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

Percentage Accurate: 97.7% → 98.4%

Time: 11.7s

Alternatives: 10

Speedup: 0.4×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t + \frac{x}{\frac{y}{t \cdot \left(-1 + \frac{z}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x y) (- z t)))))
   (if (<= t_1 (- INFINITY)) (+ t (/ x (/ y (* t (+ -1.0 (/ z t)))))) t_1)))

C

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

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t + (x / (y / (t * (-1.0 + (z / t)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + ((x / y) * (z - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t + (x / (y / (t * (-1.0 + (z / t)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(Float64(x / y) * Float64(z - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t + Float64(x / Float64(y / Float64(t * Float64(-1.0 + Float64(z / t))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + ((x / y) * (z - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t + (x / (y / (t * (-1.0 + (z / t)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < -inf.0

   1. Initial program 90.0%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. --lowering--.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around inf

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

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

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. +-commutative N/A

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

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

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

      6. /-lowering-/.f64 100.0%

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

   7. Simplified 100.0%

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

   if -inf.0 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 98.0%

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

4. Final simplification 98.4%

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

Alternative 2: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x y) (- z t)))))
   (if (<= t_1 (- INFINITY)) (/ x (/ y (- z t))) t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x / (y / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x / (y / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + ((x / y) * (z - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x / (y / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(Float64(x / y) * Float64(z - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x / Float64(y / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + ((x / y) * (z - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x / (y / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < -inf.0

   1. Initial program 90.0%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 99.9%

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

   7. Simplified 99.9%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. --lowering--.f64 99.9%

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

   9. Applied egg-rr 99.9%

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

   if -inf.0 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 98.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + \frac{x}{y} \cdot \left(z - t\right) \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5000.0)
   (/ x (/ y (- z t)))
   (if (<= (/ x y) 5e-7) (+ t (* (/ x y) z)) (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5000.0) {
		tmp = x / (y / (z - t));
	} else if ((x / y) <= 5e-7) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = x * ((z - t) / 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 ((x / y) <= (-5000.0d0)) then
        tmp = x / (y / (z - t))
    else if ((x / y) <= 5d-7) then
        tmp = t + ((x / y) * z)
    else
        tmp = x * ((z - t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5000.0) {
		tmp = x / (y / (z - t));
	} else if ((x / y) <= 5e-7) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5000.0:
		tmp = x / (y / (z - t))
	elif (x / y) <= 5e-7:
		tmp = t + ((x / y) * z)
	else:
		tmp = x * ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5000.0)
		tmp = Float64(x / Float64(y / Float64(z - t)));
	elseif (Float64(x / y) <= 5e-7)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(x * Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5000.0)
		tmp = x / (y / (z - t));
	elseif ((x / y) <= 5e-7)
		tmp = t + ((x / y) * z);
	else
		tmp = x * ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5000.0], N[(x / N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-7], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5e3

   1. Initial program 94.5%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 94.4%

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

   7. Simplified 94.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. --lowering--.f64 95.9%

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

   9. Applied egg-rr 95.9%

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

   if -5e3 < (/.f64 x y) < 4.99999999999999977e-7

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 98.2%

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

   if 4.99999999999999977e-7 < (/.f64 x y)

   1. Initial program 94.3%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 88.1%

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

   7. Simplified 88.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 90.5%

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

   9. Applied egg-rr 90.5%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -5000.0)
     t_1
     (if (<= (/ x y) 5e-7) (+ t (* (/ x y) z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -5000.0) {
		tmp = t_1;
	} else if ((x / y) <= 5e-7) {
		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 = x * ((z - t) / y)
    if ((x / y) <= (-5000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 5d-7) 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 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -5000.0) {
		tmp = t_1;
	} else if ((x / y) <= 5e-7) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -5000.0:
		tmp = t_1
	elif (x / y) <= 5e-7:
		tmp = t + ((x / y) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -5000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-7)
		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 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -5000.0)
		tmp = t_1;
	elseif ((x / y) <= 5e-7)
		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[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-7], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e3 or 4.99999999999999977e-7 < (/.f64 x y)

   1. Initial program 94.4%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 91.4%

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

   7. Simplified 91.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 93.2%

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

   9. Applied egg-rr 93.2%

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

   if -5e3 < (/.f64 x y) < 4.99999999999999977e-7

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 98.2%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 20000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -2e-11)
     t_1
     (if (<= (/ x y) 20000000000000.0) (* t (- 1.0 (/ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -2e-11) {
		tmp = t_1;
	} else if ((x / y) <= 20000000000000.0) {
		tmp = t * (1.0 - (x / 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 = x * ((z - t) / y)
    if ((x / y) <= (-2d-11)) then
        tmp = t_1
    else if ((x / y) <= 20000000000000.0d0) then
        tmp = t * (1.0d0 - (x / 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 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -2e-11) {
		tmp = t_1;
	} else if ((x / y) <= 20000000000000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -2e-11:
		tmp = t_1
	elif (x / y) <= 20000000000000.0:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -2e-11)
		tmp = t_1;
	elseif (Float64(x / y) <= 20000000000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -2e-11)
		tmp = t_1;
	elseif ((x / y) <= 20000000000000.0)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e-11], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 20000000000000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999988e-11 or 2e13 < (/.f64 x y)

   1. Initial program 94.5%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 92.3%

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

   7. Simplified 92.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 93.7%

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

   9. Applied egg-rr 93.7%

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

   if -1.99999999999999988e-11 < (/.f64 x y) < 2e13

   1. Initial program 99.0%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in t around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

