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

Percentage Accurate: 85.1% → 97.9%

Time: 10.8s

Alternatives: 14

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: 85.1% 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: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.9%

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

   1. +-commutative N/A

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

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

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

   3. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

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

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

   7. --lowering--.f64 N/A

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

   8. /-lowering-/.f64 N/A

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

   9. --lowering--.f64 97.6%

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

4. Applied egg-rr 97.6%

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

   1. associate-/r/ N/A

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

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

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

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

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

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

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

   5. --lowering--.f64 98.4%

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

6. Applied egg-rr 98.4%

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

Alternative 2: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-193}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -4.6e-193)
     (+ t x)
     (if (<= z -4.5e-274)
       t_1
       (if (<= z 1.16e-169) x (if (<= z 7.2e-79) t_1 (+ t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -4.6e-193) {
		tmp = t + x;
	} else if (z <= -4.5e-274) {
		tmp = t_1;
	} else if (z <= 1.16e-169) {
		tmp = x;
	} else if (z <= 7.2e-79) {
		tmp = t_1;
	} else {
		tmp = t + 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (z <= (-4.6d-193)) then
        tmp = t + x
    else if (z <= (-4.5d-274)) then
        tmp = t_1
    else if (z <= 1.16d-169) then
        tmp = x
    else if (z <= 7.2d-79) then
        tmp = t_1
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -4.6e-193) {
		tmp = t + x;
	} else if (z <= -4.5e-274) {
		tmp = t_1;
	} else if (z <= 1.16e-169) {
		tmp = x;
	} else if (z <= 7.2e-79) {
		tmp = t_1;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -4.6e-193:
		tmp = t + x
	elif z <= -4.5e-274:
		tmp = t_1
	elif z <= 1.16e-169:
		tmp = x
	elif z <= 7.2e-79:
		tmp = t_1
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.6e-193)
		tmp = Float64(t + x);
	elseif (z <= -4.5e-274)
		tmp = t_1;
	elseif (z <= 1.16e-169)
		tmp = x;
	elseif (z <= 7.2e-79)
		tmp = t_1;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -4.6e-193)
		tmp = t + x;
	elseif (z <= -4.5e-274)
		tmp = t_1;
	elseif (z <= 1.16e-169)
		tmp = x;
	elseif (z <= 7.2e-79)
		tmp = t_1;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e-193], N[(t + x), $MachinePrecision], If[LessEqual[z, -4.5e-274], t$95$1, If[LessEqual[z, 1.16e-169], x, If[LessEqual[z, 7.2e-79], t$95$1, N[(t + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.60000000000000017e-193 or 7.2000000000000005e-79 < z

   1. Initial program 79.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 68.9%

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

   if -4.60000000000000017e-193 < z < -4.49999999999999991e-274 or 1.16e-169 < z < 7.2000000000000005e-79

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{t \cdot y}{a - z}} \]
   4. 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 77.9%

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

   5. Simplified 77.9%

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

   if -4.49999999999999991e-274 < z < 1.16e-169

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 75.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-193}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-274}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+161}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+112}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+161)
   (+ t x)
   (if (<= z -4.2e+55)
     (* (/ (- y z) (- a z)) t)
     (if (<= z 2.4e+112) (+ x (/ y (/ (- a z) t))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+161) {
		tmp = t + x;
	} else if (z <= -4.2e+55) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (z <= 2.4e+112) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+161)) then
        tmp = t + x
    else if (z <= (-4.2d+55)) then
        tmp = ((y - z) / (a - z)) * t
    else if (z <= 2.4d+112) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+161) {
		tmp = t + x;
	} else if (z <= -4.2e+55) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (z <= 2.4e+112) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+161:
		tmp = t + x
	elif z <= -4.2e+55:
		tmp = ((y - z) / (a - z)) * t
	elif z <= 2.4e+112:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+161)
		tmp = Float64(t + x);
	elseif (z <= -4.2e+55)
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	elseif (z <= 2.4e+112)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+161)
		tmp = t + x;
	elseif (z <= -4.2e+55)
		tmp = ((y - z) / (a - z)) * t;
	elseif (z <= 2.4e+112)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+161], N[(t + x), $MachinePrecision], If[LessEqual[z, -4.2e+55], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 2.4e+112], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000008e161 or 2.4e112 < z

