Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 97.0% → 97.1%

Time: 9.9s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 97.5%

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

4. Applied egg-rr 97.5%

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

Alternative 2: 89.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+225}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+156}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e+225)
   t
   (if (<= y 3.05e+156) (* (- x y) (/ t (- z y))) (* t (- 1.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+225) {
		tmp = t;
	} else if (y <= 3.05e+156) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d+225)) then
        tmp = t
    else if (y <= 3.05d+156) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+225) {
		tmp = t;
	} else if (y <= 3.05e+156) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e+225:
		tmp = t
	elif y <= 3.05e+156:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e+225)
		tmp = t;
	elseif (y <= 3.05e+156)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e+225)
		tmp = t;
	elseif (y <= 3.05e+156)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e+225], t, If[LessEqual[y, 3.05e+156], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999999e225

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 100.0%

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

   if -2.4999999999999999e225 < y < 3.0500000000000001e156

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 91.3%

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

   4. Applied egg-rr 91.3%

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

   if 3.0500000000000001e156 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{z}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. associate-*r/ N/A

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

      6. distribute-lft-out-- N/A

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

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

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

      8. cancel-sign-sub-inv N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

      14. --lowering--.f64 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(1 - \frac{x}{y}\right)}, t\right) \]
   7. Step-by-step derivation

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

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

      2. /-lowering-/.f64 97.3%

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

   8. Simplified 97.3%

      \[\leadsto \color{blue}{\left(1 - \frac{x}{y}\right)} \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+225}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+156}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-60}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -5.8e-28) t_1 (if (<= y 5e-60) (/ t (/ (- z y) x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -5.8e-28) {
		tmp = t_1;
	} else if (y <= 5e-60) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-5.8d-28)) then
        tmp = t_1
    else if (y <= 5d-60) then
        tmp = t / ((z - y) / 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 t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -5.8e-28) {
		tmp = t_1;
	} else if (y <= 5e-60) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -5.8e-28:
		tmp = t_1
	elif y <= 5e-60:
		tmp = t / ((z - y) / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -5.8e-28)
		tmp = t_1;
	elseif (y <= 5e-60)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -5.8e-28)
		tmp = t_1;
	elseif (y <= 5e-60)
		tmp = t / ((z - y) / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e-28], t$95$1, If[LessEqual[y, 5e-60], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000026e-28 or 5.0000000000000001e-60 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{z}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. associate-*r/ N/A

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

      6. distribute-lft-out-- N/A

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

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

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

      8. cancel-sign-sub-inv N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

      14. --lowering--.f64 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(1 - \frac{x}{y}\right)}, t\right) \]
   7. Step-by-step derivation

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

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

      2. /-lowering-/.f64 77.1%

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

   8. Simplified 77.1%

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

   if -5.80000000000000026e-28 < y < 5.0000000000000001e-60

   1. Initial program 93.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 94.1%

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

   4. Applied egg-rr 94.1%

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

   5. Taylor expanded in x around inf

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

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

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

      2. --lowering--.f64 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-60}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.3e-32) t_1 (if (<= y 6.6e+39) (* t (/ (- x y) z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.3e-32) {
		tmp = t_1;
	} else if (y <= 6.6e+39) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-1.3d-32)) then
        tmp = t_1
    else if (y <= 6.6d+39) then
        tmp = t * ((x - y) / 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 t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.3e-32) {
		tmp = t_1;
	} else if (y <= 6.6e+39) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.3e-32:
		tmp = t_1
	elif y <= 6.6e+39:
		tmp = t * ((x - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.3e-32)
		tmp = t_1;
	elseif (y <= 6.6e+39)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.3e-32)
		tmp = t_1;
	elseif (y <= 6.6e+39)
		tmp = t * ((x - y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e-32], t$95$1, If[LessEqual[y, 6.6e+39], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2999999999999999e-32 or 6.60000000000000042e39 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{z}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. associate-*r/ N/A

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

      6. distribute-lft-out-- N/A

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

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

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

      8. cancel-sign-sub-inv N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

      14. --lowering--.f64 81.9%

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

   5. Simplified 81.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(1 - \frac{x}{y}\right)}, t\right) \]
   7. Step-by-step derivation

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

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

      2. /-lowering-/.f64 82.2%

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

   8. Simplified 82.2%

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

   if -1.2999999999999999e-32 < y < 6.60000000000000042e39

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 73.0%

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

   5. Simplified 73.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -3.2e-27) t_1 (if (<= y 1.2e-57) (* t (/ x (- z y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -3.2e-27) {
		tmp = t_1;
	} else if (y <= 1.2e-57) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-3.2d-27)) then
        tmp = t_1
    else if (y <= 1.2d-57) then
        tmp = t * (x / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -3.2e-27) {
		tmp = t_1;
	} else if (y <= 1.2e-57) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -3.2e-27:
		tmp = t_1
	elif y <= 1.2e-57:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -3.2e-27)
		tmp = t_1;
	elseif (y <= 1.2e-57)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -3.2e-27)
		tmp = t_1;
	elseif (y <= 1.2e-57)
		tmp = t * (x / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e-27], t$95$1, If[LessEqual[y, 1.2e-57], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999991e-27 or 1.20000000000000003e-57 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{z}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. associate-*r/ N/A

