Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 11

Speedup: 1.0×

• 34.0% 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-def 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. Final simplification 100.0%

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

Alternative 2: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+22} \lor \neg \left(z \leq 6.5 \cdot 10^{+43}\right) \land z \leq 6.6 \cdot 10^{+150}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))))
   (if (<= z -3.4e-11)
     t_1
     (if (<= z 1.55e-87)
       (+ x (* y t))
       (if (or (<= z 1.6e+22) (and (not (<= z 6.5e+43)) (<= z 6.6e+150)))
         (- x (* z t))
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double tmp;
	if (z <= -3.4e-11) {
		tmp = t_1;
	} else if (z <= 1.55e-87) {
		tmp = x + (y * t);
	} else if ((z <= 1.6e+22) || (!(z <= 6.5e+43) && (z <= 6.6e+150))) {
		tmp = x - (z * 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 + (z * x)
    if (z <= (-3.4d-11)) then
        tmp = t_1
    else if (z <= 1.55d-87) then
        tmp = x + (y * t)
    else if ((z <= 1.6d+22) .or. (.not. (z <= 6.5d+43)) .and. (z <= 6.6d+150)) then
        tmp = x - (z * 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 + (z * x);
	double tmp;
	if (z <= -3.4e-11) {
		tmp = t_1;
	} else if (z <= 1.55e-87) {
		tmp = x + (y * t);
	} else if ((z <= 1.6e+22) || (!(z <= 6.5e+43) && (z <= 6.6e+150))) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	tmp = 0
	if z <= -3.4e-11:
		tmp = t_1
	elif z <= 1.55e-87:
		tmp = x + (y * t)
	elif (z <= 1.6e+22) or (not (z <= 6.5e+43) and (z <= 6.6e+150)):
		tmp = x - (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	tmp = 0.0
	if (z <= -3.4e-11)
		tmp = t_1;
	elseif (z <= 1.55e-87)
		tmp = Float64(x + Float64(y * t));
	elseif ((z <= 1.6e+22) || (!(z <= 6.5e+43) && (z <= 6.6e+150)))
		tmp = Float64(x - Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	tmp = 0.0;
	if (z <= -3.4e-11)
		tmp = t_1;
	elseif (z <= 1.55e-87)
		tmp = x + (y * t);
	elseif ((z <= 1.6e+22) || (~((z <= 6.5e+43)) && (z <= 6.6e+150)))
		tmp = x - (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-11], t$95$1, If[LessEqual[z, 1.55e-87], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.6e+22], And[N[Not[LessEqual[z, 6.5e+43]], $MachinePrecision], LessEqual[z, 6.6e+150]]], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3999999999999999e-11 or 1.6e22 < z < 6.4999999999999998e43 or 6.59999999999999962e150 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 92.2%

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

   3. Applied egg-rr 92.2%

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

   4. Taylor expanded in y around 0 80.2%

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

   5. Taylor expanded in t around 0 52.9%

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

   if -3.3999999999999999e-11 < z < 1.54999999999999999e-87

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 80.6%

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

   3. Taylor expanded in z around 0 76.3%

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

   if 1.54999999999999999e-87 < z < 1.6e22 or 6.4999999999999998e43 < z < 6.59999999999999962e150

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 61.2%

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

   3. Taylor expanded in y around 0 52.4%

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

      1. +-commutative 52.4%

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

      2. mul-1-neg 52.4%

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

      3. unsub-neg 52.4%

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

   5. Simplified 52.4%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+22} \lor \neg \left(z \leq 6.5 \cdot 10^{+43}\right) \land z \leq 6.6 \cdot 10^{+150}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]

Alternative 3: 54.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ t_2 := x - z \cdot t\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-28}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 32:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))) (t_2 (- x (* z t))))
   (if (<= y -2.8e-28)
     (+ x (* y t))
     (if (<= y -1.55e-257)
       t_2
       (if (<= y -3e-287)
         t_1
         (if (<= y 1.4e-62) t_2 (if (<= y 32.0) t_1 (- x (* y x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -2.8e-28) {
		tmp = x + (y * t);
	} else if (y <= -1.55e-257) {
		tmp = t_2;
	} else if (y <= -3e-287) {
		tmp = t_1;
	} else if (y <= 1.4e-62) {
		tmp = t_2;
	} else if (y <= 32.0) {
		tmp = t_1;
	} else {
		tmp = x - (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * x)
    t_2 = x - (z * t)
    if (y <= (-2.8d-28)) then
        tmp = x + (y * t)
    else if (y <= (-1.55d-257)) then
        tmp = t_2
    else if (y <= (-3d-287)) then
        tmp = t_1
    else if (y <= 1.4d-62) then
        tmp = t_2
    else if (y <= 32.0d0) then
        tmp = t_1
    else
        tmp = x - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -2.8e-28) {
		tmp = x + (y * t);
	} else if (y <= -1.55e-257) {
		tmp = t_2;
	} else if (y <= -3e-287) {
		tmp = t_1;
	} else if (y <= 1.4e-62) {
		tmp = t_2;
	} else if (y <= 32.0) {
		tmp = t_1;
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	t_2 = x - (z * t)
	tmp = 0
	if y <= -2.8e-28:
		tmp = x + (y * t)
	elif y <= -1.55e-257:
		tmp = t_2
	elif y <= -3e-287:
		tmp = t_1
	elif y <= 1.4e-62:
		tmp = t_2
	elif y <= 32.0:
		tmp = t_1
	else:
		tmp = x - (y * x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	t_2 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -2.8e-28)
		tmp = Float64(x + Float64(y * t));
	elseif (y <= -1.55e-257)
		tmp = t_2;
	elseif (y <= -3e-287)
		tmp = t_1;
	elseif (y <= 1.4e-62)
		tmp = t_2;
	elseif (y <= 32.0)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	t_2 = x - (z * t);
	tmp = 0.0;
	if (y <= -2.8e-28)
		tmp = x + (y * t);
	elseif (y <= -1.55e-257)
		tmp = t_2;
	elseif (y <= -3e-287)
		tmp = t_1;
	elseif (y <= 1.4e-62)
		tmp = t_2;
	elseif (y <= 32.0)
		tmp = t_1;
	else
		tmp = x - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e-28], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.55e-257], t$95$2, If[LessEqual[y, -3e-287], t$95$1, If[LessEqual[y, 1.4e-62], t$95$2, If[LessEqual[y, 32.0], t$95$1, N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7999999999999998e-28