   1. Initial program 62.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 90.1%

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

   if -1.45000000000000008e161 < z < -4.2000000000000001e55

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 58.6%

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

   5. Simplified 58.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 83.2%

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

   7. Applied egg-rr 83.2%

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

   if -4.2000000000000001e55 < z < 2.4e112

   1. Initial program 95.6%

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

      1. +-commutative N/A

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

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

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

      7. --lowering--.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 92.6%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+161}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+112}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+112}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+161)
   (+ t x)
   (if (<= z -4.2e+55)
     (* (/ (- y z) (- a z)) t)
     (if (<= z 1.8e+112) (+ x (* t (/ y (- a z)))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+161) {
		tmp = t + x;
	} else if (z <= -4.2e+55) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (z <= 1.8e+112) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d+161)) then
        tmp = t + x
    else if (z <= (-4.2d+55)) then
        tmp = ((y - z) / (a - z)) * t
    else if (z <= 1.8d+112) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+161) {
		tmp = t + x;
	} else if (z <= -4.2e+55) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (z <= 1.8e+112) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+161:
		tmp = t + x
	elif z <= -4.2e+55:
		tmp = ((y - z) / (a - z)) * t
	elif z <= 1.8e+112:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+161)
		tmp = Float64(t + x);
	elseif (z <= -4.2e+55)
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	elseif (z <= 1.8e+112)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+161)
		tmp = t + x;
	elseif (z <= -4.2e+55)
		tmp = ((y - z) / (a - z)) * t;
	elseif (z <= 1.8e+112)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+161], N[(t + x), $MachinePrecision], If[LessEqual[z, -4.2e+55], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1.8e+112], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3499999999999999e161 or 1.8e112 < z

   1. Initial program 62.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 90.1%

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

   if -1.3499999999999999e161 < z < -4.2000000000000001e55

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 58.6%

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

   5. Simplified 58.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 83.2%

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

   7. Applied egg-rr 83.2%

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

   if -4.2000000000000001e55 < z < 1.8e112

   1. Initial program 95.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 91.3%

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

   5. Simplified 91.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+112}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+161)
   (+ t x)
   (if (<= z -1.2e+48)
     (* (/ (- y z) (- a z)) t)
     (if (<= z 2.4e-14) (+ x (/ y (/ a t))) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+161) {
		tmp = t + x;
	} else if (z <= -1.2e+48) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (z <= 2.4e-14) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.35d+161)) then
        tmp = t + x
    else if (z <= (-1.2d+48)) then
        tmp = ((y - z) / (a - z)) * t
    else if (z <= 2.4d-14) then
        tmp = x + (y / (a / t))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+161) {
		tmp = t + x;
	} else if (z <= -1.2e+48) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (z <= 2.4e-14) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+161:
		tmp = t + x
	elif z <= -1.2e+48:
		tmp = ((y - z) / (a - z)) * t
	elif z <= 2.4e-14:
		tmp = x + (y / (a / t))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+161)
		tmp = Float64(t + x);
	elseif (z <= -1.2e+48)
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	elseif (z <= 2.4e-14)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e+161)
		tmp = t + x;
	elseif (z <= -1.2e+48)
		tmp = ((y - z) / (a - z)) * t;
	elseif (z <= 2.4e-14)
		tmp = x + (y / (a / t));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+161], N[(t + x), $MachinePrecision], If[LessEqual[z, -1.2e+48], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 2.4e-14], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3499999999999999e161 or 2.4e-14 < z

   1. Initial program 70.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 83.5%

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

   if -1.3499999999999999e161 < z < -1.2000000000000001e48

   1. Initial program 78.1%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 59.8%

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

   5. Simplified 59.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 81.6%

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

   7. Applied egg-rr 81.6%

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

   if -1.2000000000000001e48 < z < 2.4e-14

   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 77.3%

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

   5. Simplified 77.3%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   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 79.6%

