Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Alternatives: 10

Speedup: 1.0×

• 34.7% 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. Final simplification 100.0%

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

Alternative 2: 70.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot y\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x + y \cdot t\\ \mathbf{if}\;z \leq -0.84:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-59}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* x y))) (t_2 (* z (- x t))) (t_3 (+ x (* y t))))
   (if (<= z -0.84)
     t_2
     (if (<= z -3.6e-59)
       t_3
       (if (<= z -1.95e-234)
         t_1
         (if (<= z 6.4e-106) t_3 (if (<= z 1.06e+26) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (x * y);
	double t_2 = z * (x - t);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -0.84) {
		tmp = t_2;
	} else if (z <= -3.6e-59) {
		tmp = t_3;
	} else if (z <= -1.95e-234) {
		tmp = t_1;
	} else if (z <= 6.4e-106) {
		tmp = t_3;
	} else if (z <= 1.06e+26) {
		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 - (x * y)
    t_2 = z * (x - t)
    t_3 = x + (y * t)
    if (z <= (-0.84d0)) then
        tmp = t_2
    else if (z <= (-3.6d-59)) then
        tmp = t_3
    else if (z <= (-1.95d-234)) then
        tmp = t_1
    else if (z <= 6.4d-106) then
        tmp = t_3
    else if (z <= 1.06d+26) 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 - (x * y);
	double t_2 = z * (x - t);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -0.84) {
		tmp = t_2;
	} else if (z <= -3.6e-59) {
		tmp = t_3;
	} else if (z <= -1.95e-234) {
		tmp = t_1;
	} else if (z <= 6.4e-106) {
		tmp = t_3;
	} else if (z <= 1.06e+26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (x * y)
	t_2 = z * (x - t)
	t_3 = x + (y * t)
	tmp = 0
	if z <= -0.84:
		tmp = t_2
	elif z <= -3.6e-59:
		tmp = t_3
	elif z <= -1.95e-234:
		tmp = t_1
	elif z <= 6.4e-106:
		tmp = t_3
	elif z <= 1.06e+26:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(x * y))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -0.84)
		tmp = t_2;
	elseif (z <= -3.6e-59)
		tmp = t_3;
	elseif (z <= -1.95e-234)
		tmp = t_1;
	elseif (z <= 6.4e-106)
		tmp = t_3;
	elseif (z <= 1.06e+26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (x * y);
	t_2 = z * (x - t);
	t_3 = x + (y * t);
	tmp = 0.0;
	if (z <= -0.84)
		tmp = t_2;
	elseif (z <= -3.6e-59)
		tmp = t_3;
	elseif (z <= -1.95e-234)
		tmp = t_1;
	elseif (z <= 6.4e-106)
		tmp = t_3;
	elseif (z <= 1.06e+26)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.84], t$95$2, If[LessEqual[z, -3.6e-59], t$95$3, If[LessEqual[z, -1.95e-234], t$95$1, If[LessEqual[z, 6.4e-106], t$95$3, If[LessEqual[z, 1.06e+26], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.839999999999999969 or 1.05999999999999997e26 < 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%

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

      1. mul-1-neg 79.6%

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

      2. distribute-rgt-neg-in 79.6%

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

      3. sub-neg 79.6%

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

      4. +-commutative 79.6%

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

      5. distribute-neg-in 79.6%

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

      6. remove-double-neg 79.6%

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

      7. sub-neg 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in z around inf 79.1%

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

   if -0.839999999999999969 < z < -3.6e-59 or -1.9500000000000001e-234 < z < 6.4e-106

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 93.7%

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

      1. *-commutative 93.7%

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

   5. Simplified 93.7%

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

   6. Taylor expanded in t around inf 75.8%

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

      1. *-commutative 75.8%

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

   8. Simplified 75.8%

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

   if -3.6e-59 < z < -1.9500000000000001e-234 or 6.4e-106 < z < 1.05999999999999997e26

