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

Percentage Accurate: 85.0% → 98.4%

Time: 10.3s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.1%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

   2. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - z}{a - z} \cdot \color{blue}{t}\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right)\right) \]

   7. --lowering--.f64 98.8%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right)\right) \]

4. Applied egg-rr 98.8%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

   7. --lowering--.f64 99.0%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

6. Applied egg-rr 99.0%

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

Alternative 2: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+15}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 0.006:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+124}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+15)
   (+ x t)
   (if (<= z 0.006)
     (+ x (/ t (/ a y)))
     (if (<= z 1.04e+124) (- x (* y (/ t z))) (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+15) {
		tmp = x + t;
	} else if (z <= 0.006) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.04e+124) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + 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 (z <= (-3d+15)) then
        tmp = x + t
    else if (z <= 0.006d0) then
        tmp = x + (t / (a / y))
    else if (z <= 1.04d+124) then
        tmp = x - (y * (t / z))
    else
        tmp = x + 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 (z <= -3e+15) {
		tmp = x + t;
	} else if (z <= 0.006) {
		tmp = x + (t / (a / y));
	} else if (z <= 1.04e+124) {
		tmp = x - (y * (t / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+15:
		tmp = x + t
	elif z <= 0.006:
		tmp = x + (t / (a / y))
	elif z <= 1.04e+124:
		tmp = x - (y * (t / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+15)
		tmp = Float64(x + t);
	elseif (z <= 0.006)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 1.04e+124)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+15)
		tmp = x + t;
	elseif (z <= 0.006)
		tmp = x + (t / (a / y));
	elseif (z <= 1.04e+124)
		tmp = x - (y * (t / z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+15], N[(x + t), $MachinePrecision], If[LessEqual[z, 0.006], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.04e+124], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e15 or 1.03999999999999994e124 < z

   1. Initial program 76.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 85.1%

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

   if -3e15 < z < 0.0060000000000000001

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), a\right)\right) \]

   5. Simplified 77.7%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{t}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{t}\right)\right) \]

      4. /-lowering-/.f64 79.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), t\right)\right) \]

   7. Applied egg-rr 79.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \frac{1}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{y}\right)}\right)\right) \]

      5. /-lowering-/.f64 80.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right)\right) \]

   9. Applied egg-rr 80.1%

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

   if 0.0060000000000000001 < z < 1.03999999999999994e124

   1. Initial program 96.4%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot \left(y - z\right)}{z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{y - z}{z}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y - z}{z}\right)}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{z}{z}\right)\right)}\right)\right)\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} + -1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(-1 + \color{blue}{\frac{y}{z}}\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(-1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right)\right) \]

      12. /-lowering-/.f64 83.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 83.9%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{z}\right)\right) \]

      2. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), z\right)\right) \]

   8. Simplified 74.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot t}{z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{t}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 77.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   10. Applied egg-rr 77.7%

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

Alternative 3: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (+ -1.0 (/ y z))))))
   (if (<= z -6.2e+36) t_1 (if (<= z 7.5e+71) (+ x (* y (/ t (- a z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (-1.0 + (y / z)));
	double tmp;
	if (z <= -6.2e+36) {
		tmp = t_1;
	} else if (z <= 7.5e+71) {
		tmp = x + (y * (t / (a - z)));
	} 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 - (t * ((-1.0d0) + (y / z)))
    if (z <= (-6.2d+36)) then
        tmp = t_1
    else if (z <= 7.5d+71) then
        tmp = x + (y * (t / (a - z)))
    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 - (t * (-1.0 + (y / z)));
	double tmp;
	if (z <= -6.2e+36) {
		tmp = t_1;
	} else if (z <= 7.5e+71) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (-1.0 + (y / z)))
	tmp = 0
	if z <= -6.2e+36:
		tmp = t_1
	elif z <= 7.5e+71:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(-1.0 + Float64(y / z))))
	tmp = 0.0
	if (z <= -6.2e+36)
		tmp = t_1;
	elseif (z <= 7.5e+71)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (-1.0 + (y / z)));
	tmp = 0.0;
	if (z <= -6.2e+36)
		tmp = t_1;
	elseif (z <= 7.5e+71)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+36], t$95$1, If[LessEqual[z, 7.5e+71], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999999e36 or 7.50000000000000007e71 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot \left(y - z\right)}{z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{y - z}{z}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y - z}{z}\right)}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{z}{z}\right)\right)}\right)\right)\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} + -1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(-1 + \color{blue}{\frac{y}{z}}\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(-1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right)\right) \]

      12. /-lowering-/.f64 94.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 94.7%