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

   7. Applied egg-rr 79.6%

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

      1. +-commutative N/A

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

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

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

      3. clear-num N/A

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

      4. div-inv N/A

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

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

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

      6. /-lowering-/.f64 80.4%

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

   9. Applied egg-rr 80.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ (- a z) t)))))
   (if (<= y -1.25e-13) t_1 (if (<= y 5e+39) (+ x (* t (/ z (- z a)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / ((a - z) / t));
	double tmp;
	if (y <= -1.25e-13) {
		tmp = t_1;
	} else if (y <= 5e+39) {
		tmp = x + (t * (z / (z - a)));
	} 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 / ((a - z) / t))
    if (y <= (-1.25d-13)) then
        tmp = t_1
    else if (y <= 5d+39) then
        tmp = x + (t * (z / (z - a)))
    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 / ((a - z) / t));
	double tmp;
	if (y <= -1.25e-13) {
		tmp = t_1;
	} else if (y <= 5e+39) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / ((a - z) / t))
	tmp = 0
	if y <= -1.25e-13:
		tmp = t_1
	elif y <= 5e+39:
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (y <= -1.25e-13)
		tmp = t_1;
	elseif (y <= 5e+39)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / ((a - z) / t));
	tmp = 0.0;
	if (y <= -1.25e-13)
		tmp = t_1;
	elseif (y <= 5e+39)
		tmp = x + (t * (z / (z - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e-13], t$95$1, If[LessEqual[y, 5e+39], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999997e-13 or 5.00000000000000015e39 < y

   1. Initial program 85.8%

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

      1. +-commutative N/A

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

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

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

      7. --lowering--.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 90.7%

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

   if -1.24999999999999997e-13 < y < 5.00000000000000015e39

   1. Initial program 81.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 75.8%

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

   5. Simplified 75.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 93.9%

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

   7. Applied egg-rr 93.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (- 1.0 (/ y z))))))
   (if (<= z -1.02e+69)
     t_1
     (if (<= z 1.25e-8) (+ x (/ y (/ (- a z) t))) 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 <= -1.02e+69) {
		tmp = t_1;
	} else if (z <= 1.25e-8) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (1.0d0 - (y / z)))
    if (z <= (-1.02d+69)) then
        tmp = t_1
    else if (z <= 1.25d-8) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (1.0 - (y / z)));
	double tmp;
	if (z <= -1.02e+69) {
		tmp = t_1;
	} else if (z <= 1.25e-8) {
		tmp = x + (y / ((a - z) / t));
	} 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 <= -1.02e+69:
		tmp = t_1
	elif z <= 1.25e-8:
		tmp = x + (y / ((a - z) / t))
	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 <= -1.02e+69)
		tmp = t_1;
	elseif (z <= 1.25e-8)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	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 <= -1.02e+69)
		tmp = t_1;
	elseif (z <= 1.25e-8)
		tmp = x + (y / ((a - z) / t));
	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, -1.02e+69], t$95$1, If[LessEqual[z, 1.25e-8], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e69 or 1.2499999999999999e-8 < z

   1. Initial program 72.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 86.5%

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

   5. Simplified 86.5%

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

   if -1.02e69 < z < 1.2499999999999999e-8

   1. Initial program 94.9%

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

      1. +-commutative N/A

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

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

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

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

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

      7. --lowering--.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 94.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+69}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+77) (+ t x) (if (<= z 1.5e-14) (+ x (/ y (/ a t))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+77) {
		tmp = t + x;
	} else if (z <= 1.5e-14) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.2d+77)) then
        tmp = t + x
    else if (z <= 1.5d-14) then
        tmp = x + (y / (a / t))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+77) {
		tmp = t + x;
	} else if (z <= 1.5e-14) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+77:
		tmp = t + x
	elif z <= 1.5e-14:
		tmp = x + (y / (a / t))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+77)
		tmp = Float64(t + x);
	elseif (z <= 1.5e-14)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+77)
		tmp = t + x;
	elseif (z <= 1.5e-14)
		tmp = x + (y / (a / t));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+77], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.5e-14], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000002e77 or 1.4999999999999999e-14 < z

   1. Initial program 70.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 80.3%

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

   if -8.2000000000000002e77 < z < 1.4999999999999999e-14

   1. Initial program 95.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 74.7%

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

   5. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   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 77.5%

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

   7. Applied egg-rr 77.5%

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

      1. +-commutative N/A

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

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

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

      3. clear-num N/A

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

      4. div-inv N/A

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

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

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

      6. /-lowering-/.f64 78.2%

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

   9. Applied egg-rr 78.2%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+84}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+84) (+ t x) (if (<= z 6.5e-14) (+ x (* y (/ t a))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+84) {
		tmp = t + x;
	} else if (z <= 6.5e-14) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+84)) then
        tmp = t + x
    else if (z <= 6.5d-14) then
        tmp = x + (y * (t / a))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+84) {
		tmp = t + x;
	} else if (z <= 6.5e-14) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+84:
		tmp = t + x
	elif z <= 6.5e-14:
		tmp = x + (y * (t / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+84)
		tmp = Float64(t + x);
	elseif (z <= 6.5e-14)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+84)
		tmp = t + x;
	elseif (z <= 6.5e-14)
		tmp = x + (y * (t / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+84], N[(t + x), $MachinePrecision], If[LessEqual[z, 6.5e-14], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.44999999999999994e84 or 6.5000000000000001e-14 < z

