Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.7s

Alternatives: 10

Speedup: 1.0×

• 34.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+24} \lor \neg \left(z \leq 7.5 \cdot 10^{+65}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.9e+24) (not (<= z 7.5e+65)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.9e+24) || !(z <= 7.5e+65)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - 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 ((z <= (-4.9d+24)) .or. (.not. (z <= 7.5d+65))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.9e+24) || !(z <= 7.5e+65)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.9e+24) or not (z <= 7.5e+65):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.9e+24) || !(z <= 7.5e+65))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.9e+24) || ~((z <= 7.5e+65)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.9e+24], N[Not[LessEqual[z, 7.5e+65]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.90000000000000029e24 or 7.50000000000000006e65 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in z around inf 85.2%

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

   if -4.90000000000000029e24 < z < 7.50000000000000006e65

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.1%

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

      1. *-commutative 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+24} \lor \neg \left(z \leq 7.5 \cdot 10^{+65}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{-30} \lor \neg \left(t \leq 55000000000\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.32e-30) (not (<= t 55000000000.0)))
   (* (- y z) t)
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.32e-30) || !(t <= 55000000000.0)) {
		tmp = (y - z) * t;
	} else {
		tmp = x + (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 <= (-1.32d-30)) .or. (.not. (t <= 55000000000.0d0))) then
        tmp = (y - z) * t
    else
        tmp = x + (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 <= -1.32e-30) || !(t <= 55000000000.0)) {
		tmp = (y - z) * t;
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.32e-30) or not (t <= 55000000000.0):
		tmp = (y - z) * t
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.32e-30) || !(t <= 55000000000.0))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.32e-30) || ~((t <= 55000000000.0)))
		tmp = (y - z) * t;
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.32e-30], N[Not[LessEqual[t, 55000000000.0]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.32e-30 or 5.5e10 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 85.8%

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

   4. Taylor expanded in t around inf 85.8%

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

   5. Taylor expanded in x around 0 80.4%

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

   if -1.32e-30 < t < 5.5e10

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 86.7%

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

      1. mul-1-neg 86.7%

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

      2. distribute-rgt-neg-in 86.7%

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

      3. sub-neg 86.7%

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

      4. +-commutative 86.7%

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

      5. distribute-neg-in 86.7%

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

      6. remove-double-neg 86.7%

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

      7. sub-neg 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{-30} \lor \neg \left(t \leq 55000000000\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19} \lor \neg \left(z \leq 4.1 \cdot 10^{+65}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.9e+19) (not (<= z 4.1e+65))) (* z (- x t)) (* y (- t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e+19) || !(z <= 4.1e+65)) {
		tmp = z * (x - t);
	} else {
		tmp = y * (t - 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 ((z <= (-1.9d+19)) .or. (.not. (z <= 4.1d+65))) then
        tmp = z * (x - t)
    else
        tmp = y * (t - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e+19) || !(z <= 4.1e+65)) {
		tmp = z * (x - t);
	} else {
		tmp = y * (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.9e+19) or not (z <= 4.1e+65):
		tmp = z * (x - t)
	else:
		tmp = y * (t - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.9e+19) || !(z <= 4.1e+65))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(y * Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.9e+19) || ~((z <= 4.1e+65)))
		tmp = z * (x - t);
	else
		tmp = y * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.9e+19], N[Not[LessEqual[z, 4.1e+65]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e19 or 4.1000000000000001e65 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in z around inf 85.2%

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

   if -1.9e19 < z < 4.1000000000000001e65

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.1%

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

      1. *-commutative 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in y around inf 70.1%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19} \lor \neg \left(z \leq 4.1 \cdot 10^{+65}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+38} \lor \neg \left(z \leq 1.2 \cdot 10^{+67}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e+38) (not (<= z 1.2e+67))) (* z x) (* y (- t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+38) || !(z <= 1.2e+67)) {
		tmp = z * x;
	} else {
		tmp = y * (t - 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 ((z <= (-1.6d+38)) .or. (.not. (z <= 1.2d+67))) then
        tmp = z * x
    else
        tmp = y * (t - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+38) || !(z <= 1.2e+67)) {
		tmp = z * x;
	} else {
		tmp = y * (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e+38) or not (z <= 1.2e+67):
		tmp = z * x
	else:
		tmp = y * (t - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e+38) || !(z <= 1.2e+67))
		tmp = Float64(z * x);
	else
		tmp = Float64(y * Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e+38) || ~((z <= 1.2e+67)))
		tmp = z * x;
	else
		tmp = y * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e+38], N[Not[LessEqual[z, 1.2e+67]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999993e38 or 1.20000000000000001e67 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. distribute-rgt-neg-in 65.6%