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.4%

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

      1. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in t around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. *-commutative 68.4%

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

      3. distribute-rgt-neg-out 68.4%

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

   8. Simplified 68.4%

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

      1. distribute-rgt-neg-out 68.4%

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

      2. unsub-neg 68.4%

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

   10. Applied egg-rr 68.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.84:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-234}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-106}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+26}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-235}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* (- y z) t))))
   (if (<= z -2.15e+26)
     t_1
     (if (<= z -1.9e-63)
       t_2
       (if (<= z -6.1e-235) (- x (* x y)) (if (<= z 1e+103) 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 - z) * t);
	double tmp;
	if (z <= -2.15e+26) {
		tmp = t_1;
	} else if (z <= -1.9e-63) {
		tmp = t_2;
	} else if (z <= -6.1e-235) {
		tmp = x - (x * y);
	} else if (z <= 1e+103) {
		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 - z) * t)
    if (z <= (-2.15d+26)) then
        tmp = t_1
    else if (z <= (-1.9d-63)) then
        tmp = t_2
    else if (z <= (-6.1d-235)) then
        tmp = x - (x * y)
    else if (z <= 1d+103) 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 - z) * t);
	double tmp;
	if (z <= -2.15e+26) {
		tmp = t_1;
	} else if (z <= -1.9e-63) {
		tmp = t_2;
	} else if (z <= -6.1e-235) {
		tmp = x - (x * y);
	} else if (z <= 1e+103) {
		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 - z) * t)
	tmp = 0
	if z <= -2.15e+26:
		tmp = t_1
	elif z <= -1.9e-63:
		tmp = t_2
	elif z <= -6.1e-235:
		tmp = x - (x * y)
	elif z <= 1e+103:
		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(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -2.15e+26)
		tmp = t_1;
	elseif (z <= -1.9e-63)
		tmp = t_2;
	elseif (z <= -6.1e-235)
		tmp = Float64(x - Float64(x * y));
	elseif (z <= 1e+103)
		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 - z) * t);
	tmp = 0.0;
	if (z <= -2.15e+26)
		tmp = t_1;
	elseif (z <= -1.9e-63)
		tmp = t_2;
	elseif (z <= -6.1e-235)
		tmp = x - (x * y);
	elseif (z <= 1e+103)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+26], t$95$1, If[LessEqual[z, -1.9e-63], t$95$2, If[LessEqual[z, -6.1e-235], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+103], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1499999999999999e26 or 1e103 < 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 86.3%

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

      1. mul-1-neg 86.3%

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

      2. distribute-rgt-neg-in 86.3%

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

      3. sub-neg 86.3%

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

      4. +-commutative 86.3%

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

      5. distribute-neg-in 86.3%

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

      6. remove-double-neg 86.3%

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

      7. sub-neg 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in z around inf 86.3%

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

   if -2.1499999999999999e26 < z < -1.90000000000000009e-63 or -6.09999999999999988e-235 < z < 1e103

