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

Percentage Accurate: 84.8% → 99.3%

Time: 8.4s

Alternatives: 11

Speedup: 0.8×

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: 84.8% 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: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+250}\right):\\ \;\;\;\;x - \frac{1}{\frac{\frac{z - a}{y}}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

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 2e+250)))
     (- x (/ 1.0 (/ (/ (- z a) y) (- t z))))
     (+ 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 <= 2e+250)) {
		tmp = x - (1.0 / (((z - a) / y) / (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 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+250)) {
		tmp = x - (1.0 / (((z - a) / y) / (t - z)));
	} 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 <= 2e+250):
		tmp = x - (1.0 / (((z - a) / y) / (t - z)))
	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 <= 2e+250))
		tmp = Float64(x - Float64(1.0 / Float64(Float64(Float64(z - a) / y) / 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 = (y * (z - t)) / (z - a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+250)))
		tmp = x - (1.0 / (((z - a) / y) / (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[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+250]], $MachinePrecision]], N[(x - N[(1.0 / N[(N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $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 1.9999999999999998e250 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 44.6%

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

      1. clear-num 44.7%

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

      2. inv-pow 44.7%

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

   4. Applied egg-rr 44.7%

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

      1. unpow-1 44.7%

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

      2. associate-/r* 99.9%

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

   6. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.9999999999999998e250

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{+250}\right):\\ \;\;\;\;x - \frac{1}{\frac{\frac{z - a}{y}}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.7%

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

   1. +-commutative 86.7%

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

   2. associate-/l* 97.0%

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

   3. fma-define 97.0%

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

3. Simplified 97.0%

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

5. Final simplification 97.0%

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

Alternative 3: 77.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-220}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (+ (/ t z) -1.0)))))
   (if (<= a -6.2e+62)
     (+ x (* t (/ y a)))
     (if (<= a -4e-169)
       t_1
       (if (<= a -7.4e-220)
         (+ x (/ (* y t) a))
         (if (<= a 7e+56) t_1 (+ x (/ y (/ a t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t / z) + -1.0));
	double tmp;
	if (a <= -6.2e+62) {
		tmp = x + (t * (y / a));
	} else if (a <= -4e-169) {
		tmp = t_1;
	} else if (a <= -7.4e-220) {
		tmp = x + ((y * t) / a);
	} else if (a <= 7e+56) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * ((t / z) + (-1.0d0)))
    if (a <= (-6.2d+62)) then
        tmp = x + (t * (y / a))
    else if (a <= (-4d-169)) then
        tmp = t_1
    else if (a <= (-7.4d-220)) then
        tmp = x + ((y * t) / a)
    else if (a <= 7d+56) then
        tmp = t_1
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * ((t / z) + -1.0));
	double tmp;
	if (a <= -6.2e+62) {
		tmp = x + (t * (y / a));
	} else if (a <= -4e-169) {
		tmp = t_1;
	} else if (a <= -7.4e-220) {
		tmp = x + ((y * t) / a);
	} else if (a <= 7e+56) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * ((t / z) + -1.0))
	tmp = 0
	if a <= -6.2e+62:
		tmp = x + (t * (y / a))
	elif a <= -4e-169:
		tmp = t_1
	elif a <= -7.4e-220:
		tmp = x + ((y * t) / a)
	elif a <= 7e+56:
		tmp = t_1
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(Float64(t / z) + -1.0)))
	tmp = 0.0
	if (a <= -6.2e+62)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= -4e-169)
		tmp = t_1;
	elseif (a <= -7.4e-220)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= 7e+56)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * ((t / z) + -1.0));
	tmp = 0.0;
	if (a <= -6.2e+62)
		tmp = x + (t * (y / a));
	elseif (a <= -4e-169)
		tmp = t_1;
	elseif (a <= -7.4e-220)
		tmp = x + ((y * t) / a);
	elseif (a <= 7e+56)
		tmp = t_1;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+62], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4e-169], t$95$1, If[LessEqual[a, -7.4e-220], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+56], t$95$1, N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.20000000000000029e62

   1. Initial program 84.0%

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

   3. Taylor expanded in z around 0 79.9%

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

      1. associate-/l* 87.0%

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

      2. *-commutative 87.0%

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

   5. Applied egg-rr 87.0%

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

   if -6.20000000000000029e62 < a < -4.00000000000000008e-169 or -7.4000000000000003e-220 < a < 6.99999999999999999e56

