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

Percentage Accurate: 97.6% → 97.7%

Time: 7.5s

Alternatives: 10

Speedup: 1.1×

• 24.8% 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: 97.6% 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: 97.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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 - t) / (y / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. lift--.f64 N/A

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

   2. associate-*l/ N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. associate-/r/ N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 98.1

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

4. Applied rewrites 98.1%

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

5. Final simplification 98.1%

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

Alternative 2: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) (- INFINITY))
   (* z (/ x y))
   (if (<= (/ x y) -2e+44)
     (* (/ x y) (- t))
     (if (<= (/ x y) 2e+31) (fma (/ x y) z t) (/ (* t x) (- y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -((double) INFINITY)) {
		tmp = z * (x / y);
	} else if ((x / y) <= -2e+44) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 2e+31) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = (t * x) / -y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= Float64(-Inf))
		tmp = Float64(z * Float64(x / y));
	elseif (Float64(x / y) <= -2e+44)
		tmp = Float64(Float64(x / y) * Float64(-t));
	elseif (Float64(x / y) <= 2e+31)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = Float64(Float64(t * x) / Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], (-Infinity)], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2e+44], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+31], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -inf.0

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 75.7

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

   5. Applied rewrites 75.7%

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

      1. *-rgt-identity N/A

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

      2. times-frac N/A

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

      3. lift-/.f64 N/A

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

      4. /-rgt-identity N/A

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

      5. lower-*.f64 87.3

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

   7. Applied rewrites 87.3%

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

   if -inf.0 < (/.f64 x y) < -2.0000000000000002e44

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 63.1

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

   8. Applied rewrites 63.1%

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

      1. lift-neg.f64 N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 65.6

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

   10. Applied rewrites 65.6%

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

   if -2.0000000000000002e44 < (/.f64 x y) < 1.9999999999999999e31

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 92.7

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

   5. Applied rewrites 92.7%

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

      1. associate-*l/ N/A

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

      2. lift-/.f64 N/A

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

      3. lower-fma.f64 93.9

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

   7. Applied rewrites 93.9%

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

   if 1.9999999999999999e31 < (/.f64 x y)

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 69.0

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

   5. Applied rewrites 69.0%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 69.0

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

   8. Applied rewrites 69.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- t))))
   (if (<= (/ x y) (- INFINITY))
     (* z (/ x y))
     (if (<= (/ x y) -2e+44)
       t_1
       (if (<= (/ x y) 2e+31) (fma (/ x y) z t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -((double) INFINITY)) {
		tmp = z * (x / y);
	} else if ((x / y) <= -2e+44) {
		tmp = t_1;
	} else if ((x / y) <= 2e+31) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(-t))
	tmp = 0.0
	if (Float64(x / y) <= Float64(-Inf))
		tmp = Float64(z * Float64(x / y));
	elseif (Float64(x / y) <= -2e+44)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e+31)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], (-Infinity)], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2e+44], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e+31], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -inf.0

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 75.7

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

   5. Applied rewrites 75.7%

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

      1. *-rgt-identity N/A

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

      2. times-frac N/A

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

      3. lift-/.f64 N/A

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

      4. /-rgt-identity N/A

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

      5. lower-*.f64 87.3

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

   7. Applied rewrites 87.3%

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

   if -inf.0 < (/.f64 x y) < -2.0000000000000002e44 or 1.9999999999999999e31 < (/.f64 x y)

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 66.4

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

   8. Applied rewrites 66.4%

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

      1. lift-neg.f64 N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 66.5

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

   10. Applied rewrites 66.5%

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

   if -2.0000000000000002e44 < (/.f64 x y) < 1.9999999999999999e31

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 92.7

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

   5. Applied rewrites 92.7%

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

      1. associate-*l/ N/A

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

      2. lift-/.f64 N/A

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

      3. lower-fma.f64 93.9

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

   7. Applied rewrites 93.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, z, t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- y)))))
   (if (<= (/ x y) (- INFINITY))
     (* z (/ x y))
     (if (<= (/ x y) -2e+44)
       t_1
       (if (<= (/ x y) 2e+55) (fma (/ x y) z t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / -y);
	double tmp;
	if ((x / y) <= -((double) INFINITY)) {
		tmp = z * (x / y);
	} else if ((x / y) <= -2e+44) {
		tmp = t_1;
	} else if ((x / y) <= 2e+55) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(-y)))
	tmp = 0.0
	if (Float64(x / y) <= Float64(-Inf))
		tmp = Float64(z * Float64(x / y));
	elseif (Float64(x / y) <= -2e+44)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e+55)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], (-Infinity)], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2e+44], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e+55], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -inf.0

