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

Percentage Accurate: 85.2% → 98.3%

Time: 7.8s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

   1. +-commutative 88.9%

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

   2. associate-*r/ 97.6%

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

   3. fma-def 97.6%

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

3. Simplified 97.6%

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

   1. fma-udef 97.6%

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

5. Applied egg-rr 97.6%

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

6. Final simplification 97.6%

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

Alternative 2: 96.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+205} \lor \neg \left(t \leq 1.3 \cdot 10^{+219}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.2e+205) (not (<= t 1.3e+219)))
   (+ x (/ y (/ t (- t z))))
   (+ x (* (- z t) (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e+205) || !(t <= 1.3e+219)) {
		tmp = x + (y / (t / (t - z)));
	} else {
		tmp = x + ((z - t) * (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) :: tmp
    if ((t <= (-2.2d+205)) .or. (.not. (t <= 1.3d+219))) then
        tmp = x + (y / (t / (t - z)))
    else
        tmp = x + ((z - t) * (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 tmp;
	if ((t <= -2.2e+205) || !(t <= 1.3e+219)) {
		tmp = x + (y / (t / (t - z)));
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.2e+205) or not (t <= 1.3e+219):
		tmp = x + (y / (t / (t - z)))
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.2e+205) || !(t <= 1.3e+219))
		tmp = Float64(x + Float64(y / Float64(t / Float64(t - z))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.2e+205) || ~((t <= 1.3e+219)))
		tmp = x + (y / (t / (t - z)));
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.2e+205], N[Not[LessEqual[t, 1.3e+219]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1999999999999998e205 or 1.3e219 < t

   1. Initial program 66.5%

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

      1. +-commutative 66.5%

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

      2. associate-*r/ 99.9%

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

      3. 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%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. neg-mul-1 64.9%

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

      3. distribute-rgt-neg-in 64.9%

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

      4. associate-/l* 98.5%

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

      5. neg-sub0 98.5%

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

      6. associate--r- 98.5%

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

      7. neg-sub0 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in y around 0 64.9%

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

       1. associate-/l* 98.5%

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

   11. Simplified 98.5%

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

   if -2.1999999999999998e205 < t < 1.3e219

   1. Initial program 93.3%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+205} \lor \neg \left(t \leq 1.3 \cdot 10^{+219}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 3: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-42}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 10^{-80}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+44}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e-42)
   (+ y x)
   (if (<= t 1e-80)
     (+ x (/ y (/ a z)))
     (if (<= t 1.4e+44) (- x (* z (/ y t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e-42) {
		tmp = y + x;
	} else if (t <= 1e-80) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.4e+44) {
		tmp = x - (z * (y / 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 <= (-2.5d-42)) then
        tmp = y + x
    else if (t <= 1d-80) then
        tmp = x + (y / (a / z))
    else if (t <= 1.4d+44) then
        tmp = x - (z * (y / 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 <= -2.5e-42) {
		tmp = y + x;
	} else if (t <= 1e-80) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.4e+44) {
		tmp = x - (z * (y / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e-42:
		tmp = y + x
	elif t <= 1e-80:
		tmp = x + (y / (a / z))
	elif t <= 1.4e+44:
		tmp = x - (z * (y / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e-42)
		tmp = Float64(y + x);
	elseif (t <= 1e-80)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.4e+44)
		tmp = Float64(x - Float64(z * Float64(y / 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 <= -2.5e-42)
		tmp = y + x;
	elseif (t <= 1e-80)
		tmp = x + (y / (a / z));
	elseif (t <= 1.4e+44)
		tmp = x - (z * (y / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e-42], N[(y + x), $MachinePrecision], If[LessEqual[t, 1e-80], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+44], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.50000000000000001e-42 or 1.4e44 < t

   1. Initial program 80.3%

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

      1. +-commutative 80.3%

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

      2. associate-*r/ 99.9%

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

      3. 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. Taylor expanded in t around inf 78.5%

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

   if -2.50000000000000001e-42 < t < 9.99999999999999961e-81

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. associate-*r/ 96.1%

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

      3. fma-def 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in t around 0 83.4%

