Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.3s

Alternatives: 11

Speedup: 1.0×

• 34.4% 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. Final simplification 100.0%

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

Alternative 2: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-65}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-229}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 159000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))) (t_2 (* z (- x t))) (t_3 (* x (+ (- z y) 1.0))))
   (if (<= z -4.4e+129)
     t_2
     (if (<= z -7.4e-65)
       t_3
       (if (<= z -2.7e-307)
         t_1
         (if (<= z 1.5e-229) t_3 (if (<= z 159000000000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = z * (x - t);
	double t_3 = x * ((z - y) + 1.0);
	double tmp;
	if (z <= -4.4e+129) {
		tmp = t_2;
	} else if (z <= -7.4e-65) {
		tmp = t_3;
	} else if (z <= -2.7e-307) {
		tmp = t_1;
	} else if (z <= 1.5e-229) {
		tmp = t_3;
	} else if (z <= 159000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x + (y * t)
    t_2 = z * (x - t)
    t_3 = x * ((z - y) + 1.0d0)
    if (z <= (-4.4d+129)) then
        tmp = t_2
    else if (z <= (-7.4d-65)) then
        tmp = t_3
    else if (z <= (-2.7d-307)) then
        tmp = t_1
    else if (z <= 1.5d-229) then
        tmp = t_3
    else if (z <= 159000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = z * (x - t);
	double t_3 = x * ((z - y) + 1.0);
	double tmp;
	if (z <= -4.4e+129) {
		tmp = t_2;
	} else if (z <= -7.4e-65) {
		tmp = t_3;
	} else if (z <= -2.7e-307) {
		tmp = t_1;
	} else if (z <= 1.5e-229) {
		tmp = t_3;
	} else if (z <= 159000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	t_2 = z * (x - t)
	t_3 = x * ((z - y) + 1.0)
	tmp = 0
	if z <= -4.4e+129:
		tmp = t_2
	elif z <= -7.4e-65:
		tmp = t_3
	elif z <= -2.7e-307:
		tmp = t_1
	elif z <= 1.5e-229:
		tmp = t_3
	elif z <= 159000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (z <= -4.4e+129)
		tmp = t_2;
	elseif (z <= -7.4e-65)
		tmp = t_3;
	elseif (z <= -2.7e-307)
		tmp = t_1;
	elseif (z <= 1.5e-229)
		tmp = t_3;
	elseif (z <= 159000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	t_2 = z * (x - t);
	t_3 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (z <= -4.4e+129)
		tmp = t_2;
	elseif (z <= -7.4e-65)
		tmp = t_3;
	elseif (z <= -2.7e-307)
		tmp = t_1;
	elseif (z <= 1.5e-229)
		tmp = t_3;
	elseif (z <= 159000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+129], t$95$2, If[LessEqual[z, -7.4e-65], t$95$3, If[LessEqual[z, -2.7e-307], t$95$1, If[LessEqual[z, 1.5e-229], t$95$3, If[LessEqual[z, 159000000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3999999999999999e129 or 1.59e11 < 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 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around inf 81.6%

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

   if -4.3999999999999999e129 < z < -7.4e-65 or -2.69999999999999985e-307 < z < 1.50000000000000001e-229

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. unsub-neg 70.3%

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

   5. Simplified 70.3%

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

   if -7.4e-65 < z < -2.69999999999999985e-307 or 1.50000000000000001e-229 < z < 1.59e11

   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 84.4%

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

   4. Taylor expanded in y around inf 78.0%

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

      1. *-commutative 78.0%

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

   6. Simplified 78.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+129}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-307}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;z \leq 159000000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -9.4 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+95} \lor \neg \left(y \leq 5.7 \cdot 10^{+113}\right) \land y \leq 3.2 \cdot 10^{+219}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -9.4e+117)
     t_1
     (if (<= y 1.45e+15)
       (* x (+ z 1.0))
       (if (or (<= y 8.8e+95) (and (not (<= y 5.7e+113)) (<= y 3.2e+219)))
         t_1
         (* y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -9.4e+117) {
		tmp = t_1;
	} else if (y <= 1.45e+15) {
		tmp = x * (z + 1.0);
	} else if ((y <= 8.8e+95) || (!(y <= 5.7e+113) && (y <= 3.2e+219))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (y <= (-9.4d+117)) then
        tmp = t_1
    else if (y <= 1.45d+15) then
        tmp = x * (z + 1.0d0)
    else if ((y <= 8.8d+95) .or. (.not. (y <= 5.7d+113)) .and. (y <= 3.2d+219)) then
        tmp = t_1
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -9.4e+117) {
		tmp = t_1;
	} else if (y <= 1.45e+15) {
		tmp = x * (z + 1.0);
	} else if ((y <= 8.8e+95) || (!(y <= 5.7e+113) && (y <= 3.2e+219))) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -9.4e+117:
		tmp = t_1
	elif y <= 1.45e+15:
		tmp = x * (z + 1.0)
	elif (y <= 8.8e+95) or (not (y <= 5.7e+113) and (y <= 3.2e+219)):
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -9.4e+117)
		tmp = t_1;
	elseif (y <= 1.45e+15)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((y <= 8.8e+95) || (!(y <= 5.7e+113) && (y <= 3.2e+219)))
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -9.4e+117)
		tmp = t_1;
	elseif (y <= 1.45e+15)
		tmp = x * (z + 1.0);
	elseif ((y <= 8.8e+95) || (~((y <= 5.7e+113)) && (y <= 3.2e+219)))
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -9.4e+117], t$95$1, If[LessEqual[y, 1.45e+15], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.8e+95], And[N[Not[LessEqual[y, 5.7e+113]], $MachinePrecision], LessEqual[y, 3.2e+219]]], t$95$1, N[(y * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.40000000000000011e117 or 1.45e15 < y < 8.7999999999999996e95 or 5.6999999999999998e113 < y < 3.20000000000000026e219