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 52.6%

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

   3. Taylor expanded in z around 0 48.2%

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

   if -2.7999999999999998e-28 < y < -1.55000000000000004e-257 or -2.99999999999999992e-287 < y < 1.40000000000000001e-62

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 82.7%

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

   3. Taylor expanded in y around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. mul-1-neg 74.4%

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

      3. unsub-neg 74.4%

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

   5. Simplified 74.4%

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

   if -1.55000000000000004e-257 < y < -2.99999999999999992e-287 or 1.40000000000000001e-62 < y < 32

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 94.6%

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

   5. Taylor expanded in t around 0 76.6%

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

   if 32 < y

   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-def 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. Taylor expanded in t around 0 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in y around inf 53.4%

      \[\leadsto x - \color{blue}{y \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-28}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-257}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-287}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 32:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]

Alternative 4: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+118}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+257}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))))
   (if (<= x -1.1e+145)
     t_1
     (if (<= x 6.4e+118)
       (- x (* t (- z y)))
       (if (<= x 4.5e+257) t_1 (- x (* y x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double tmp;
	if (x <= -1.1e+145) {
		tmp = t_1;
	} else if (x <= 6.4e+118) {
		tmp = x - (t * (z - y));
	} else if (x <= 4.5e+257) {
		tmp = t_1;
	} else {
		tmp = x - (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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * x)
    if (x <= (-1.1d+145)) then
        tmp = t_1
    else if (x <= 6.4d+118) then
        tmp = x - (t * (z - y))
    else if (x <= 4.5d+257) then
        tmp = t_1
    else
        tmp = x - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double tmp;
	if (x <= -1.1e+145) {
		tmp = t_1;
	} else if (x <= 6.4e+118) {
		tmp = x - (t * (z - y));
	} else if (x <= 4.5e+257) {
		tmp = t_1;
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	tmp = 0
	if x <= -1.1e+145:
		tmp = t_1
	elif x <= 6.4e+118:
		tmp = x - (t * (z - y))
	elif x <= 4.5e+257:
		tmp = t_1
	else:
		tmp = x - (y * x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	tmp = 0.0
	if (x <= -1.1e+145)
		tmp = t_1;
	elseif (x <= 6.4e+118)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	elseif (x <= 4.5e+257)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	tmp = 0.0;
	if (x <= -1.1e+145)
		tmp = t_1;
	elseif (x <= 6.4e+118)
		tmp = x - (t * (z - y));
	elseif (x <= 4.5e+257)
		tmp = t_1;
	else
		tmp = x - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+145], t$95$1, If[LessEqual[x, 6.4e+118], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+257], t$95$1, N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.10000000000000004e145 or 6.40000000000000032e118 < x < 4.4999999999999999e257

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 92.4%

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

   3. Applied egg-rr 92.4%

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

   4. Taylor expanded in y around 0 73.0%

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

   5. Taylor expanded in t around 0 69.5%

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

   if -1.10000000000000004e145 < x < 6.40000000000000032e118

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 77.1%

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

   if 4.4999999999999999e257 < x

   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-def 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. Taylor expanded in t around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 91.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+145}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+118}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+257}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]

Alternative 5: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.028 \lor \neg \left(z \leq 190\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.028) (not (<= z 190.0)))
   (+ x (* z (- x t)))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.028) || !(z <= 190.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (t * (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 ((z <= (-0.028d0)) .or. (.not. (z <= 190.0d0))) then
        tmp = x + (z * (x - t))
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.028) || !(z <= 190.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.028) or not (z <= 190.0):
		tmp = x + (z * (x - t))
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.028) || !(z <= 190.0))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.028) || ~((z <= 190.0)))
		tmp = x + (z * (x - t));
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.028], N[Not[LessEqual[z, 190.0]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0280000000000000006 or 190 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in y around 0 73.9%

