Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Percentage Accurate: 98.2% → 98.2%

Time: 8.5s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. +-commutative 99.2%

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

   2. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+38} \lor \neg \left(z \leq 5.7 \cdot 10^{-27}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+38) (not (<= z 5.7e-27)))
   (+ x (* y (/ z (- a t))))
   (+ x (* t (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+38) || !(z <= 5.7e-27)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (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 <= (-5.2d+38)) .or. (.not. (z <= 5.7d-27))) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x + (t * (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 <= -5.2e+38) || !(z <= 5.7e-27)) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + (t * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+38) or not (z <= 5.7e-27):
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + (t * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+38) || !(z <= 5.7e-27))
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e+38) || ~((z <= 5.7e-27)))
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + (t * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+38], N[Not[LessEqual[z, 5.7e-27]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999998e38 or 5.6999999999999996e-27 < z

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 77.8%

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

      1. associate-*r/ 85.9%

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

   4. Simplified 85.9%

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

   if -5.1999999999999998e38 < z < 5.6999999999999996e-27

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

      4. frac-2neg 99.9%

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

      5. associate-/r/ 97.2%

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

      6. neg-sub0 97.2%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(a - t\right)}} \cdot \left(-\left(z - t\right)\right) + x \]

      7. sub-neg 97.2%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(a + \left(-t\right)\right)}} \cdot \left(-\left(z - t\right)\right) + x \]

      8. +-commutative 97.2%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(\left(-t\right) + a\right)}} \cdot \left(-\left(z - t\right)\right) + x \]

      9. associate--r+ 97.2%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - a}} \cdot \left(-\left(z - t\right)\right) + x \]

      10. neg-sub0 97.2%

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

      11. remove-double-neg 97.2%

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

      12. neg-sub0 97.2%

          \[\leadsto \frac{y}{t - a} \cdot \color{blue}{\left(0 - \left(z - t\right)\right)} + x \]

      13. sub-neg 97.2%

          \[\leadsto \frac{y}{t - a} \cdot \left(0 - \color{blue}{\left(z + \left(-t\right)\right)}\right) + x \]

      14. +-commutative 97.2%

          \[\leadsto \frac{y}{t - a} \cdot \left(0 - \color{blue}{\left(\left(-t\right) + z\right)}\right) + x \]

      15. associate--r+ 97.2%

          \[\leadsto \frac{y}{t - a} \cdot \color{blue}{\left(\left(0 - \left(-t\right)\right) - z\right)} + x \]

      16. neg-sub0 97.2%

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

      17. remove-double-neg 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in z around 0 81.6%

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

      1. associate-*r/ 92.3%

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

      2. *-commutative 92.3%

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

   8. Applied egg-rr 92.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+38} \lor \neg \left(z \leq 5.7 \cdot 10^{-27}\right):\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \end{array} \]

Alternative 3: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.12 \cdot 10^{+99} \lor \neg \left(t \leq 8 \cdot 10^{+88}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.12e+99) (not (<= t 8e+88)))
   (- x (/ y (/ t (- z t))))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.12e+99) || !(t <= 8e+88)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (y * (z / (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) :: tmp
    if ((t <= (-2.12d+99)) .or. (.not. (t <= 8d+88))) then
        tmp = x - (y / (t / (z - t)))
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.12e+99) || !(t <= 8e+88)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.12e+99) or not (t <= 8e+88):
		tmp = x - (y / (t / (z - t)))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.12e+99) || !(t <= 8e+88))
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.12e+99) || ~((t <= 8e+88)))
		tmp = x - (y / (t / (z - t)));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.12e+99], N[Not[LessEqual[t, 8e+88]], $MachinePrecision]], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.11999999999999999e99 or 7.99999999999999968e88 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 61.2%

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

      1. associate-/l* 95.0%

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

      2. associate-*r/ 95.0%

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

      3. neg-mul-1 95.0%

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

   4. Simplified 95.0%

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

   if -2.11999999999999999e99 < t < 7.99999999999999968e88

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 83.8%

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

      1. associate-*r/ 85.6%

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

   4. Simplified 85.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.12 \cdot 10^{+99} \lor \neg \left(t \leq 8 \cdot 10^{+88}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 4: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+81}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+86}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.4e+81)
   (+ y x)
   (if (<= t 8.5e+86) (+ x (* y (/ z (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.4e+81) {
		tmp = y + x;
	} else if (t <= 8.5e+86) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.4d+81)) then
        tmp = y + x
    else if (t <= 8.5d+86) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.4e+81) {
		tmp = y + x;
	} else if (t <= 8.5e+86) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.4e+81:
		tmp = y + x
	elif t <= 8.5e+86:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.4e+81)
		tmp = Float64(y + x);
	elseif (t <= 8.5e+86)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.4e+81)
		tmp = y + x;
	elseif (t <= 8.5e+86)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.4e+81], N[(y + x), $MachinePrecision], If[LessEqual[t, 8.5e+86], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.39999999999999997e81 or 8.5000000000000005e86 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 90.2%