   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 73.4%

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

   if -1.90000000000000009e-63 < z < -6.09999999999999988e-235

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.0%

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

      1. *-commutative 95.0%

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

   5. Simplified 95.0%

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

   6. Taylor expanded in t around 0 72.7%

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

      1. mul-1-neg 72.7%

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

      2. *-commutative 72.7%

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

      3. distribute-rgt-neg-out 72.7%

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

   8. Simplified 72.7%

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

      1. distribute-rgt-neg-out 72.7%

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

      2. unsub-neg 72.7%

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

   10. Applied egg-rr 72.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-235}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 10^{+103}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* x (- y))))
   (if (<= z -3.2e-55)
     t_1
     (if (<= z -2.45e-198)
       t_2
       (if (<= z 2.9e-160) x (if (<= z 2.6e+26) 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;
	double tmp;
	if (z <= -3.2e-55) {
		tmp = t_1;
	} else if (z <= -2.45e-198) {
		tmp = t_2;
	} else if (z <= 2.9e-160) {
		tmp = x;
	} else if (z <= 2.6e+26) {
		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
    if (z <= (-3.2d-55)) then
        tmp = t_1
    else if (z <= (-2.45d-198)) then
        tmp = t_2
    else if (z <= 2.9d-160) then
        tmp = x
    else if (z <= 2.6d+26) 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;
	double tmp;
	if (z <= -3.2e-55) {
		tmp = t_1;
	} else if (z <= -2.45e-198) {
		tmp = t_2;
	} else if (z <= 2.9e-160) {
		tmp = x;
	} else if (z <= 2.6e+26) {
		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
	tmp = 0
	if z <= -3.2e-55:
		tmp = t_1
	elif z <= -2.45e-198:
		tmp = t_2
	elif z <= 2.9e-160:
		tmp = x
	elif z <= 2.6e+26:
		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))
	tmp = 0.0
	if (z <= -3.2e-55)
		tmp = t_1;
	elseif (z <= -2.45e-198)
		tmp = t_2;
	elseif (z <= 2.9e-160)
		tmp = x;
	elseif (z <= 2.6e+26)
		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;
	tmp = 0.0;
	if (z <= -3.2e-55)
		tmp = t_1;
	elseif (z <= -2.45e-198)
		tmp = t_2;
	elseif (z <= 2.9e-160)
		tmp = x;
	elseif (z <= 2.6e+26)
		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 * (-y)), $MachinePrecision]}, If[LessEqual[z, -3.2e-55], t$95$1, If[LessEqual[z, -2.45e-198], t$95$2, If[LessEqual[z, 2.9e-160], x, If[LessEqual[z, 2.6e+26], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2000000000000001e-55 or 2.60000000000000002e26 < 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%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

      3. sub-neg 76.9%

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

      4. +-commutative 76.9%

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

      5. distribute-neg-in 76.9%

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

      6. remove-double-neg 76.9%

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

      7. sub-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in z around inf 75.7%

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

   if -3.2000000000000001e-55 < z < -2.4500000000000001e-198 or 2.8999999999999999e-160 < z < 2.60000000000000002e26

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.2%

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

      1. *-commutative 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in t around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. *-commutative 64.6%