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

      1. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

   if 9.99999999999999961e-81 < t < 1.4e44

   1. Initial program 99.8%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in z around inf 75.9%

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

   5. Taylor expanded in a around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. associate-*r* 75.6%

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

      3. *-commutative 75.6%

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

      4. neg-mul-1 75.6%

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

   7. Simplified 75.6%

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

      1. div-inv 75.6%

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

      2. *-commutative 75.6%

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

      3. *-commutative 75.6%

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

      4. add-sqr-sqrt 20.0%

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

      5. sqrt-unprod 55.4%

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

      6. sqr-neg 55.4%

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

      7. sqrt-unprod 35.7%

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

      8. add-sqr-sqrt 45.7%

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

      9. distribute-lft-neg-in 45.7%

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

      10. cancel-sign-sub-inv 45.7%

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

      11. associate-*l* 45.7%

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

      12. add-sqr-sqrt 10.1%

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

      13. sqrt-unprod 50.6%

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

      14. sqr-neg 50.6%

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

      15. sqrt-unprod 50.1%

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

      16. add-sqr-sqrt 75.6%

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

      17. div-inv 75.7%

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

   9. Applied egg-rr 75.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-42}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 10^{-80}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+44}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-40} \lor \neg \left(t \leq 800\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.4e-40) (not (<= t 800.0)))
   (+ x (/ y (/ t (- t z))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.4e-40) || !(t <= 800.0)) {
		tmp = x + (y / (t / (t - z)));
	} else {
		tmp = x + (z * (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) :: tmp
    if ((t <= (-3.4d-40)) .or. (.not. (t <= 800.0d0))) then
        tmp = x + (y / (t / (t - z)))
    else
        tmp = x + (z * (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 tmp;
	if ((t <= -3.4e-40) || !(t <= 800.0)) {
		tmp = x + (y / (t / (t - z)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.4e-40) or not (t <= 800.0):
		tmp = x + (y / (t / (t - z)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.4e-40) || !(t <= 800.0))
		tmp = Float64(x + Float64(y / Float64(t / Float64(t - z))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.4e-40) || ~((t <= 800.0)))
		tmp = x + (y / (t / (t - z)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.4e-40], N[Not[LessEqual[t, 800.0]], $MachinePrecision]], N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.39999999999999984e-40 or 800 < t

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 99.9%

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

      3. 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%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around 0 71.8%

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

      1. associate-*r/ 71.8%

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

      2. neg-mul-1 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. associate-/l* 89.2%

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

      5. neg-sub0 89.2%

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

      6. associate--r- 89.2%

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

      7. neg-sub0 89.2%

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

   8. Simplified 89.2%

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

   9. Taylor expanded in y around 0 71.8%

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

       1. associate-/l* 89.2%

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

   11. Simplified 89.2%

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

   if -3.39999999999999984e-40 < t < 800

   1. Initial program 97.6%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 92.2%

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

      1. associate-*l/ 93.0%

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

      2. *-commutative 93.0%

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

   6. Simplified 93.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-40} \lor \neg \left(t \leq 800\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 5: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e+53)
   (+ y x)
   (if (<= t 1.02e+43) (+ x (* z (/ y (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e+53) {
		tmp = y + x;
	} else if (t <= 1.02e+43) {
		tmp = x + (z * (y / (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 <= (-6.8d+53)) then
        tmp = y + x
    else if (t <= 1.02d+43) then
        tmp = x + (z * (y / (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 <= -6.8e+53) {
		tmp = y + x;
	} else if (t <= 1.02e+43) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e+53:
		tmp = y + x
	elif t <= 1.02e+43:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e+53)
		tmp = Float64(y + x);
	elseif (t <= 1.02e+43)
		tmp = Float64(x + Float64(z * Float64(y / 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 <= -6.8e+53)
		tmp = y + x;
	elseif (t <= 1.02e+43)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e+53], N[(y + x), $MachinePrecision], If[LessEqual[t, 1.02e+43], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.79999999999999995e53 or 1.02e43 < t

   1. Initial program 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-*r/ 100.0%

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

      3. 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. Taylor expanded in t around inf 83.9%

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

   if -6.79999999999999995e53 < t < 1.02e43

   1. Initial program 97.5%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 87.5%

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

      1. associate-*l/ 88.8%

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

      2. *-commutative 88.8%

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

   6. Simplified 88.8%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+53}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-37}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e-39)
   (+ x (/ y (/ t (- t z))))
   (if (<= t 8.5e-37) (+ x (* z (/ y (- a t)))) (- x (/ y (+ (/ a t) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e-39) {
		tmp = x + (y / (t / (t - z)));
	} else if (t <= 8.5e-37) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	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 <= (-1.2d-39)) then
        tmp = x + (y / (t / (t - z)))
    else if (t <= 8.5d-37) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y / ((a / t) + (-1.0d0)))
    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 <= -1.2e-39) {
		tmp = x + (y / (t / (t - z)));
	} else if (t <= 8.5e-37) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e-39:
		tmp = x + (y / (t / (t - z)))
	elif t <= 8.5e-37:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y / ((a / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e-39)
		tmp = Float64(x + Float64(y / Float64(t / Float64(t - z))));
	elseif (t <= 8.5e-37)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e-39)
		tmp = x + (y / (t / (t - z)));
	elseif (t <= 8.5e-37)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y / ((a / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e-39], N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-37], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.20000000000000008e-39

