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

Percentage Accurate: 97.6% → 97.6%

Time: 6.6s

Alternatives: 11

Speedup: 1.0×

• 25.7% 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: 97.6% 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 96.9%

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

   1. *-commutative 96.9%

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

   2. clear-num 96.9%

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

   3. un-div-inv 97.2%

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

4. Applied egg-rr 97.2%

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

5. Final simplification 97.2%

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

Alternative 2: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-94} \lor \neg \left(t \leq 2.05 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7e-94) (not (<= t 2.05e-10)))
   (/ t (/ y (- y x)))
   (+ t (/ x (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7e-94) || !(t <= 2.05e-10)) {
		tmp = t / (y / (y - x));
	} 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 ((t <= (-7d-94)) .or. (.not. (t <= 2.05d-10))) then
        tmp = t / (y / (y - x))
    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 ((t <= -7e-94) || !(t <= 2.05e-10)) {
		tmp = t / (y / (y - x));
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7e-94) or not (t <= 2.05e-10):
		tmp = t / (y / (y - x))
	else:
		tmp = t + (x / (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7e-94) || !(t <= 2.05e-10))
		tmp = Float64(t / Float64(y / Float64(y - x)));
	else
		tmp = Float64(t + Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7e-94) || ~((t <= 2.05e-10)))
		tmp = t / (y / (y - x));
	else
		tmp = t + (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7e-94], N[Not[LessEqual[t, 2.05e-10]], $MachinePrecision]], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.99999999999999996e-94 or 2.0499999999999999e-10 < t

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

      3. *-rgt-identity 82.0%

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

      4. associate-/l* 89.4%

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

      5. distribute-lft-out-- 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in y around 0 89.4%

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

      1. clear-num 89.4%

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

      2. un-div-inv 89.6%

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

   8. Applied egg-rr 89.6%

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

   if -6.99999999999999996e-94 < t < 2.0499999999999999e-10

   1. Initial program 93.9%

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

      1. associate-*l/ 91.5%

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

      2. associate-*r/ 96.4%

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

      3. clear-num 96.4%

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

      4. un-div-inv 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in z around inf 90.4%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-94} \lor \neg \left(t \leq 2.05 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-94} \lor \neg \left(t \leq 0.00014\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.8e-94) (not (<= t 0.00014)))
   (* t (/ (- y x) y))
   (+ t (/ x (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.8e-94) || !(t <= 0.00014)) {
		tmp = t * ((y - x) / 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 ((t <= (-4.8d-94)) .or. (.not. (t <= 0.00014d0))) then
        tmp = t * ((y - x) / 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 ((t <= -4.8e-94) || !(t <= 0.00014)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.8e-94) or not (t <= 0.00014):
		tmp = t * ((y - x) / y)
	else:
		tmp = t + (x / (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.8e-94) || !(t <= 0.00014))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t + Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.8e-94) || ~((t <= 0.00014)))
		tmp = t * ((y - x) / y);
	else
		tmp = t + (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.8e-94], N[Not[LessEqual[t, 0.00014]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8e-94 or 1.3999999999999999e-4 < t

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

      3. *-rgt-identity 82.0%

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

      4. associate-/l* 89.4%

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

      5. distribute-lft-out-- 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in y around 0 89.4%

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

   if -4.8e-94 < t < 1.3999999999999999e-4

   1. Initial program 93.9%

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

      1. associate-*l/ 91.5%

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

      2. associate-*r/ 96.4%

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

      3. clear-num 96.4%

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

      4. un-div-inv 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in z around inf 90.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-94} \lor \neg \left(t \leq 0.00014\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-94} \lor \neg \left(t \leq 0.0003\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7e-94) (not (<= t 0.0003)))
   (* t (/ (- y x) y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7e-94) || !(t <= 0.0003)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t + (x * (z / 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 <= (-7d-94)) .or. (.not. (t <= 0.0003d0))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7e-94) || !(t <= 0.0003)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7e-94) or not (t <= 0.0003):
		tmp = t * ((y - x) / y)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7e-94) || !(t <= 0.0003))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7e-94) || ~((t <= 0.0003)))
		tmp = t * ((y - x) / y);
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7e-94], N[Not[LessEqual[t, 0.0003]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.99999999999999996e-94 or 2.99999999999999974e-4 < t