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

   if -6.1999999999999999e36 < z < 7.50000000000000007e71

   1. Initial program 96.5%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{a - z} \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{t}{a - z}\right), \color{blue}{\left(y - z\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(a - z\right)\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \left(y - z\right)\right)\right) \]

      6. --lowering--.f64 98.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \color{blue}{y}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 88.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+36}:\\ \;\;\;\;x - t \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+126}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+123}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+126)
   (+ x t)
   (if (<= z 5.3e+123) (+ x (* y (/ t (- a z)))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+126) {
		tmp = x + t;
	} else if (z <= 5.3e+123) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + 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 (z <= (-2.5d+126)) then
        tmp = x + t
    else if (z <= 5.3d+123) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + 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 (z <= -2.5e+126) {
		tmp = x + t;
	} else if (z <= 5.3e+123) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+126:
		tmp = x + t
	elif z <= 5.3e+123:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+126)
		tmp = Float64(x + t);
	elseif (z <= 5.3e+123)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+126)
		tmp = x + t;
	elseif (z <= 5.3e+123)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+126], N[(x + t), $MachinePrecision], If[LessEqual[z, 5.3e+123], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999989e126 or 5.3e123 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 86.8%

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

   if -2.49999999999999989e126 < z < 5.3e123

   1. Initial program 96.0%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{a - z} \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{t}{a - z}\right), \color{blue}{\left(y - z\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(a - z\right)\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \left(y - z\right)\right)\right) \]

      6. --lowering--.f64 98.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \color{blue}{y}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 87.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+126}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+123}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e+16) (+ x t) (if (<= z 7.5e-62) (+ x (/ t (/ a y))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+16) {
		tmp = x + t;
	} else if (z <= 7.5e-62) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + 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 (z <= (-1.55d+16)) then
        tmp = x + t
    else if (z <= 7.5d-62) then
        tmp = x + (t / (a / y))
    else
        tmp = x + 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 (z <= -1.55e+16) {
		tmp = x + t;
	} else if (z <= 7.5e-62) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.55e+16:
		tmp = x + t
	elif z <= 7.5e-62:
		tmp = x + (t / (a / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e+16)
		tmp = Float64(x + t);
	elseif (z <= 7.5e-62)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.55e+16)
		tmp = x + t;
	elseif (z <= 7.5e-62)
		tmp = x + (t / (a / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e+16], N[(x + t), $MachinePrecision], If[LessEqual[z, 7.5e-62], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e16 or 7.5000000000000003e-62 < z

   1. Initial program 81.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 78.5%

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

   if -1.55e16 < z < 7.5000000000000003e-62

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), a\right)\right) \]

   5. Simplified 79.4%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{t}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{t}\right)\right) \]

      4. /-lowering-/.f64 81.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), t\right)\right) \]

   7. Applied egg-rr 81.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \frac{1}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{\color{blue}{\frac{a}{y}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a}{y}\right)}\right)\right) \]

      5. /-lowering-/.f64 81.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right)\right) \]

   9. Applied egg-rr 81.9%

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

Alternative 6: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+17) (+ x t) (if (<= z 7.5e-62) (+ x (* t (/ y a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+17) {
		tmp = x + t;
	} else if (z <= 7.5e-62) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + 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 (z <= (-4.4d+17)) then
        tmp = x + t
    else if (z <= 7.5d-62) then
        tmp = x + (t * (y / a))
    else
        tmp = x + 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 (z <= -4.4e+17) {
		tmp = x + t;
	} else if (z <= 7.5e-62) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e+17:
		tmp = x + t
	elif z <= 7.5e-62:
		tmp = x + (t * (y / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+17)
		tmp = Float64(x + t);
	elseif (z <= 7.5e-62)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e+17)
		tmp = x + t;
	elseif (z <= 7.5e-62)
		tmp = x + (t * (y / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+17], N[(x + t), $MachinePrecision], If[LessEqual[z, 7.5e-62], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e17 or 7.5000000000000003e-62 < z

   1. Initial program 81.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 78.5%

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

   if -4.4e17 < z < 7.5000000000000003e-62

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), a\right)\right) \]

   5. Simplified 79.4%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{t}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{t}\right)\right) \]

      4. /-lowering-/.f64 81.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), t\right)\right) \]