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

      6. distribute-lft-out-- N/A

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

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

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

      8. cancel-sign-sub-inv N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

      14. --lowering--.f64 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(1 - \frac{x}{y}\right)}, t\right) \]
   7. Step-by-step derivation

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

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

      2. /-lowering-/.f64 77.1%

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

   8. Simplified 77.1%

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

   if -3.19999999999999991e-27 < y < 1.20000000000000003e-57

   1. Initial program 93.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

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

      2. --lowering--.f64 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -5e-33) t_1 (if (<= y 1.55e-63) (/ t (/ z x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -5e-33) {
		tmp = t_1;
	} else if (y <= 1.55e-63) {
		tmp = t / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-5d-33)) then
        tmp = t_1
    else if (y <= 1.55d-63) then
        tmp = t / (z / 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 t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -5e-33) {
		tmp = t_1;
	} else if (y <= 1.55e-63) {
		tmp = t / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -5e-33:
		tmp = t_1
	elif y <= 1.55e-63:
		tmp = t / (z / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -5e-33)
		tmp = t_1;
	elseif (y <= 1.55e-63)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -5e-33)
		tmp = t_1;
	elseif (y <= 1.55e-63)
		tmp = t / (z / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-33], t$95$1, If[LessEqual[y, 1.55e-63], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000028e-33 or 1.54999999999999992e-63 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{z}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

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

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

      5. associate-*r/ N/A

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

      6. distribute-lft-out-- N/A

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

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

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

      8. cancel-sign-sub-inv N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

      14. --lowering--.f64 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(1 - \frac{x}{y}\right)}, t\right) \]
   7. Step-by-step derivation

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

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

      2. /-lowering-/.f64 77.2%

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

   8. Simplified 77.2%

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

   if -5.00000000000000028e-33 < y < 1.54999999999999992e-63

   1. Initial program 93.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 66.4%

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

   5. Simplified 66.4%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 66.4%

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

   7. Applied egg-rr 66.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.8e-32) t (if (<= y 3.9e-55) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.8e-32) {
		tmp = t;
	} else if (y <= 3.9e-55) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.8d-32)) then
        tmp = t
    else if (y <= 3.9d-55) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.8e-32) {
		tmp = t;
	} else if (y <= 3.9e-55) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.8e-32:
		tmp = t
	elif y <= 3.9e-55:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.8e-32)
		tmp = t;
	elseif (y <= 3.9e-55)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.8e-32)
		tmp = t;
	elseif (y <= 3.9e-55)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.8e-32], t, If[LessEqual[y, 3.9e-55], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.8000000000000003e-32 or 3.9e-55 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 62.0%

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

   if -7.8000000000000003e-32 < y < 3.9e-55

   1. Initial program 93.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 65.8%

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

   5. Simplified 65.8%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 65.8%

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

   7. Applied egg-rr 65.8%

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

Alternative 8: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e-31) t (if (<= y 1.22e-52) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-31) {
		tmp = t;
	} else if (y <= 1.22e-52) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.8d-31)) then
        tmp = t
    else if (y <= 1.22d-52) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-31) {
		tmp = t;
	} else if (y <= 1.22e-52) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e-31:
		tmp = t
	elif y <= 1.22e-52:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e-31)
		tmp = t;
	elseif (y <= 1.22e-52)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e-31)
		tmp = t;
	elseif (y <= 1.22e-52)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e-31], t, If[LessEqual[y, 1.22e-52], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999999e-31 or 1.22e-52 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 62.0%

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

   if -2.7999999999999999e-31 < y < 1.22e-52

   1. Initial program 93.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 65.8%

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

   5. Simplified 65.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-33) t (if (<= y 3.3e-55) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-33) {
		tmp = t;
	} else if (y <= 3.3e-55) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.5d-33)) then
        tmp = t
    else if (y <= 3.3d-55) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-33) {
		tmp = t;
	} else if (y <= 3.3e-55) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-33:
		tmp = t
	elif y <= 3.3e-55:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-33)
		tmp = t;
	elseif (y <= 3.3e-55)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e-33)
		tmp = t;
	elseif (y <= 3.3e-55)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-33], t, If[LessEqual[y, 3.3e-55], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e-33 or 3.2999999999999999e-55 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 62.0%

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

   if -5.5e-33 < y < 3.2999999999999999e-55

   1. Initial program 93.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot t}{z} \]

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 63.0%

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

   5. Simplified 63.0%

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

Alternative 10: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Final simplification 97.3%

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

Alternative 11: 35.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

5. Simplified 39.7%

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

Developer Target 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

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