   1. Initial program 84.9%

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

   3. Taylor expanded in a around 0 70.9%

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

      1. associate-/l* 83.3%

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

      2. div-sub 83.3%

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

      3. *-inverses 83.3%

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

   5. Simplified 83.3%

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

   if -4.00000000000000008e-169 < a < -7.4000000000000003e-220

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 90.4%

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

   if 6.99999999999999999e56 < a

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-/l* 98.3%

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

      3. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in a around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. unsub-neg 81.5%

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

      3. associate-/l* 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in z around 0 87.4%

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

      1. neg-mul-1 87.4%

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

      2. distribute-neg-frac2 87.4%

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

   10. Simplified 87.4%

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

       1. *-commutative 87.4%

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

       2. associate-*l/ 79.7%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 65.4%

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

       5. sqr-neg 65.4%

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

       6. sqrt-unprod 65.4%

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

       7. add-sqr-sqrt 65.4%

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

       8. frac-2neg 65.4%

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

       9. *-commutative 65.4%

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

       10. distribute-lft-neg-in 65.4%

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

       11. associate-*r/ 68.4%

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

       12. clear-num 68.4%

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

       13. un-div-inv 68.4%

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

       14. add-sqr-sqrt 0.0%

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

       15. sqrt-unprod 75.0%

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

       16. sqr-neg 75.0%

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

       17. sqrt-unprod 87.4%

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

       18. add-sqr-sqrt 87.4%

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

   12. Applied egg-rr 87.4%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{elif}\;a \leq -7.4 \cdot 10^{-220}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+91} \lor \neg \left(z \leq 2.2 \cdot 10^{+200}\right):\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.08e+91) (not (<= z 2.2e+200)))
   (- x (* y (+ (/ t z) -1.0)))
   (+ x (/ (* y (- z t)) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.08e+91) || !(z <= 2.2e+200)) {
		tmp = x - (y * ((t / z) + -1.0));
	} else {
		tmp = x + ((y * (z - t)) / (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 <= (-1.08d+91)) .or. (.not. (z <= 2.2d+200))) then
        tmp = x - (y * ((t / z) + (-1.0d0)))
    else
        tmp = x + ((y * (z - t)) / (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 <= -1.08e+91) || !(z <= 2.2e+200)) {
		tmp = x - (y * ((t / z) + -1.0));
	} else {
		tmp = x + ((y * (z - t)) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.08e+91) or not (z <= 2.2e+200):
		tmp = x - (y * ((t / z) + -1.0))
	else:
		tmp = x + ((y * (z - t)) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.08e+91) || !(z <= 2.2e+200))
		tmp = Float64(x - Float64(y * Float64(Float64(t / z) + -1.0)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.08e+91) || ~((z <= 2.2e+200)))
		tmp = x - (y * ((t / z) + -1.0));
	else
		tmp = x + ((y * (z - t)) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.08e+91], N[Not[LessEqual[z, 2.2e+200]], $MachinePrecision]], N[(x - N[(y * N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.08e91 or 2.2e200 < z

   1. Initial program 63.9%

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

   3. Taylor expanded in a around 0 63.8%

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

      1. associate-/l* 100.0%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   5. Simplified 100.0%

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

   if -1.08e91 < z < 2.2e200

   1. Initial program 94.4%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+91} \lor \neg \left(z \leq 2.2 \cdot 10^{+200}\right):\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+25} \lor \neg \left(z \leq 1.05 \cdot 10^{+23}\right):\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+25) (not (<= z 1.05e+23)))
   (- x (* y (+ (/ t z) -1.0)))
   (- x (/ (* y t) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+25) || !(z <= 1.05e+23)) {
		tmp = x - (y * ((t / z) + -1.0));
	} else {
		tmp = x - ((y * t) / (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 <= (-8d+25)) .or. (.not. (z <= 1.05d+23))) then
        tmp = x - (y * ((t / z) + (-1.0d0)))
    else
        tmp = x - ((y * t) / (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 <= -8e+25) || !(z <= 1.05e+23)) {
		tmp = x - (y * ((t / z) + -1.0));
	} else {
		tmp = x - ((y * t) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+25) or not (z <= 1.05e+23):
		tmp = x - (y * ((t / z) + -1.0))
	else:
		tmp = x - ((y * t) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+25) || !(z <= 1.05e+23))
		tmp = Float64(x - Float64(y * Float64(Float64(t / z) + -1.0)));
	else
		tmp = Float64(x - Float64(Float64(y * t) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+25) || ~((z <= 1.05e+23)))
		tmp = x - (y * ((t / z) + -1.0));
	else
		tmp = x - ((y * t) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+25], N[Not[LessEqual[z, 1.05e+23]], $MachinePrecision]], N[(x - N[(y * N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000072e25 or 1.0500000000000001e23 < z