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

      1. +-commutative 90.2%

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

   4. Simplified 90.2%

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

   if -1.39999999999999997e81 < t < 8.5000000000000005e86

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 84.6%

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

      1. associate-*r/ 85.8%

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

   4. Simplified 85.8%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+81}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+86}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+99}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+87}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e+99)
   (+ x (* (/ y t) (- t z)))
   (if (<= t 2.2e+87) (+ x (* y (/ z (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+99) {
		tmp = x + ((y / t) * (t - z));
	} else if (t <= 2.2e+87) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.95d+99)) then
        tmp = x + ((y / t) * (t - z))
    else if (t <= 2.2d+87) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+99) {
		tmp = x + ((y / t) * (t - z));
	} else if (t <= 2.2e+87) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e+99:
		tmp = x + ((y / t) * (t - z))
	elif t <= 2.2e+87:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e+99)
		tmp = Float64(x + Float64(Float64(y / t) * Float64(t - z)));
	elseif (t <= 2.2e+87)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.95e+99)
		tmp = x + ((y / t) * (t - z));
	elseif (t <= 2.2e+87)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e+99], N[(x + N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+87], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.94999999999999997e99

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

      4. frac-2neg 99.9%

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

      5. associate-/r/ 97.6%

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

      6. neg-sub0 97.6%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(a - t\right)}} \cdot \left(-\left(z - t\right)\right) + x \]

      7. sub-neg 97.6%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(a + \left(-t\right)\right)}} \cdot \left(-\left(z - t\right)\right) + x \]

      8. +-commutative 97.6%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(\left(-t\right) + a\right)}} \cdot \left(-\left(z - t\right)\right) + x \]

      9. associate--r+ 97.6%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - a}} \cdot \left(-\left(z - t\right)\right) + x \]

      10. neg-sub0 97.6%

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

      11. remove-double-neg 97.6%

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

      12. neg-sub0 97.6%

          \[\leadsto \frac{y}{t - a} \cdot \color{blue}{\left(0 - \left(z - t\right)\right)} + x \]

      13. sub-neg 97.6%

          \[\leadsto \frac{y}{t - a} \cdot \left(0 - \color{blue}{\left(z + \left(-t\right)\right)}\right) + x \]

      14. +-commutative 97.6%

          \[\leadsto \frac{y}{t - a} \cdot \left(0 - \color{blue}{\left(\left(-t\right) + z\right)}\right) + x \]

      15. associate--r+ 97.6%

          \[\leadsto \frac{y}{t - a} \cdot \color{blue}{\left(\left(0 - \left(-t\right)\right) - z\right)} + x \]

      16. neg-sub0 97.6%

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

      17. remove-double-neg 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in t around inf 89.4%

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

   if -1.94999999999999997e99 < t < 2.2000000000000001e87

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 83.7%

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

      1. associate-*r/ 85.5%

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

   4. Simplified 85.5%

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

   if 2.2000000000000001e87 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 95.9%

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

      1. +-commutative 95.9%

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

   4. Simplified 95.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+99}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+87}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+82}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.4:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+82) (+ y x) (if (<= t 3.4) (+ x (* y (/ z a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+82) {
		tmp = y + x;
	} else if (t <= 3.4) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7d+82)) then
        tmp = y + x
    else if (t <= 3.4d0) then
        tmp = x + (y * (z / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+82) {
		tmp = y + x;
	} else if (t <= 3.4) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+82:
		tmp = y + x
	elif t <= 3.4:
		tmp = x + (y * (z / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+82)
		tmp = Float64(y + x);
	elseif (t <= 3.4)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7e+82)
		tmp = y + x;
	elseif (t <= 3.4)
		tmp = x + (y * (z / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+82], N[(y + x), $MachinePrecision], If[LessEqual[t, 3.4], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.0000000000000001e82 or 3.39999999999999991 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 87.1%

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

      1. +-commutative 87.1%

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

   4. Simplified 87.1%

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

   if -7.0000000000000001e82 < t < 3.39999999999999991

   1. Initial program 98.6%

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

   2. Taylor expanded in t around 0 77.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+82}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3.4:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternative 8: 62.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{+190}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 8.5e+190) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 8.5e+190) {
		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 <= 8.5d+190) 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 <= 8.5e+190) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 8.5e+190:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 8.5e+190)
		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 <= 8.5e+190)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 8.5e+190], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 8.50000000000000022e190

   1. Initial program 99.1%

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

   2. Taylor expanded in t around inf 65.3%

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

      1. +-commutative 65.3%

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

   4. Simplified 65.3%

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

   if 8.50000000000000022e190 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 87.0%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{+190}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 50.7% 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 99.2%

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

2. Taylor expanded in x around inf 51.0%

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

3. Final simplification 51.0%

   \[\leadsto x \]

Developer target: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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