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in y around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. distribute-lft-neg-out 59.4%

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

      3. *-commutative 59.4%

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

   8. Simplified 59.4%

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

   if -9.40000000000000011e117 < y < 1.45e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in y around 0 59.3%

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

      1. +-commutative 59.3%

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

   8. Simplified 59.3%

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

   if 8.7999999999999996e95 < y < 5.6999999999999998e113 or 3.20000000000000026e219 < y

   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 85.0%

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

   4. Taylor expanded in y around inf 78.0%

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

      1. *-commutative 78.0%

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

   6. Simplified 78.0%

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

   7. Taylor expanded in x around 0 78.0%

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

      1. *-commutative 78.0%

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

   9. Simplified 78.0%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+95} \lor \neg \left(y \leq 5.7 \cdot 10^{+113}\right) \land y \leq 3.2 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-300}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 159000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y t))))
   (if (<= z -1.65e-19)
     t_1
     (if (<= z 2.9e-300)
       t_2
       (if (<= z 6e-230)
         (* x (- 1.0 y))
         (if (<= z 159000000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -1.65e-19) {
		tmp = t_1;
	} else if (z <= 2.9e-300) {
		tmp = t_2;
	} else if (z <= 6e-230) {
		tmp = x * (1.0 - y);
	} else if (z <= 159000000000.0) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = x + (y * t)
    if (z <= (-1.65d-19)) then
        tmp = t_1
    else if (z <= 2.9d-300) then
        tmp = t_2
    else if (z <= 6d-230) then
        tmp = x * (1.0d0 - y)
    else if (z <= 159000000000.0d0) then
        tmp = t_2
    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 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -1.65e-19) {
		tmp = t_1;
	} else if (z <= 2.9e-300) {
		tmp = t_2;
	} else if (z <= 6e-230) {
		tmp = x * (1.0 - y);
	} else if (z <= 159000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -1.65e-19:
		tmp = t_1
	elif z <= 2.9e-300:
		tmp = t_2
	elif z <= 6e-230:
		tmp = x * (1.0 - y)
	elif z <= 159000000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -1.65e-19)
		tmp = t_1;
	elseif (z <= 2.9e-300)
		tmp = t_2;
	elseif (z <= 6e-230)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 159000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -1.65e-19)
		tmp = t_1;
	elseif (z <= 2.9e-300)
		tmp = t_2;
	elseif (z <= 6e-230)
		tmp = x * (1.0 - y);
	elseif (z <= 159000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-19], t$95$1, If[LessEqual[z, 2.9e-300], t$95$2, If[LessEqual[z, 6e-230], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 159000000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6499999999999999e-19 or 1.59e11 < 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 76.7%

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

      1. mul-1-neg 76.7%

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

      2. unsub-neg 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in z around inf 75.3%

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

   if -1.6499999999999999e-19 < z < 2.89999999999999992e-300 or 6e-230 < z < 1.59e11

   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 83.8%

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

   4. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if 2.89999999999999992e-300 < z < 6e-230

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in z around 0 79.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-300}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 159000000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-5}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.02e-5)
   (* z x)
   (if (<= z 1.32e-225) x (if (<= z 4.5e+80) (* y t) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02e-5) {
		tmp = z * x;
	} else if (z <= 1.32e-225) {
		tmp = x;
	} else if (z <= 4.5e+80) {
		tmp = y * 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 (z <= (-1.02d-5)) then
        tmp = z * x
    else if (z <= 1.32d-225) then
        tmp = x
    else if (z <= 4.5d+80) then
        tmp = y * 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 (z <= -1.02e-5) {
		tmp = z * x;
	} else if (z <= 1.32e-225) {
		tmp = x;
	} else if (z <= 4.5e+80) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.02e-5:
		tmp = z * x
	elif z <= 1.32e-225:
		tmp = x
	elif z <= 4.5e+80:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.02e-5)
		tmp = Float64(z * x);
	elseif (z <= 1.32e-225)
		tmp = x;
	elseif (z <= 4.5e+80)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.02e-5)
		tmp = z * x;
	elseif (z <= 1.32e-225)
		tmp = x;
	elseif (z <= 4.5e+80)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.02e-5], N[(z * x), $MachinePrecision], If[LessEqual[z, 1.32e-225], x, If[LessEqual[z, 4.5e+80], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0200000000000001e-5 or 4.50000000000000007e80 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in z around inf 51.4%