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

      3. *-rgt-identity 82.0%

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

      4. associate-/l* 89.4%

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

      5. distribute-lft-out-- 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in y around 0 89.4%

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

   if -6.99999999999999996e-94 < t < 2.99999999999999974e-4

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf 85.4%

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

      1. associate-/l* 90.3%

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

   5. Simplified 90.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-94} \lor \neg \left(t \leq 0.0003\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-94}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;t \leq 0.00058:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7e-94)
   (/ t (/ y (- y x)))
   (if (<= t 0.00058) (+ t (/ x (/ y z))) (- t (/ t (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-94) {
		tmp = t / (y / (y - x));
	} else if (t <= 0.00058) {
		tmp = t + (x / (y / z));
	} else {
		tmp = t - (t / (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 (t <= (-7d-94)) then
        tmp = t / (y / (y - x))
    else if (t <= 0.00058d0) then
        tmp = t + (x / (y / z))
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7e-94) {
		tmp = t / (y / (y - x));
	} else if (t <= 0.00058) {
		tmp = t + (x / (y / z));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7e-94:
		tmp = t / (y / (y - x))
	elif t <= 0.00058:
		tmp = t + (x / (y / z))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7e-94)
		tmp = Float64(t / Float64(y / Float64(y - x)));
	elseif (t <= 0.00058)
		tmp = Float64(t + Float64(x / Float64(y / z)));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7e-94)
		tmp = t / (y / (y - x));
	elseif (t <= 0.00058)
		tmp = t + (x / (y / z));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7e-94], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00058], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.99999999999999996e-94

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. *-rgt-identity 79.5%

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

      4. associate-/l* 85.3%

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

      5. distribute-lft-out-- 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in y around 0 85.3%

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

      1. clear-num 85.2%

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

      2. un-div-inv 85.6%

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

   8. Applied egg-rr 85.6%

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

   if -6.99999999999999996e-94 < t < 5.8e-4

   1. Initial program 93.9%

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

      1. associate-*l/ 91.5%

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

      2. associate-*r/ 96.4%

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

      3. clear-num 96.4%

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

      4. un-div-inv 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in z around inf 90.4%

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

   if 5.8e-4 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-/l* 87.2%

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

      4. distribute-rgt-neg-in 87.2%

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

      5. distribute-neg-frac2 87.2%

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

   5. Simplified 87.2%

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

      1. *-commutative 87.2%

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

      2. add-sqr-sqrt 43.9%

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

      3. sqrt-unprod 61.9%

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

      4. sqr-neg 61.9%

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

      5. sqrt-unprod 23.6%

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

      6. add-sqr-sqrt 55.9%

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

      7. associate-/r/ 59.8%

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

      8. frac-2neg 59.8%

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

      9. distribute-neg-frac 59.8%

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

      10. add-sqr-sqrt 32.4%

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

      11. sqrt-unprod 73.7%

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

      12. sqr-neg 73.7%

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

      13. sqrt-unprod 49.3%

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

      14. add-sqr-sqrt 94.6%

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

   7. Applied egg-rr 94.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-94}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;t \leq 0.00058:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+101} \lor \neg \left(x \leq 10^{+96}\right):\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.3e+101) (not (<= x 1e+96))) (/ t (/ (- y) x)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e+101) || !(x <= 1e+96)) {
		tmp = t / (-y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.3d+101)) .or. (.not. (x <= 1d+96))) then
        tmp = t / (-y / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e+101) || !(x <= 1e+96)) {
		tmp = t / (-y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.3e+101) or not (x <= 1e+96):
		tmp = t / (-y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.3e+101) || !(x <= 1e+96))
		tmp = Float64(t / Float64(Float64(-y) / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.3e+101) || ~((x <= 1e+96)))
		tmp = t / (-y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.3e+101], N[Not[LessEqual[x, 1e+96]], $MachinePrecision]], N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -4.3000000000000001e101 or 1.00000000000000005e96 < x