   1. Initial program 77.5%

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

   3. Taylor expanded in a around 0 67.2%

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

      1. associate-/l* 89.0%

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

      2. div-sub 89.0%

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

      3. *-inverses 89.0%

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

   5. Simplified 89.0%

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

   if -8.00000000000000072e25 < z < 1.0500000000000001e23

   1. Initial program 95.5%

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

   3. Taylor expanded in t around inf 88.7%

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

      1. mul-1-neg 88.7%

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

      2. distribute-neg-frac2 88.7%

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

      3. associate-*r/ 89.7%

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

      4. sub-neg 89.7%

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

      5. distribute-neg-in 89.7%

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

      6. remove-double-neg 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in t around 0 88.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+25} \lor \neg \left(z \leq 1.05 \cdot 10^{+23}\right):\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+22} \lor \neg \left(z \leq 3.3 \cdot 10^{+25}\right):\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+22) (not (<= z 3.3e+25)))
   (- x (* y (+ (/ t z) -1.0)))
   (- x (* t (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+22) || !(z <= 3.3e+25)) {
		tmp = x - (y * ((t / z) + -1.0));
	} 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 <= (-3.5d+22)) .or. (.not. (z <= 3.3d+25))) then
        tmp = x - (y * ((t / z) + (-1.0d0)))
    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 <= -3.5e+22) || !(z <= 3.3e+25)) {
		tmp = x - (y * ((t / z) + -1.0));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+22) or not (z <= 3.3e+25):
		tmp = x - (y * ((t / z) + -1.0))
	else:
		tmp = x - (t * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+22) || !(z <= 3.3e+25))
		tmp = Float64(x - Float64(y * Float64(Float64(t / z) + -1.0)));
	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 <= -3.5e+22) || ~((z <= 3.3e+25)))
		tmp = x - (y * ((t / z) + -1.0));
	else
		tmp = x - (t * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+22], N[Not[LessEqual[z, 3.3e+25]], $MachinePrecision]], N[(x - N[(y * N[(N[(t / z), $MachinePrecision] + -1.0), $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 < -3.5e22 or 3.3000000000000001e25 < z

   1. Initial program 77.5%

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

   3. Taylor expanded in a around 0 67.2%

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

      1. associate-/l* 89.0%

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

      2. div-sub 89.0%

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

      3. *-inverses 89.0%

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

   5. Simplified 89.0%

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

   if -3.5e22 < z < 3.3000000000000001e25

   1. Initial program 95.5%

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

   3. Taylor expanded in t around inf 88.7%

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

      1. mul-1-neg 88.7%

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

      2. distribute-neg-frac2 88.7%

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

      3. associate-*r/ 89.7%

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

      4. sub-neg 89.7%

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

      5. distribute-neg-in 89.7%

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

      6. remove-double-neg 89.7%

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

   5. Simplified 89.7%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+22} \lor \neg \left(z \leq 3.3 \cdot 10^{+25}\right):\\ \;\;\;\;x - y \cdot \left(\frac{t}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+25} \lor \neg \left(z \leq 1250000000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+25) (not (<= z 1250000000000.0)))
   (+ y x)
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+25) || !(z <= 1250000000000.0)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / 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+25)) .or. (.not. (z <= 1250000000000.0d0))) then
        tmp = y + x
    else
        tmp = x + (y * (t / 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+25) || !(z <= 1250000000000.0)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+25) or not (z <= 1250000000000.0):
		tmp = y + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+25) || !(z <= 1250000000000.0))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e+25) || ~((z <= 1250000000000.0)))
		tmp = y + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+25], N[Not[LessEqual[z, 1250000000000.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000005e25 or 1.25e12 < z