      5. /-lowering-/.f64 70.8%

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

   7. Simplified 70.8%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 20000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-55}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e-11)
   (* (/ x y) z)
   (if (<= (/ x y) 1e-55) t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e-11) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 1e-55) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	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 ((x / y) <= (-2d-11)) then
        tmp = (x / y) * z
    else if ((x / y) <= 1d-55) then
        tmp = t
    else
        tmp = z / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e-11) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 1e-55) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e-11:
		tmp = (x / y) * z
	elif (x / y) <= 1e-55:
		tmp = t
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e-11)
		tmp = Float64(Float64(x / y) * z);
	elseif (Float64(x / y) <= 1e-55)
		tmp = t;
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e-11)
		tmp = (x / y) * z;
	elseif ((x / y) <= 1e-55)
		tmp = t;
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e-11], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-55], t, N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.99999999999999988e-11

   1. Initial program 95.1%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around 0

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

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

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

      2. *-lowering-*.f64 66.1%

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

   7. Simplified 66.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. /-lowering-/.f64 67.1%

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

   9. Applied egg-rr 67.1%

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

   if -1.99999999999999988e-11 < (/.f64 x y) < 9.99999999999999995e-56

   1. Initial program 98.8%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 75.5%

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

   if 9.99999999999999995e-56 < (/.f64 x y)

   1. Initial program 95.2%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around 0

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

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

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

      2. *-lowering-*.f64 51.6%

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

   7. Simplified 51.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/r/ N/A

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

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

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

      5. /-lowering-/.f64 58.1%

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

   9. Applied egg-rr 58.1%

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

Alternative 7: 64.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-55}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= (/ x y) -2e-11) t_1 (if (<= (/ x y) 1e-55) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if ((x / y) <= -2e-11) {
		tmp = t_1;
	} else if ((x / y) <= 1e-55) {
		tmp = t;
	} 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 = (x / y) * z
    if ((x / y) <= (-2d-11)) then
        tmp = t_1
    else if ((x / y) <= 1d-55) then
        tmp = 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 t_1 = (x / y) * z;
	double tmp;
	if ((x / y) <= -2e-11) {
		tmp = t_1;
	} else if ((x / y) <= 1e-55) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if (x / y) <= -2e-11:
		tmp = t_1
	elif (x / y) <= 1e-55:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (Float64(x / y) <= -2e-11)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-55)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if ((x / y) <= -2e-11)
		tmp = t_1;
	elseif ((x / y) <= 1e-55)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e-11], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-55], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.99999999999999988e-11 or 9.99999999999999995e-56 < (/.f64 x y)

   1. Initial program 95.2%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in t around 0

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

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

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

      2. *-lowering-*.f64 58.8%

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

   7. Simplified 58.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. /-lowering-/.f64 62.4%

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

   9. Applied egg-rr 62.4%

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

   if -1.99999999999999988e-11 < (/.f64 x y) < 9.99999999999999995e-56

   1. Initial program 98.8%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 75.5%

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

Alternative 8: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= t -8.5e-11) t_1 (if (<= t 1.5e-129) (/ 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 (t <= -8.5e-11) {
		tmp = t_1;
	} else if (t <= 1.5e-129) {
		tmp = 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 (t <= (-8.5d-11)) then
        tmp = t_1
    else if (t <= 1.5d-129) then
        tmp = 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 (t <= -8.5e-11) {
		tmp = t_1;
	} else if (t <= 1.5e-129) {
		tmp = 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 t <= -8.5e-11:
		tmp = t_1
	elif t <= 1.5e-129:
		tmp = 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 (t <= -8.5e-11)
		tmp = t_1;
	elseif (t <= 1.5e-129)
		tmp = Float64(z / Float64(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 (t <= -8.5e-11)
		tmp = t_1;
	elseif (t <= 1.5e-129)
		tmp = 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[t, -8.5e-11], t$95$1, If[LessEqual[t, 1.5e-129], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000037e-11 or 1.4999999999999999e-129 < t

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in t around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

      5. /-lowering-/.f64 79.2%

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

   7. Simplified 79.2%

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

   if -8.50000000000000037e-11 < t < 1.4999999999999999e-129

   1. Initial program 92.0%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around 0

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

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

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

      2. *-lowering-*.f64 69.8%

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

   7. Simplified 69.8%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/r/ N/A

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

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

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

      5. /-lowering-/.f64 70.6%

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

   9. Applied egg-rr 70.6%

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

Alternative 9: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+131}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 2.5e+131) (+ t (/ (* x (- z t)) y)) (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2.5e+131) {
		tmp = t + ((x * (z - t)) / y);
	} else {
		tmp = t + ((x / y) * z);
	}
	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 (z <= 2.5d+131) then
        tmp = t + ((x * (z - t)) / y)
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2.5e+131) {
		tmp = t + ((x * (z - t)) / y);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 2.5e+131:
		tmp = t + ((x * (z - t)) / y)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2.5e+131)
		tmp = Float64(t + Float64(Float64(x * Float64(z - t)) / y));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 2.5e+131)
		tmp = t + ((x * (z - t)) / y);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 2.5e+131], N[(t + N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.49999999999999998e131

   1. Initial program 96.0%

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

      1. +-commutative N/A

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

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

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

      3. associate-*l/ N/A

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

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

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

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

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

      6. --lowering--.f64 94.2%

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

   3. Simplified 94.2%

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

   if 2.49999999999999998e131 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 99.9%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{+131}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.6% 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 96.5%

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

   1. +-commutative N/A

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

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

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

   3. associate-*l/ N/A

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

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

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

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

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

   6. --lowering--.f64 92.4%

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

3. Simplified 92.4%

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

5. Taylor expanded in x around 0

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

7. Simplified 31.7%

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

Developer Target 1: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} 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 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + 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 t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024158 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))

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