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

      3. distribute-rgt-neg-out 64.6%

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

   8. Simplified 64.6%

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

   9. Taylor expanded in y around inf 44.6%

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

       1. mul-1-neg 44.6%

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

       2. *-commutative 44.6%

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

       3. distribute-lft-neg-in 44.6%

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

   11. Simplified 44.6%

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

   if -2.4500000000000001e-198 < z < 2.8999999999999999e-160

   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 45.9%

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

      1. mul-1-neg 45.9%

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

      2. distribute-rgt-neg-in 45.9%

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

      3. sub-neg 45.9%

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

      4. +-commutative 45.9%

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

      5. distribute-neg-in 45.9%

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

      6. remove-double-neg 45.9%

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

      7. sub-neg 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in z around 0 43.9%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+99}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -1.9e+22)
     t_1
     (if (<= y -7.5e-87)
       (* x z)
       (if (<= y 3e-118) x (if (<= y 1.6e+99) (* x z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.9e+22) {
		tmp = t_1;
	} else if (y <= -7.5e-87) {
		tmp = x * z;
	} else if (y <= 3e-118) {
		tmp = x;
	} else if (y <= 1.6e+99) {
		tmp = x * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * -y
    if (y <= (-1.9d+22)) then
        tmp = t_1
    else if (y <= (-7.5d-87)) then
        tmp = x * z
    else if (y <= 3d-118) then
        tmp = x
    else if (y <= 1.6d+99) then
        tmp = x * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.9e+22) {
		tmp = t_1;
	} else if (y <= -7.5e-87) {
		tmp = x * z;
	} else if (y <= 3e-118) {
		tmp = x;
	} else if (y <= 1.6e+99) {
		tmp = x * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -1.9e+22:
		tmp = t_1
	elif y <= -7.5e-87:
		tmp = x * z
	elif y <= 3e-118:
		tmp = x
	elif y <= 1.6e+99:
		tmp = x * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.9e+22)
		tmp = t_1;
	elseif (y <= -7.5e-87)
		tmp = Float64(x * z);
	elseif (y <= 3e-118)
		tmp = x;
	elseif (y <= 1.6e+99)
		tmp = Float64(x * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	tmp = 0.0;
	if (y <= -1.9e+22)
		tmp = t_1;
	elseif (y <= -7.5e-87)
		tmp = x * z;
	elseif (y <= 3e-118)
		tmp = x;
	elseif (y <= 1.6e+99)
		tmp = x * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.9e+22], t$95$1, If[LessEqual[y, -7.5e-87], N[(x * z), $MachinePrecision], If[LessEqual[y, 3e-118], x, If[LessEqual[y, 1.6e+99], N[(x * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000002e22 or 1.6e99 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.2%

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

      1. *-commutative 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in t around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. *-commutative 49.2%

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

      3. distribute-rgt-neg-out 49.2%

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

   8. Simplified 49.2%

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

   9. Taylor expanded in y around inf 49.2%

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

       1. mul-1-neg 49.2%

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

       2. *-commutative 49.2%

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

       3. distribute-lft-neg-in 49.2%

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

   11. Simplified 49.2%

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

   if -1.9000000000000002e22 < y < -7.5000000000000002e-87 or 3.00000000000000018e-118 < y < 1.6e99

   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%

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

      1. mul-1-neg 76.7%

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

      2. distribute-rgt-neg-in 76.7%

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

      3. sub-neg 76.7%

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

      4. +-commutative 76.7%

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

      5. distribute-neg-in 76.7%

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

      6. remove-double-neg 76.7%

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

      7. sub-neg 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 54.0%

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

   7. Taylor expanded in z around inf 42.1%

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

      1. *-commutative 42.1%

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

   9. Simplified 42.1%

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

   if -7.5000000000000002e-87 < y < 3.00000000000000018e-118

   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 95.3%

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

      1. mul-1-neg 95.3%

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

      2. distribute-rgt-neg-in 95.3%

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

      3. sub-neg 95.3%

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

      4. +-commutative 95.3%

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

      5. distribute-neg-in 95.3%

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

      6. remove-double-neg 95.3%

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

      7. sub-neg 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in z around 0 40.4%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+99}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-28} \lor \neg \left(t \leq 7 \cdot 10^{+14}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.7e-28) (not (<= t 7e+14)))
   (+ x (* (- y z) t))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.7e-28) || !(t <= 7e+14)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.7d-28)) .or. (.not. (t <= 7d+14))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.7e-28) || !(t <= 7e+14)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.7e-28) or not (t <= 7e+14):
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.7e-28) || !(t <= 7e+14))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.7e-28) || ~((t <= 7e+14)))
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.7e-28], N[Not[LessEqual[t, 7e+14]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6999999999999999e-28 or 7e14 < 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 84.5%

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

   if -2.6999999999999999e-28 < t < 7e14

   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 87.0%

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

      1. mul-1-neg 87.0%

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

      2. distribute-rgt-neg-in 87.0%

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

      3. sub-neg 87.0%

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

      4. +-commutative 87.0%

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

      5. distribute-neg-in 87.0%

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

      6. remove-double-neg 87.0%

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

      7. sub-neg 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-28} \lor \neg \left(t \leq 7 \cdot 10^{+14}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00085 \lor \neg \left(z \leq 4.5 \cdot 10^{+103}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00085) (not (<= z 4.5e+103)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00085) || !(z <= 4.5e+103)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.00085d0)) .or. (.not. (z <= 4.5d+103))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00085) || !(z <= 4.5e+103)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00085) or not (z <= 4.5e+103):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00085) || !(z <= 4.5e+103))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00085) || ~((z <= 4.5e+103)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00085], N[Not[LessEqual[z, 4.5e+103]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999953e-4 or 4.50000000000000001e103 < 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 86.1%