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

   if -1.0200000000000001e-5 < z < 1.32e-225

   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 77.7%

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

   4. Taylor expanded in x around inf 42.7%

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

   if 1.32e-225 < z < 4.50000000000000007e80

   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 77.1%

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

   4. Taylor expanded in y around inf 62.5%

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

      1. *-commutative 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in x around 0 38.5%

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

      1. *-commutative 38.5%

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

   9. Simplified 38.5%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-5}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+54} \lor \neg \left(t \leq 7.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.2e+54) (not (<= t 7.2e+37)))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e+54) || !(t <= 7.2e+37)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	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 <= (-5.2d+54)) .or. (.not. (t <= 7.2d+37))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e+54) || !(t <= 7.2e+37)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.2e+54) or not (t <= 7.2e+37):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.2e+54) || !(t <= 7.2e+37))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.2e+54) || ~((t <= 7.2e+37)))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.2e+54], N[Not[LessEqual[t, 7.2e+37]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.20000000000000013e54 or 7.19999999999999995e37 < 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 92.8%

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

   if -5.20000000000000013e54 < t < 7.19999999999999995e37

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

   5. Simplified 82.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \left(y - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+54} \lor \neg \left(t \leq 7.2 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-5} \lor \neg \left(z \leq 159000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e-5) (not (<= z 159000000000.0)))
   (* z (- x t))
   (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-5) || !(z <= 159000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x * (1.0 - 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 <= (-1d-5)) .or. (.not. (z <= 159000000000.0d0))) then
        tmp = z * (x - t)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-5) || !(z <= 159000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e-5) or not (z <= 159000000000.0):
		tmp = z * (x - t)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e-5) || !(z <= 159000000000.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1e-5) || ~((z <= 159000000000.0)))
		tmp = z * (x - t);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e-5], N[Not[LessEqual[z, 159000000000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000008e-5 or 1.59e11 < 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 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in z around inf 76.3%

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

   if -1.00000000000000008e-5 < z < 1.59e11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around 0 61.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-5} \lor \neg \left(z \leq 159000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -18000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -18000000.0)
   (* x (+ z 1.0))
   (if (<= z 5e+116) (* x (- 1.0 y)) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -18000000.0) {
		tmp = x * (z + 1.0);
	} else if (z <= 5e+116) {
		tmp = x * (1.0 - y);
	} 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 (z <= (-18000000.0d0)) then
        tmp = x * (z + 1.0d0)
    else if (z <= 5d+116) then
        tmp = x * (1.0d0 - y)
    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 (z <= -18000000.0) {
		tmp = x * (z + 1.0);
	} else if (z <= 5e+116) {
		tmp = x * (1.0 - y);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -18000000.0:
		tmp = x * (z + 1.0)
	elif z <= 5e+116:
		tmp = x * (1.0 - y)
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -18000000.0)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (z <= 5e+116)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -18000000.0)
		tmp = x * (z + 1.0);
	elseif (z <= 5e+116)
		tmp = x * (1.0 - y);
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -18000000.0], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+116], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8e7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. unsub-neg 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in y around 0 46.3%

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

      1. +-commutative 46.3%

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

   8. Simplified 46.3%

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

   if -1.8e7 < z < 5.00000000000000025e116

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in z around 0 55.8%

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

   if 5.00000000000000025e116 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.6%

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

      1. mul-1-neg 72.6%

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

      2. unsub-neg 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-5} \lor \neg \left(z \leq 159000000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02e-5) (not (<= z 159000000000.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e-5) || !(z <= 159000000000.0)) {
		tmp = z * x;
	} 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 <= (-1.02d-5)) .or. (.not. (z <= 159000000000.0d0))) then
        tmp = z * x
    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 <= -1.02e-5) || !(z <= 159000000000.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.02e-5) or not (z <= 159000000000.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.02e-5) || !(z <= 159000000000.0))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.02e-5) || ~((z <= 159000000000.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.02e-5], N[Not[LessEqual[z, 159000000000.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.0200000000000001e-5 or 1.59e11 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in z around inf 47.1%

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

   if -1.0200000000000001e-5 < z < 1.59e11

   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 79.2%

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

   4. Taylor expanded in x around inf 40.3%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-5} \lor \neg \left(z \leq 159000000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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. Final simplification 100.0%

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

Alternative 11: 17.7% 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 63.2%

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

4. Taylor expanded in x around inf 21.3%

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

5. Final simplification 21.3%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.2% 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 2024068 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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