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 75.7

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

   5. Applied rewrites 75.7%

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

      1. *-rgt-identity N/A

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

      2. times-frac N/A

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

      3. lift-/.f64 N/A

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

      4. /-rgt-identity N/A

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

      5. lower-*.f64 87.3

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

   7. Applied rewrites 87.3%

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

   if -inf.0 < (/.f64 x y) < -2.0000000000000002e44 or 2.00000000000000002e55 < (/.f64 x y)

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 66.3

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

   5. Applied rewrites 66.3%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 66.3

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

   8. Applied rewrites 66.3%

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

      1. lift-neg.f64 N/A

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

      2. associate-*l/ N/A

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

      3. lift-/.f64 N/A

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

      4. lower-*.f64 64.2

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

   10. Applied rewrites 64.2%

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

   if -2.0000000000000002e44 < (/.f64 x y) < 2.00000000000000002e55

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 91.5

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

   5. Applied rewrites 91.5%

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

      1. associate-*l/ N/A

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

      2. lift-/.f64 N/A

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

      3. lower-fma.f64 92.7

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

   7. Applied rewrites 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, z, t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) x) y)))
   (if (<= (/ x y) -100000.0)
     t_1
     (if (<= (/ x y) 2e+20) (fma (/ x y) z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) * x) / y;
	double tmp;
	if ((x / y) <= -100000.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e+20) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - t) * x) / y)
	tmp = 0.0
	if (Float64(x / y) <= -100000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e+20)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -100000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e+20], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e5 or 2e20 < (/.f64 x y)

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 95.6

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

   5. Applied rewrites 95.6%

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

   if -1e5 < (/.f64 x y) < 2e20

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 94.2

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

   5. Applied rewrites 94.2%

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

      1. associate-*l/ N/A

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

      2. lift-/.f64 N/A

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

      3. lower-fma.f64 95.4

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

   7. Applied rewrites 95.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, z, t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{t \cdot x}{y}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-37}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, z, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (/ (* t x) y))))
   (if (<= t -2.15e+15) t_1 (if (<= t 4e-37) (fma (/ x y) z t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - ((t * x) / y);
	double tmp;
	if (t <= -2.15e+15) {
		tmp = t_1;
	} else if (t <= 4e-37) {
		tmp = fma((x / y), z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(Float64(t * x) / y))
	tmp = 0.0
	if (t <= -2.15e+15)
		tmp = t_1;
	elseif (t <= 4e-37)
		tmp = fma(Float64(x / y), z, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e+15], t$95$1, If[LessEqual[t, 4e-37], N[(N[(x / y), $MachinePrecision] * z + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.15e15 or 4.00000000000000027e-37 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 89.7

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

   5. Applied rewrites 89.7%

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

   if -2.15e15 < t < 4.00000000000000027e-37

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 87.6

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

   5. Applied rewrites 87.6%

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

      1. associate-*l/ N/A

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

      2. lift-/.f64 N/A

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

      3. lower-fma.f64 90.5

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

   7. Applied rewrites 90.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, z, t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Final simplification 98.0%

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

Alternative 8: 97.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{y}, z - t, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lower-fma.f64 98.0

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

4. Applied rewrites 98.0%

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

Alternative 9: 76.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{y}, z, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 73.0

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

5. Applied rewrites 73.0%

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

   1. associate-*l/ N/A

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

   2. lift-/.f64 N/A

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

   3. lower-fma.f64 76.1

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

7. Applied rewrites 76.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, z, t\right)} \]
8. Add Preprocessing

Alternative 10: 40.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 37.7

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

5. Applied rewrites 37.7%

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

   1. *-rgt-identity N/A

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

   2. times-frac N/A

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

   3. lift-/.f64 N/A

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

   4. /-rgt-identity N/A

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

   5. lower-*.f64 40.8

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

7. Applied rewrites 40.8%

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

8. Final simplification 40.8%

   \[\leadsto z \cdot \frac{x}{y} \]
9. Add Preprocessing

Developer Target 1: 97.5% accurate, 0.7× 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 2024219 
(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))