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

      3. sub-neg 65.6%

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

      4. +-commutative 65.6%

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

      5. distribute-neg-in 65.6%

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

      6. remove-double-neg 65.6%

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

      7. sub-neg 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in z around inf 57.5%

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

   7. Taylor expanded in z around inf 57.5%

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

   if -1.59999999999999993e38 < z < 1.20000000000000001e67

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.0%

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

      1. *-commutative 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in y around inf 68.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+38} \lor \neg \left(z \leq 1.2 \cdot 10^{+67}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-63} \lor \neg \left(t \leq 1.18 \cdot 10^{-33}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.9e-63) (not (<= t 1.18e-33))) (* (- y z) t) (* z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e-63) || !(t <= 1.18e-33)) {
		tmp = (y - z) * t;
	} else {
		tmp = z * 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 <= (-2.9d-63)) .or. (.not. (t <= 1.18d-33))) then
        tmp = (y - z) * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e-63) || !(t <= 1.18e-33)) {
		tmp = (y - z) * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.9e-63) or not (t <= 1.18e-33):
		tmp = (y - z) * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.9e-63) || !(t <= 1.18e-33))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.9e-63) || ~((t <= 1.18e-33)))
		tmp = (y - z) * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.9e-63], N[Not[LessEqual[t, 1.18e-33]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999975e-63 or 1.18e-33 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.6%

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

   4. Taylor expanded in t around inf 82.6%

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

   5. Taylor expanded in x around 0 74.9%

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

   if -2.89999999999999975e-63 < t < 1.18e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. distribute-rgt-neg-in 89.8%

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

      3. sub-neg 89.8%

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

      4. +-commutative 89.8%

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

      5. distribute-neg-in 89.8%

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

      6. remove-double-neg 89.8%

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

      7. sub-neg 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in z around inf 58.9%

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

   7. Taylor expanded in z around inf 44.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-63} \lor \neg \left(t \leq 1.18 \cdot 10^{-33}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+38} \lor \neg \left(z \leq 7.6 \cdot 10^{+65}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.35e+38) (not (<= z 7.6e+65))) (* z x) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e+38) || !(z <= 7.6e+65)) {
		tmp = z * x;
	} else {
		tmp = y * 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 ((z <= (-1.35d+38)) .or. (.not. (z <= 7.6d+65))) then
        tmp = z * x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e+38) || !(z <= 7.6e+65)) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.35e+38) or not (z <= 7.6e+65):
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.35e+38) || !(z <= 7.6e+65))
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.35e+38) || ~((z <= 7.6e+65)))
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.35e+38], N[Not[LessEqual[z, 7.6e+65]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999998e38 or 7.60000000000000022e65 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. distribute-rgt-neg-in 65.6%

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

      3. sub-neg 65.6%

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

      4. +-commutative 65.6%

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

      5. distribute-neg-in 65.6%

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

      6. remove-double-neg 65.6%

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

      7. sub-neg 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in z around inf 57.5%

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

   7. Taylor expanded in z around inf 57.5%

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

   if -1.34999999999999998e38 < z < 7.60000000000000022e65

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 70.2%

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

   4. Taylor expanded in t around inf 68.9%

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

   5. Taylor expanded in y around inf 41.1%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+38} \lor \neg \left(z \leq 7.6 \cdot 10^{+65}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-57} \lor \neg \left(y \leq 1.2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e-57) (not (<= y 1.2e-18))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e-57) || !(y <= 1.2e-18)) {
		tmp = y * t;
	} else {
		tmp = 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 ((y <= (-8d-57)) .or. (.not. (y <= 1.2d-18))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e-57) || !(y <= 1.2e-18)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e-57) or not (y <= 1.2e-18):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e-57) || !(y <= 1.2e-18))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8e-57) || ~((y <= 1.2e-18)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e-57], N[Not[LessEqual[y, 1.2e-18]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999964e-57 or 1.19999999999999997e-18 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 51.6%

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

   4. Taylor expanded in t around inf 56.9%

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

   5. Taylor expanded in y around inf 41.0%

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

   if -7.99999999999999964e-57 < y < 1.19999999999999997e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 69.3%

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

   4. Taylor expanded in x around inf 29.0%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-57} \lor \neg \left(y \leq 1.2 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 10: 18.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 58.6%

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

4. Taylor expanded in x around inf 13.2%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Developer Target 1: 96.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

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 * (y - z)) + (-x * (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024150 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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