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 80.0%

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

      1. +-commutative 80.0%

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

   7. Simplified 80.0%

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

   if -6.50000000000000005e25 < z < 1.25e12

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. *-un-lft-identity 78.5%

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

      2. associate-*l/ 78.5%

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

      3. associate-*r* 78.4%

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

      4. associate-*l/ 78.4%

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

      5. *-un-lft-identity 78.4%

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

   5. Applied egg-rr 78.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+25} \lor \neg \left(z \leq 1250000000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+28} \lor \neg \left(z \leq 10200000000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.65e+28) (not (<= z 10200000000000.0)))
   (+ y x)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.65e+28) || !(z <= 10200000000000.0)) {
		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 <= (-2.65d+28)) .or. (.not. (z <= 10200000000000.0d0))) 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 <= -2.65e+28) || !(z <= 10200000000000.0)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.65e+28) or not (z <= 10200000000000.0):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.65e+28) || !(z <= 10200000000000.0))
		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 <= -2.65e+28) || ~((z <= 10200000000000.0)))
		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, -2.65e+28], N[Not[LessEqual[z, 10200000000000.0]], $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 < -2.6500000000000002e28 or 1.02e13 < z

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 80.0%

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

      1. +-commutative 80.0%

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

   7. Simplified 80.0%

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

   if -2.6500000000000002e28 < z < 1.02e13

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. associate-/l* 79.5%

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

      2. *-commutative 79.5%

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

   5. Applied egg-rr 79.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+28} \lor \neg \left(z \leq 10200000000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+220}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e+62) x (if (<= a 2.8e+220) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+62) {
		tmp = x;
	} else if (a <= 2.8e+220) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d+62)) then
        tmp = x
    else if (a <= 2.8d+220) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+62) {
		tmp = x;
	} else if (a <= 2.8e+220) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e+62:
		tmp = x
	elif a <= 2.8e+220:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e+62)
		tmp = x;
	elseif (a <= 2.8e+220)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e+62)
		tmp = x;
	elseif (a <= 2.8e+220)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e+62], x, If[LessEqual[a, 2.8e+220], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.59999999999999992e62 or 2.8000000000000001e220 < a

   1. Initial program 82.6%

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

      1. +-commutative 82.6%

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

      2. associate-/l* 98.2%

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

      3. fma-define 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around 0 71.7%

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

   if -1.59999999999999992e62 < a < 2.8000000000000001e220

   1. Initial program 87.9%

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

      1. +-commutative 87.9%

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

      2. associate-/l* 96.6%

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

      3. fma-define 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around inf 68.2%

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

      1. +-commutative 68.2%

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

   7. Simplified 68.2%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+220}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{-1}{\frac{\frac{z - a}{t - z}}{y}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (/ -1.0 (/ (/ (- z a) (- t z)) y))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (-1.0 / (((z - a) / (t - 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 + ((-1.0d0) / (((z - a) / (t - z)) / y))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (-1.0 / (((z - a) / (t - z)) / y));
}

Python

def code(x, y, z, t, a):
	return x + (-1.0 / (((z - a) / (t - z)) / y))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(-1.0 / Float64(Float64(Float64(z - a) / Float64(t - z)) / y)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (-1.0 / (((z - a) / (t - z)) / y));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(-1.0 / N[(N[(N[(z - a), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.7%

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

   1. clear-num 86.6%

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

   2. inv-pow 86.6%

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

4. Applied egg-rr 86.6%

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

   1. unpow-1 86.6%

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

   2. *-commutative 86.6%

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

   3. associate-/r* 96.8%

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

6. Simplified 96.8%

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

7. Final simplification 96.8%

   \[\leadsto x + \frac{-1}{\frac{\frac{z - a}{t - z}}{y}} \]
8. Add Preprocessing

Alternative 11: 51.0% 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 86.7%

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

   1. +-commutative 86.7%

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

   2. associate-/l* 97.0%

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

   3. fma-define 97.0%

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

3. Simplified 97.0%

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

5. Taylor expanded in y around 0 52.2%

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

6. Final simplification 52.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.5% 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 2024130 
(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))))