   1. Initial program 70.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 80.3%

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

   if -1.44999999999999994e84 < z < 6.5000000000000001e-14

   1. Initial program 95.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 74.7%

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

   5. Simplified 74.7%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   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 77.5%

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

   7. Applied egg-rr 77.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+84}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+199}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= t -1.4e+141) t_1 (if (<= t 1.45e+199) (+ t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (t <= -1.4e+141) {
		tmp = t_1;
	} else if (t <= 1.45e+199) {
		tmp = t + x;
	} 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 = t * (1.0d0 - (y / z))
    if (t <= (-1.4d+141)) then
        tmp = t_1
    else if (t <= 1.45d+199) then
        tmp = t + x
    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 = t * (1.0 - (y / z));
	double tmp;
	if (t <= -1.4e+141) {
		tmp = t_1;
	} else if (t <= 1.45e+199) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if t <= -1.4e+141:
		tmp = t_1
	elif t <= 1.45e+199:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (t <= -1.4e+141)
		tmp = t_1;
	elseif (t <= 1.45e+199)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (t <= -1.4e+141)
		tmp = t_1;
	elseif (t <= 1.45e+199)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+141], t$95$1, If[LessEqual[t, 1.45e+199], N[(t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.39999999999999996e141 or 1.4499999999999999e199 < t

   1. Initial program 57.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(t \cdot \left(\frac{y}{z} - 1\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. sub-neg N/A

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

      12. --lowering--.f64 N/A

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

      13. /-lowering-/.f64 62.7%

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

   8. Simplified 62.7%

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

   if -1.39999999999999996e141 < t < 1.4499999999999999e199

   1. Initial program 91.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 68.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+199}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+60}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.7e+60) (+ t x) (if (<= z 8.5e-15) x (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e+60) {
		tmp = t + x;
	} else if (z <= 8.5e-15) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.7d+60)) then
        tmp = t + x
    else if (z <= 8.5d-15) then
        tmp = x
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e+60) {
		tmp = t + x;
	} else if (z <= 8.5e-15) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.7e+60:
		tmp = t + x
	elif z <= 8.5e-15:
		tmp = x
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.7e+60)
		tmp = Float64(t + x);
	elseif (z <= 8.5e-15)
		tmp = x;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.7e+60)
		tmp = t + x;
	elseif (z <= 8.5e-15)
		tmp = x;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.7e+60], N[(t + x), $MachinePrecision], If[LessEqual[z, 8.5e-15], x, N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999988e60 or 8.50000000000000007e-15 < z

   1. Initial program 71.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 78.8%

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

   if -3.69999999999999988e60 < z < 8.50000000000000007e-15

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 53.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+60}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+141}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+159}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.55e+141) t (if (<= t 4.1e+159) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.55e+141) {
		tmp = t;
	} else if (t <= 4.1e+159) {
		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 <= (-2.55d+141)) then
        tmp = t
    else if (t <= 4.1d+159) 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 <= -2.55e+141) {
		tmp = t;
	} else if (t <= 4.1e+159) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.55e+141:
		tmp = t
	elif t <= 4.1e+159:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.55e+141)
		tmp = t;
	elseif (t <= 4.1e+159)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.55e+141)
		tmp = t;
	elseif (t <= 4.1e+159)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.55e+141], t, If[LessEqual[t, 4.1e+159], x, t]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5499999999999999e141 or 4.10000000000000014e159 < t

   1. Initial program 55.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 41.8%

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

   6. Taylor expanded in x around 0

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

   8. Simplified 33.0%

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

   if -2.5499999999999999e141 < t < 4.10000000000000014e159

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 64.3%

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

Alternative 13: 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 83.9%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
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 97.9%

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

4. Applied egg-rr 97.9%

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

5. Final simplification 97.9%

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

Alternative 14: 19.2% 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 83.9%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
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 61.3%

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

6. Taylor expanded in x around 0

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

8. Simplified 18.0%

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

Developer Target 1: 99.1% 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 2024138 
(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))))