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

      1. associate-*r* 73.9%

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

      2. *-commutative 73.9%

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

      3. distribute-rgt-in 79.9%

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

      4. +-commutative 79.9%

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

      5. mul-1-neg 79.9%

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

      6. sub-neg 79.9%

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

   6. Simplified 79.9%

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

   if -0.0280000000000000006 < z < 190

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 77.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.028 \lor \neg \left(z \leq 190\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]

Alternative 6: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+39} \lor \neg \left(y \leq 2.6 \cdot 10^{+15}\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.2e+39) (not (<= y 2.6e+15)))
   (- x (* y (- x t)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e+39) || !(y <= 2.6e+15)) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + (z * (x - 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 ((y <= (-6.2d+39)) .or. (.not. (y <= 2.6d+15))) then
        tmp = x - (y * (x - t))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e+39) || !(y <= 2.6e+15)) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.2e+39) or not (y <= 2.6e+15):
		tmp = x - (y * (x - t))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.2e+39) || !(y <= 2.6e+15))
		tmp = Float64(x - Float64(y * Float64(x - t)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.2e+39) || ~((y <= 2.6e+15)))
		tmp = x - (y * (x - t));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.2e+39], N[Not[LessEqual[y, 2.6e+15]], $MachinePrecision]], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000005e39 or 2.6e15 < y

   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-def 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. Taylor expanded in z around 0 81.6%

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

   if -6.2000000000000005e39 < y < 2.6e15

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 88.2%

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

      1. associate-*r* 88.2%

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

      2. *-commutative 88.2%

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

      3. distribute-rgt-in 88.2%

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

      4. +-commutative 88.2%

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

      5. mul-1-neg 88.2%

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

      6. sub-neg 88.2%

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

   6. Simplified 88.2%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+39} \lor \neg \left(y \leq 2.6 \cdot 10^{+15}\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 7: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-65} \lor \neg \left(t \leq 2.95 \cdot 10^{+16}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.4e-65) (not (<= t 2.95e+16)))
   (- x (* t (- z y)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.4e-65) || !(t <= 2.95e+16)) {
		tmp = x - (t * (z - y));
	} 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 <= (-3.4d-65)) .or. (.not. (t <= 2.95d+16))) then
        tmp = x - (t * (z - y))
    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 <= -3.4e-65) || !(t <= 2.95e+16)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.4e-65) or not (t <= 2.95e+16):
		tmp = x - (t * (z - y))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.4e-65) || !(t <= 2.95e+16))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	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 <= -3.4e-65) || ~((t <= 2.95e+16)))
		tmp = x - (t * (z - y));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.4e-65], N[Not[LessEqual[t, 2.95e+16]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.39999999999999987e-65 or 2.95e16 < t

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 83.9%

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

   if -3.39999999999999987e-65 < t < 2.95e16

   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-def 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. Taylor expanded in t around 0 88.2%

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

      1. +-commutative 88.2%

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

      2. mul-1-neg 88.2%

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

      3. unsub-neg 88.2%

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

      4. *-commutative 88.2%

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

   6. Simplified 88.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-65} \lor \neg \left(t \leq 2.95 \cdot 10^{+16}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 8: 53.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-11} \lor \neg \left(z \leq 5300000\right):\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.6e-11) (not (<= z 5300000.0))) (+ x (* z x)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e-11) || !(z <= 5300000.0)) {
		tmp = x + (z * x);
	} 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 <= (-8.6d-11)) .or. (.not. (z <= 5300000.0d0))) then
        tmp = x + (z * x)
    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 <= -8.6e-11) || !(z <= 5300000.0)) {
		tmp = x + (z * x);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.6e-11) or not (z <= 5300000.0):
		tmp = x + (z * x)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.6e-11) || !(z <= 5300000.0))
		tmp = Float64(x + Float64(z * x));
	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 <= -8.6e-11) || ~((z <= 5300000.0)))
		tmp = x + (z * x);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.6e-11], N[Not[LessEqual[z, 5300000.0]], $MachinePrecision]], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000003e-11 or 5.3e6 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in y around 0 80.0%

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

   5. Taylor expanded in t around 0 46.0%

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

   if -8.60000000000000003e-11 < z < 5.3e6

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 78.8%

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

   3. Taylor expanded in z around 0 66.9%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-11} \lor \neg \left(z \leq 5300000\right):\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]

2. Final simplification 100.0%

   \[\leadsto x - \left(y - z\right) \cdot \left(x - t\right) \]

Alternative 10: 41.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]

2. Taylor expanded in t around inf 60.4%

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

3. Taylor expanded in z around 0 38.8%

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

4. Final simplification 38.8%

   \[\leadsto x + y \cdot t \]

Alternative 11: 17.5% 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. Taylor expanded in t around inf 60.4%

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

3. Taylor expanded in x around inf 16.5%

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

4. Final simplification 16.5%

   \[\leadsto x \]

Developer target: 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 2023182 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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