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 72.6%

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

      1. associate-*r/ 72.6%

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

      2. neg-mul-1 72.6%

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

      3. distribute-rgt-neg-in 72.6%

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

      4. associate-/l* 90.2%

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

      5. neg-sub0 90.2%

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

      6. associate--r- 90.2%

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

      7. neg-sub0 90.2%

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

   8. Simplified 90.2%

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

   9. Taylor expanded in y around 0 72.6%

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

       1. associate-/l* 90.2%

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

   11. Simplified 90.2%

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

   if -1.20000000000000008e-39 < t < 8.5000000000000007e-37

   1. Initial program 97.5%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 92.8%

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

      1. associate-*l/ 93.6%

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

      2. *-commutative 93.6%

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

   6. Simplified 93.6%

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

   if 8.5000000000000007e-37 < t

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-*r/ 100.0%

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

      3. 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. Taylor expanded in z around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. mul-1-neg 73.3%

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

      3. unsub-neg 73.3%

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

      4. associate-/l* 91.3%

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

      5. div-sub 91.3%

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

      6. sub-neg 91.3%

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

      7. *-inverses 91.3%

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

      8. metadata-eval 91.3%

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

   6. Simplified 91.3%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{t} + -1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-37}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]

Alternative 7: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-42} \lor \neg \left(t \leq 490\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.7e-42) (not (<= t 490.0))) (+ y x) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.7e-42) || !(t <= 490.0)) {
		tmp = y + x;
	} else {
		tmp = x + (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 ((t <= (-4.7d-42)) .or. (.not. (t <= 490.0d0))) then
        tmp = y + x
    else
        tmp = x + (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 ((t <= -4.7e-42) || !(t <= 490.0)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.7e-42) or not (t <= 490.0):
		tmp = y + x
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.7e-42) || !(t <= 490.0))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.7e-42) || ~((t <= 490.0)))
		tmp = y + x;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.7e-42], N[Not[LessEqual[t, 490.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.7000000000000001e-42 or 490 < t

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 99.9%

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

      3. 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. Taylor expanded in t around inf 77.3%

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

   if -4.7000000000000001e-42 < t < 490

   1. Initial program 97.6%

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

      1. +-commutative 97.6%

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

      2. associate-*r/ 95.0%

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

      3. fma-def 95.0%

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

   3. Simplified 95.0%

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

      1. fma-udef 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in t around 0 81.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-42} \lor \neg \left(t \leq 490\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 8: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 860:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e-40) (+ y x) (if (<= t 860.0) (+ x (/ y (/ a z))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e-40) {
		tmp = y + x;
	} else if (t <= 860.0) {
		tmp = x + (y / (a / z));
	} 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 <= (-2.6d-40)) then
        tmp = y + x
    else if (t <= 860.0d0) then
        tmp = x + (y / (a / z))
    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 <= -2.6e-40) {
		tmp = y + x;
	} else if (t <= 860.0) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e-40:
		tmp = y + x
	elif t <= 860.0:
		tmp = x + (y / (a / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e-40)
		tmp = Float64(y + x);
	elseif (t <= 860.0)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e-40)
		tmp = y + x;
	elseif (t <= 860.0)
		tmp = x + (y / (a / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e-40], N[(y + x), $MachinePrecision], If[LessEqual[t, 860.0], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6000000000000001e-40 or 860 < t

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 99.9%

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

      3. 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. Taylor expanded in t around inf 77.3%

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

   if -2.6000000000000001e-40 < t < 860

   1. Initial program 97.6%

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

      1. +-commutative 97.6%

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

      2. associate-*r/ 95.0%

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

      3. fma-def 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around 0 79.8%

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

      1. associate-/l* 81.3%

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

   6. Simplified 81.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 860:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

   1. associate-/l* 97.5%

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

3. Simplified 97.5%

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

4. Final simplification 97.5%

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

Alternative 10: 63.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-43}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 95:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e-43) (+ y x) (if (<= t 95.0) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e-43) {
		tmp = y + x;
	} else if (t <= 95.0) {
		tmp = x;
	} 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 <= (-4.5d-43)) then
        tmp = y + x
    else if (t <= 95.0d0) then
        tmp = x
    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 <= -4.5e-43) {
		tmp = y + x;
	} else if (t <= 95.0) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e-43:
		tmp = y + x
	elif t <= 95.0:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e-43)
		tmp = Float64(y + x);
	elseif (t <= 95.0)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e-43)
		tmp = y + x;
	elseif (t <= 95.0)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e-43], N[(y + x), $MachinePrecision], If[LessEqual[t, 95.0], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.50000000000000025e-43 or 95 < t

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-*r/ 99.9%

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

      3. 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. Taylor expanded in t around inf 77.3%

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

   if -4.50000000000000025e-43 < t < 95

   1. Initial program 97.6%

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

      1. +-commutative 97.6%

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

      2. associate-*r/ 95.0%

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

      3. fma-def 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around 0 52.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-43}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 95:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11: 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 88.9%

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

   1. +-commutative 88.9%

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

   2. associate-*r/ 97.6%

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

   3. fma-def 97.6%

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

3. Simplified 97.6%

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

4. Taylor expanded in y around 0 50.5%

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

5. Final simplification 50.5%

   \[\leadsto x \]

Developer target: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023181 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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