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

Percentage Accurate: 98.1% → 98.1%

Time: 8.4s

Alternatives: 8

Speedup: 1.0×

• 25.4% 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: 98.1% 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: 98.1% accurate, 1.0× 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 97.7%

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

   1. *-commutative 97.7%

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

   2. clear-num 97.6%

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

   3. un-div-inv 97.7%

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

4. Applied egg-rr 97.7%

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

5. Final simplification 97.7%

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

Alternative 2: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+131} \lor \neg \left(t \leq 0.116\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.3e+131) (not (<= t 0.116)))
   (* t (- 1.0 (/ x y)))
   (+ t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e+131) || !(t <= 0.116)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.3d+131)) .or. (.not. (t <= 0.116d0))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e+131) || !(t <= 0.116)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.3e+131) or not (t <= 0.116):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.3e+131) || !(t <= 0.116))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.3e+131) || ~((t <= 0.116)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.3e+131], N[Not[LessEqual[t, 0.116]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2999999999999998e131 or 0.116000000000000006 < 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 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

      3. *-rgt-identity 86.2%

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

      4. associate-*r/ 95.0%

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

      5. distribute-lft-out-- 95.0%

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

   5. Simplified 95.0%

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

   if -3.2999999999999998e131 < t < 0.116000000000000006

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 84.4%

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

      1. associate-*l/ 85.6%

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

      2. *-commutative 85.6%

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

   5. Simplified 85.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+131} \lor \neg \left(t \leq 0.116\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+130} \lor \neg \left(t \leq 0.235\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.3e+130) (not (<= t 0.235)))
   (- t (* t (/ x y)))
   (+ t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.3e+130) || !(t <= 0.235)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.3d+130)) .or. (.not. (t <= 0.235d0))) then
        tmp = t - (t * (x / y))
    else
        tmp = t + (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.3e+130) || !(t <= 0.235)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.3e+130) or not (t <= 0.235):
		tmp = t - (t * (x / y))
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.3e+130) || !(t <= 0.235))
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = Float64(t + Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.3e+130) || ~((t <= 0.235)))
		tmp = t - (t * (x / y));
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.3e+130], N[Not[LessEqual[t, 0.235]], $MachinePrecision]], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.29999999999999984e130 or 0.23499999999999999 < t

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. associate-*r/ 95.0%

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

      3. sub-neg 95.0%

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

   7. Simplified 95.0%

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

   if -4.29999999999999984e130 < t < 0.23499999999999999

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 84.4%

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

      1. associate-*l/ 85.6%

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

      2. *-commutative 85.6%

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

   5. Simplified 85.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+130} \lor \neg \left(t \leq 0.235\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+102} \lor \neg \left(x \leq 7.4\right):\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.2e+102) (not (<= x 7.4))) (* x (/ (- t) y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+102) || !(x <= 7.4)) {
		tmp = x * (-t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.2d+102)) .or. (.not. (x <= 7.4d0))) then
        tmp = x * (-t / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+102) || !(x <= 7.4)) {
		tmp = x * (-t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.2e+102) or not (x <= 7.4):
		tmp = x * (-t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.2e+102) || !(x <= 7.4))
		tmp = Float64(x * Float64(Float64(-t) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.2e+102) || ~((x <= 7.4)))
		tmp = x * (-t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.2e+102], N[Not[LessEqual[x, 7.4]], $MachinePrecision]], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -5.20000000000000013e102 or 7.4000000000000004 < x

