Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.4s

Alternatives: 8

Speedup: 1.0×

• 34.5% 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, 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 2: 37.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+161}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -1.75e+161)
     (* x z)
     (if (<= z -2.55e-51)
       t_1
       (if (<= z 5.7e-69) x (if (<= z 3.6e+146) t_1 (* x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.75e+161) {
		tmp = x * z;
	} else if (z <= -2.55e-51) {
		tmp = t_1;
	} else if (z <= 5.7e-69) {
		tmp = x;
	} else if (z <= 3.6e+146) {
		tmp = t_1;
	} else {
		tmp = x * 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-1.75d+161)) then
        tmp = x * z
    else if (z <= (-2.55d-51)) then
        tmp = t_1
    else if (z <= 5.7d-69) then
        tmp = x
    else if (z <= 3.6d+146) then
        tmp = t_1
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.75e+161) {
		tmp = x * z;
	} else if (z <= -2.55e-51) {
		tmp = t_1;
	} else if (z <= 5.7e-69) {
		tmp = x;
	} else if (z <= 3.6e+146) {
		tmp = t_1;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -1.75e+161:
		tmp = x * z
	elif z <= -2.55e-51:
		tmp = t_1
	elif z <= 5.7e-69:
		tmp = x
	elif z <= 3.6e+146:
		tmp = t_1
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -1.75e+161)
		tmp = Float64(x * z);
	elseif (z <= -2.55e-51)
		tmp = t_1;
	elseif (z <= 5.7e-69)
		tmp = x;
	elseif (z <= 3.6e+146)
		tmp = t_1;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -1.75e+161)
		tmp = x * z;
	elseif (z <= -2.55e-51)
		tmp = t_1;
	elseif (z <= 5.7e-69)
		tmp = x;
	elseif (z <= 3.6e+146)
		tmp = t_1;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -1.75e+161], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.55e-51], t$95$1, If[LessEqual[z, 5.7e-69], x, If[LessEqual[z, 3.6e+146], t$95$1, N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.74999999999999994e161 or 3.5999999999999998e146 < 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 84.7%

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

      1. mul-1-neg 84.7%

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

      2. unsub-neg 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in z around inf 84.7%

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

   7. Taylor expanded in x around inf 54.5%

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

   if -1.74999999999999994e161 < z < -2.5499999999999999e-51 or 5.7e-69 < z < 3.5999999999999998e146

   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 59.1%

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

      1. mul-1-neg 59.1%

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

      2. unsub-neg 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in x around 0 58.0%

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

      1. sub-neg 58.0%

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

      2. neg-mul-1 58.0%

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

      3. remove-double-neg 58.0%

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

      4. +-commutative 58.0%

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

   8. Simplified 58.0%

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

   9. Taylor expanded in x around 0 37.0%

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

       1. mul-1-neg 37.0%

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

       2. distribute-rgt-neg-in 37.0%

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

   11. Simplified 37.0%

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

   if -2.5499999999999999e-51 < z < 5.7e-69

   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 78.9%

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

   4. Taylor expanded in x around inf 40.4%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+161}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+81} \lor \neg \left(x \leq 3.1 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.25e+81) (not (<= x 3.1e+55)))
   (* x (- (+ z 1.0) y))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e+81) || !(x <= 3.1e+55)) {
		tmp = x * ((z + 1.0) - y);
	} else {
		tmp = x + ((y - z) * 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 <= (-1.25d+81)) .or. (.not. (x <= 3.1d+55))) then
        tmp = x * ((z + 1.0d0) - y)
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e+81) || !(x <= 3.1e+55)) {
		tmp = x * ((z + 1.0) - y);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.25e+81) or not (x <= 3.1e+55):
		tmp = x * ((z + 1.0) - y)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.25e+81) || !(x <= 3.1e+55))
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.25e+81) || ~((x <= 3.1e+55)))
		tmp = x * ((z + 1.0) - y);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.25e+81], N[Not[LessEqual[x, 3.1e+55]], $MachinePrecision]], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e81 or 3.09999999999999994e55 < x

   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 93.4%

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

      1. mul-1-neg 93.4%

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

      2. distribute-rgt-neg-in 93.4%

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

      3. sub-neg 93.4%

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

      4. +-commutative 93.4%

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

      5. distribute-neg-in 93.4%

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

      6. remove-double-neg 93.4%

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

      7. sub-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in x around 0 93.4%

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

   if -1.25e81 < x < 3.09999999999999994e55

   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 79.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+81} \lor \neg \left(x \leq 3.1 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \lor \neg \left(z \leq 0.053\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.3) (not (<= z 0.053))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3) || !(z <= 0.053)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (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 <= (-3.3d0)) .or. (.not. (z <= 0.053d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (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 <= -3.3) || !(z <= 0.053)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.3) or not (z <= 0.053):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.3) || !(z <= 0.053))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.3) || ~((z <= 0.053)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.3], N[Not[LessEqual[z, 0.053]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999998 or 0.0529999999999999985 < 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 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in z around inf 74.8%

