000000000001e43 < z

   1. Initial program 73.7%

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

   3. Taylor expanded in z around inf 75.4%

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

      1. +-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -1.3e20 < z < 1.00000000000000001e43

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 59.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+20} \lor \neg \left(z \leq 10^{+43}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.3% 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 86.9%

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

3. Taylor expanded in x around inf 53.1%

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

4. Final simplification 53.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 98.3% 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 2024055 
(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))))