   7. Applied egg-rr 81.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+16}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-113}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+16)
   (+ x t)
   (if (<= z 1.55e-113) (+ x (* y (/ t a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+16) {
		tmp = x + t;
	} else if (z <= 1.55e-113) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + 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 (z <= (-4.2d+16)) then
        tmp = x + t
    else if (z <= 1.55d-113) then
        tmp = x + (y * (t / a))
    else
        tmp = x + 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 (z <= -4.2e+16) {
		tmp = x + t;
	} else if (z <= 1.55e-113) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+16:
		tmp = x + t
	elif z <= 1.55e-113:
		tmp = x + (y * (t / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+16)
		tmp = Float64(x + t);
	elseif (z <= 1.55e-113)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+16)
		tmp = x + t;
	elseif (z <= 1.55e-113)
		tmp = x + (y * (t / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+16], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.55e-113], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e16 or 1.55000000000000006e-113 < z

   1. Initial program 82.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 77.8%

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

   if -4.2e16 < z < 1.55000000000000006e-113

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 80.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), a\right)\right) \]

   5. Simplified 80.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 82.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 82.3%

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

Alternative 8: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+185}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.95e+153) x (if (<= a 1.5e+185) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.95e+153) {
		tmp = x;
	} else if (a <= 1.5e+185) {
		tmp = x + t;
	} 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 <= (-1.95d+153)) then
        tmp = x
    else if (a <= 1.5d+185) then
        tmp = x + t
    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 <= -1.95e+153) {
		tmp = x;
	} else if (a <= 1.5e+185) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.95e+153:
		tmp = x
	elif a <= 1.5e+185:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.95e+153)
		tmp = x;
	elseif (a <= 1.5e+185)
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.95e+153)
		tmp = x;
	elseif (a <= 1.5e+185)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.95e+153], x, If[LessEqual[a, 1.5e+185], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.94999999999999992e153 or 1.49999999999999997e185 < a

   1. Initial program 89.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 73.5%

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

   if -1.94999999999999992e153 < a < 1.49999999999999997e185

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 66.4%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 62.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.35e+177) (* t (/ y (- a z))) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.35e+177) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + 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 (y <= (-1.35d+177)) then
        tmp = t * (y / (a - z))
    else
        tmp = x + 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 (y <= -1.35e+177) {
		tmp = t * (y / (a - z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.35e+177:
		tmp = t * (y / (a - z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.35e+177)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.35e+177)
		tmp = t * (y / (a - z));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.35e+177], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.34999999999999995e177

   1. Initial program 86.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - z}{a - z} \cdot \color{blue}{t}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right)\right) \]

      7. --lowering--.f64 96.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right)\right) \]

   4. Applied egg-rr 96.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{\color{blue}{\frac{a - z}{y - z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{a - z}{y - z}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(a - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      7. --lowering--.f64 96.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      4. --lowering--.f64 69.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   9. Simplified 69.0%

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

   if -1.34999999999999995e177 < y

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 65.9%

      \[\leadsto x + \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.1%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t \cdot \left(y - z\right)}{\color{blue}{a} - z}\right)\right) \]

   2. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(t \cdot \color{blue}{\frac{y - z}{a - z}}\right)\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - z}{a - z} \cdot \color{blue}{t}\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - z}{a - z}\right), \color{blue}{t}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(a - z\right)\right), t\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(a - z\right)\right), t\right)\right) \]

   7. --lowering--.f64 98.8%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(a, z\right)\right), t\right)\right) \]

4. Applied egg-rr 98.8%

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

5. Final simplification 98.8%

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

Alternative 11: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.1%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{a - z} \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{t}{a - z}\right), \color{blue}{\left(y - z\right)}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(a - z\right)\right), \left(\color{blue}{y} - z\right)\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \left(y - z\right)\right)\right) \]

   6. --lowering--.f64 97.1%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

4. Applied egg-rr 97.1%

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

5. Final simplification 97.1%

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

Alternative 12: 52.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 8e+179) x t))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 8e+179) {
		tmp = x;
	} else {
		tmp = 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 <= 8d+179) then
        tmp = x
    else
        tmp = 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 <= 8e+179) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 8e+179:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 8e+179)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 8e+179)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 8e+179], x, t]

Derivation

1. Split input into 2 regimes

2. if t < 7.99999999999999984e179

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 57.6%

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

   if 7.99999999999999984e179 < t

   1. Initial program 65.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 52.7%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   7. Step-by-step derivation

   8. Simplified 52.7%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 18.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.1%

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

3. Taylor expanded in z around inf

   \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
4. Step-by-step derivation

5. Simplified 62.2%

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

6. Taylor expanded in x around 0

   \[\leadsto \color{blue}{t} \]
7. Step-by-step derivation

8. Simplified 18.3%

   \[\leadsto \color{blue}{t} \]
9. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} 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) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    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) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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