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

   if -3.2999999999999998 < z < 0.0529999999999999985

   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 78.0%

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

   4. Taylor expanded in y around inf 72.2%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \lor \neg \left(z \leq 0.053\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-51} \lor \neg \left(z \leq 5.7 \cdot 10^{-69}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.55e-51) (not (<= z 5.7e-69))) (* z (- x t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.55e-51) || !(z <= 5.7e-69)) {
		tmp = z * (x - 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 ((z <= (-2.55d-51)) .or. (.not. (z <= 5.7d-69))) then
        tmp = z * (x - 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 ((z <= -2.55e-51) || !(z <= 5.7e-69)) {
		tmp = z * (x - t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.55e-51) or not (z <= 5.7e-69):
		tmp = z * (x - t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.55e-51) || !(z <= 5.7e-69))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.55e-51) || ~((z <= 5.7e-69)))
		tmp = z * (x - t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.55e-51], N[Not[LessEqual[z, 5.7e-69]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e-51 or 5.7e-69 < 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 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in z around inf 68.0%

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

   if -2.5499999999999999e-51 < z < 5.7e-69

   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 78.9%

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

   4. Taylor expanded in x around inf 40.4%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-51} \lor \neg \left(z \leq 5.7 \cdot 10^{-69}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \lor \neg \left(z \leq 0.05\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2) (not (<= z 0.05))) (* x z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2) || !(z <= 0.05)) {
		tmp = x * z;
	} 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 ((z <= (-6.2d0)) .or. (.not. (z <= 0.05d0))) then
        tmp = x * z
    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 ((z <= -6.2) || !(z <= 0.05)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2) or not (z <= 0.05):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2) || !(z <= 0.05))
		tmp = Float64(x * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2) || ~((z <= 0.05)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2], N[Not[LessEqual[z, 0.05]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000018 or 0.050000000000000003 < 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 74.7%

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

      1. mul-1-neg 74.7%

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

      2. unsub-neg 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in z around inf 74.1%

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

   7. Taylor expanded in x around inf 40.6%

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

   if -6.20000000000000018 < z < 0.050000000000000003

   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 78.0%

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

   4. Taylor expanded in x around inf 34.2%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \lor \neg \left(z \leq 0.05\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 19.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9200 \lor \neg \left(z \leq 5.8 \cdot 10^{+100}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9200.0) (not (<= z 5.8e+100))) (* z t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9200.0) || !(z <= 5.8e+100)) {
		tmp = z * 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 ((z <= (-9200.0d0)) .or. (.not. (z <= 5.8d+100))) then
        tmp = z * 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 ((z <= -9200.0) || !(z <= 5.8e+100)) {
		tmp = z * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9200.0) or not (z <= 5.8e+100):
		tmp = z * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9200.0) || !(z <= 5.8e+100))
		tmp = Float64(z * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9200.0) || ~((z <= 5.8e+100)))
		tmp = z * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9200.0], N[Not[LessEqual[z, 5.8e+100]], $MachinePrecision]], N[(z * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9200 or 5.8000000000000001e100 < 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 79.6%

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

      1. mul-1-neg 79.6%

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

      2. unsub-neg 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in x around 0 72.5%

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

      1. sub-neg 72.5%

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

      2. neg-mul-1 72.5%

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

      3. remove-double-neg 72.5%

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

      4. +-commutative 72.5%

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

   8. Simplified 72.5%

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

   9. Taylor expanded in x around 0 40.9%

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

       1. mul-1-neg 40.9%

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

       2. distribute-rgt-neg-in 40.9%

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

   11. Simplified 40.9%

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

       1. add-sqr-sqrt 23.2%

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

       2. sqrt-unprod 30.9%

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

       3. sqr-neg 30.9%

          \[\leadsto t \cdot \sqrt{\color{blue}{z \cdot z}} \]

       4. sqrt-unprod 6.0%

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

       5. add-sqr-sqrt 12.4%

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

       6. pow1 12.4%

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

       7. *-commutative 12.4%

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

   13. Applied egg-rr 12.4%

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

       1. unpow1 12.4%

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

   15. Simplified 12.4%

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

   if -9200 < z < 5.8000000000000001e100

   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 73.2%

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

   4. Taylor expanded in x around inf 28.3%

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

4. Final simplification 21.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9200 \lor \neg \left(z \leq 5.8 \cdot 10^{+100}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 65.5%

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

4. Taylor expanded in x around inf 16.9%

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

Developer Target 1: 96.3% 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 2024165 
(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))))