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

Percentage Accurate: 97.1% → 97.0%

Time: 8.1s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. *-commutative 98.3%

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

   2. clear-num 98.3%

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

   3. un-div-inv 98.4%

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

4. Applied egg-rr 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 3: 50.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in x around inf 47.2%

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

   1. *-commutative 47.2%

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

   2. associate-*r/ 47.7%

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

5. Simplified 47.7%

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

6. Final simplification 47.7%

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

Alternative 4: 53.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in x around inf 50.8%

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

4. Final simplification 50.8%

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

Alternative 5: 54.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{t}{1 - \frac{z}{y}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ t (- 1.0 (/ z y))))

C

double code(double x, double y, double z, double t) {
	return t / (1.0 - (z / y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t / (1.0d0 - (z / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t / (1.0 - (z / y));
}

Python

def code(x, y, z, t):
	return t / (1.0 - (z / y))

Julia

function code(x, y, z, t)
	return Float64(t / Float64(1.0 - Float64(z / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t / (1.0 - (z / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in x around 0 49.0%

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

   1. mul-1-neg 49.0%

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

   2. associate-/l* 58.7%

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

   3. distribute-neg-frac 58.7%

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

   4. div-sub 58.7%

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

   5. *-inverses 58.7%

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

5. Simplified 58.7%

   \[\leadsto \color{blue}{\frac{-t}{\frac{z}{y} - 1}} \]
6. Step-by-step derivation

   1. frac-2neg 58.7%

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

   2. div-inv 58.7%

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

   3. remove-double-neg 58.7%

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

   4. sub-neg 58.7%

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

   5. distribute-neg-in 58.7%

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

   6. metadata-eval 58.7%

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

   7. metadata-eval 58.7%

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

7. Applied egg-rr 58.7%

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

   1. associate-*r/ 58.7%

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

   2. *-rgt-identity 58.7%

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

   3. +-commutative 58.7%

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

   4. unsub-neg 58.7%

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

9. Simplified 58.7%

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

10. Final simplification 58.7%

    \[\leadsto \frac{t}{1 - \frac{z}{y}} \]
11. Add Preprocessing

Alternative 6: 34.2% 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 98.3%

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

3. Taylor expanded in y around inf 34.9%

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

4. Final simplification 34.9%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024033 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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