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. unsub-neg 50.0%

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

      3. *-rgt-identity 50.0%

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

      4. associate-/l* 59.8%

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

      5. distribute-lft-out-- 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in x around inf 44.3%

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

      1. mul-1-neg 44.3%

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

      2. distribute-frac-neg2 44.3%

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

      3. *-commutative 44.3%

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

      4. associate-/l* 49.4%

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

   8. Simplified 49.4%

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

      1. *-commutative 58.8%

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

      2. add-sqr-sqrt 24.5%

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

      3. sqrt-unprod 30.7%

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

      4. sqr-neg 30.7%

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

      5. sqrt-unprod 7.4%

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

      6. add-sqr-sqrt 17.4%

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

      7. associate-/r/ 20.0%

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

      8. frac-2neg 20.0%

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

      9. distribute-neg-frac 20.0%

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

      10. add-sqr-sqrt 10.8%

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

      11. sqrt-unprod 41.1%

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

      12. sqr-neg 41.1%

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

      13. sqrt-unprod 33.5%

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

      14. add-sqr-sqrt 60.1%

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

   10. Applied egg-rr 50.7%

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

   if -4.3000000000000001e101 < x < 1.00000000000000005e96

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 59.9%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+101} \lor \neg \left(x \leq 10^{+96}\right):\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+101} \lor \neg \left(x \leq 1.1 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.6e+101) (not (<= x 1.1e+95))) (* t (/ x (- y))) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.6e+101) || !(x <= 1.1e+95)) {
		tmp = t * (x / -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 <= (-3.6d+101)) .or. (.not. (x <= 1.1d+95))) then
        tmp = t * (x / -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 <= -3.6e+101) || !(x <= 1.1e+95)) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.6e+101) or not (x <= 1.1e+95):
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.6e+101) || !(x <= 1.1e+95))
		tmp = Float64(t * Float64(x / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.6e+101) || ~((x <= 1.1e+95)))
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.6e+101], N[Not[LessEqual[x, 1.1e+95]], $MachinePrecision]], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -3.60000000000000029e101 or 1.0999999999999999e95 < x

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. unsub-neg 50.0%

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

      3. *-rgt-identity 50.0%

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

      4. associate-/l* 59.8%

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

      5. distribute-lft-out-- 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in x around inf 50.4%

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

      1. mul-1-neg 50.4%

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

      2. distribute-frac-neg2 50.4%

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

   8. Simplified 50.4%

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

   if -3.60000000000000029e101 < x < 1.0999999999999999e95

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 59.9%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+101} \lor \neg \left(x \leq 1.1 \cdot 10^{+95}\right):\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 96.9%

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

3. Final simplification 96.9%

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

Alternative 9: 65.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in z around 0 61.5%

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

   1. mul-1-neg 61.5%

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

   2. unsub-neg 61.5%

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

   3. *-rgt-identity 61.5%

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

   4. associate-/l* 66.3%

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

   5. distribute-lft-out-- 66.3%

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

5. Simplified 66.3%

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

6. Taylor expanded in y around 0 66.3%

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

Alternative 10: 65.4% 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 96.9%

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

3. Taylor expanded in z around 0 61.5%

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

   1. mul-1-neg 61.5%

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

   2. unsub-neg 61.5%

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

   3. *-rgt-identity 61.5%

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

   4. associate-/l* 66.3%

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

   5. distribute-lft-out-- 66.3%

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

5. Simplified 66.3%

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

Alternative 11: 38.1% 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 96.9%

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

3. Taylor expanded in x around 0 41.2%

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

Developer target: 97.2% 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 2024107 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (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))