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

      1. mul-1-neg 86.1%

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

      2. distribute-rgt-neg-in 86.1%

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

      3. sub-neg 86.1%

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

      4. +-commutative 86.1%

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

      5. distribute-neg-in 86.1%

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

      6. remove-double-neg 86.1%

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

      7. sub-neg 86.1%

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

   5. Simplified 86.1%

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

   if -8.49999999999999953e-4 < z < 4.50000000000000001e103

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.2%

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

      1. *-commutative 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00085 \lor \neg \left(z \leq 4.5 \cdot 10^{+103}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \lor \neg \left(z \leq 1.35 \cdot 10^{+103}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.55) (not (<= z 1.35e+103))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55) || !(z <= 1.35e+103)) {
		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 <= (-1.55d0)) .or. (.not. (z <= 1.35d+103))) 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 <= -1.55) || !(z <= 1.35e+103)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.55) or not (z <= 1.35e+103):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.55) || !(z <= 1.35e+103))
		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 <= -1.55) || ~((z <= 1.35e+103)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.55], N[Not[LessEqual[z, 1.35e+103]], $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 < -1.55000000000000004 or 1.34999999999999996e103 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.3%

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

      1. mul-1-neg 85.3%

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

      2. distribute-rgt-neg-in 85.3%

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

      3. sub-neg 85.3%

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

      4. +-commutative 85.3%

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

      5. distribute-neg-in 85.3%

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

      6. remove-double-neg 85.3%

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

      7. sub-neg 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in z around inf 84.8%

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

   if -1.55000000000000004 < z < 1.34999999999999996e103

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in t around inf 61.2%

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

      1. *-commutative 61.2%

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

   8. Simplified 61.2%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \lor \neg \left(z \leq 1.35 \cdot 10^{+103}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -190 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -190.0) (not (<= z 1.0))) (* x z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -190.0) || !(z <= 1.0)) {
		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 <= (-190.0d0)) .or. (.not. (z <= 1.0d0))) 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 <= -190.0) || !(z <= 1.0)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -190.0) or not (z <= 1.0):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -190.0) || !(z <= 1.0))
		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 <= -190.0) || ~((z <= 1.0)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -190.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -190 or 1 < 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 77.1%

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

      1. mul-1-neg 77.1%

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

      2. distribute-rgt-neg-in 77.1%

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

      3. sub-neg 77.1%

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

      4. +-commutative 77.1%

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

      5. distribute-neg-in 77.1%

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

      6. remove-double-neg 77.1%

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

      7. sub-neg 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in t around 0 41.7%

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

   7. Taylor expanded in z around inf 40.6%

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

      1. *-commutative 40.6%

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

   9. Simplified 40.6%

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

   if -190 < z < 1

   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 40.3%

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

      1. mul-1-neg 40.3%

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

      2. distribute-rgt-neg-in 40.3%

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

      3. sub-neg 40.3%

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

      4. +-commutative 40.3%

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

      5. distribute-neg-in 40.3%

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

      6. remove-double-neg 40.3%

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

      7. sub-neg 40.3%

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

   5. Simplified 40.3%

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

   6. Taylor expanded in z around 0 32.2%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -190 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 17.4% 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 y around 0 58.6%

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

   1. mul-1-neg 58.6%

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

   2. distribute-rgt-neg-in 58.6%

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

   3. sub-neg 58.6%

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

   4. +-commutative 58.6%

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

   5. distribute-neg-in 58.6%

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

   6. remove-double-neg 58.6%

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

   7. sub-neg 58.6%

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

5. Simplified 58.6%

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

6. Taylor expanded in z around 0 17.7%

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

7. Final simplification 17.7%

   \[\leadsto x \]
8. 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 2024071 
(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))))