   1. Initial program 97.3%

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

      1. *-commutative 97.3%

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

      2. clear-num 97.2%

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

      3. un-div-inv 97.6%

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

   4. Applied egg-rr 97.6%

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

   5. Taylor expanded in z around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. associate-*r/ 55.2%

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

      3. sub-neg 55.2%

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

   7. Simplified 55.2%

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

      1. *-commutative 55.2%

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

      2. add-sqr-sqrt 30.2%

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

      3. sqrt-unprod 28.9%

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

      4. sqr-neg 28.9%

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

      5. sqrt-unprod 5.8%

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

      6. add-sqr-sqrt 15.7%

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

      7. associate-/r/ 14.1%

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

      8. add-sqr-sqrt 5.9%

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

      9. sqrt-unprod 27.9%

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

      10. sqr-neg 27.9%

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

      11. sqrt-unprod 29.2%

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

      12. add-sqr-sqrt 51.6%

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

   9. Applied egg-rr 51.6%

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

   10. Taylor expanded in x around inf 42.1%

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

       1. associate-*r/ 42.1%

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

       2. *-commutative 42.1%

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

       3. neg-mul-1 42.1%

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

       4. distribute-rgt-neg-out 42.1%

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

       5. associate-*r/ 44.6%

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

   12. Simplified 44.6%

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

   if -5.20000000000000013e102 < x < 7.4000000000000004

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 60.3%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+102} \lor \neg \left(x \leq 7.4\right):\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{\frac{-y}{t}}\\ \mathbf{elif}\;x \leq 12.2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.3e+103) (/ x (/ (- y) t)) (if (<= x 12.2) t (* x (/ (- t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3e+103) {
		tmp = x / (-y / t);
	} else if (x <= 12.2) {
		tmp = t;
	} else {
		tmp = x * (-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 <= (-3.3d+103)) then
        tmp = x / (-y / t)
    else if (x <= 12.2d0) then
        tmp = t
    else
        tmp = x * (-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 <= -3.3e+103) {
		tmp = x / (-y / t);
	} else if (x <= 12.2) {
		tmp = t;
	} else {
		tmp = x * (-t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.3e+103:
		tmp = x / (-y / t)
	elif x <= 12.2:
		tmp = t
	else:
		tmp = x * (-t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.3e+103)
		tmp = Float64(x / Float64(Float64(-y) / t));
	elseif (x <= 12.2)
		tmp = t;
	else
		tmp = Float64(x * Float64(Float64(-t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.3e+103)
		tmp = x / (-y / t);
	elseif (x <= 12.2)
		tmp = t;
	else
		tmp = x * (-t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.3e+103], N[(x / N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 12.2], t, N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.30000000000000009e103

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 97.9%

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

      3. un-div-inv 97.9%

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in z around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. associate-*r/ 56.7%

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

      3. sub-neg 56.7%

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

   7. Simplified 56.7%

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

      1. *-commutative 56.7%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 11.0%

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

      4. sqr-neg 11.0%

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

      5. sqrt-unprod 13.2%

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

      6. add-sqr-sqrt 13.2%

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

      7. associate-/r/ 13.4%

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

      8. add-sqr-sqrt 13.4%

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

      9. sqrt-unprod 10.9%

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

      10. sqr-neg 10.9%

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

      11. sqrt-unprod 0.0%

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

      12. add-sqr-sqrt 50.8%

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

   9. Applied egg-rr 50.8%

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

   10. Taylor expanded in x around inf 47.5%

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

       1. associate-*r/ 47.5%

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

       2. *-commutative 47.5%

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

       3. neg-mul-1 47.5%

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

       4. distribute-rgt-neg-out 47.5%

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

       5. associate-*r/ 48.6%

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

       6. neg-mul-1 48.6%

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

       7. associate-/l* 48.6%

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

       8. metadata-eval 48.6%

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

       9. associate-/r* 48.6%

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

       10. neg-mul-1 48.6%

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

       11. associate-*r/ 48.7%

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

       12. *-rgt-identity 48.7%

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

       13. distribute-neg-frac 48.7%

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

   12. Simplified 48.7%

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

   if -3.30000000000000009e103 < x < 12.199999999999999

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 60.3%

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

   if 12.199999999999999 < x

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. clear-num 96.7%

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

      3. un-div-inv 97.4%

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

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in z around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. associate-*r/ 53.9%

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

      3. sub-neg 53.9%

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

   7. Simplified 53.9%

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

      1. *-commutative 53.9%

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

      2. add-sqr-sqrt 53.9%

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

      3. sqrt-unprod 43.0%

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

      4. sqr-neg 43.0%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 17.7%

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

      7. associate-/r/ 14.6%

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

      8. add-sqr-sqrt 0.0%

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

      9. sqrt-unprod 41.3%

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

      10. sqr-neg 41.3%

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

      11. sqrt-unprod 52.1%

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

      12. add-sqr-sqrt 52.2%

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

   9. Applied egg-rr 52.2%

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

   10. Taylor expanded in x around inf 37.9%

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

       1. associate-*r/ 37.9%

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

       2. *-commutative 37.9%

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

       3. neg-mul-1 37.9%

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

       4. distribute-rgt-neg-out 37.9%

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

       5. associate-*r/ 41.4%

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

   12. Simplified 41.4%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{\frac{-y}{t}}\\ \mathbf{elif}\;x \leq 12.2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.1% 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 97.7%

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

3. Final simplification 97.7%

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

Alternative 7: 65.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(1 - \frac{x}{y}\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return t * (1.0 - (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 * (1.0d0 - (x / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Taylor expanded in z around 0 61.9%

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

   1. mul-1-neg 61.9%

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

   2. unsub-neg 61.9%

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

   3. *-rgt-identity 61.9%

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

   4. associate-*r/ 66.8%

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

   5. distribute-lft-out-- 66.8%

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

5. Simplified 66.8%

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

6. Final simplification 66.8%

   \[\leadsto t \cdot \left(1 - \frac{x}{y}\right) \]
7. Add Preprocessing

Alternative 8: 38.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Taylor expanded in x around 0 38.5%

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

4. Final simplification 38.5%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.7% 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 2024021 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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