Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.2s

Alternatives: 13

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, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. flip-- 76.5%

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

   2. associate-*r/ 70.9%

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

3. Applied egg-rr 70.9%

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

   1. *-commutative 70.9%

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

   2. associate-*l/ 76.5%

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

   3. difference-of-squares 79.3%

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

   4. associate-/l* 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 37.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+56}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq -20.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-87}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= y -3.4e+56)
     (* t y)
     (if (<= y -20.5)
       t_1
       (if (<= y -1.1e-87)
         (* t y)
         (if (<= y -1.8e-192)
           x
           (if (<= y 4e-194)
             t_1
             (if (<= y 5.5e-76) x (if (<= y 5e-21) t_1 (* x (- y)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (y <= -3.4e+56) {
		tmp = t * y;
	} else if (y <= -20.5) {
		tmp = t_1;
	} else if (y <= -1.1e-87) {
		tmp = t * y;
	} else if (y <= -1.8e-192) {
		tmp = x;
	} else if (y <= 4e-194) {
		tmp = t_1;
	} else if (y <= 5.5e-76) {
		tmp = x;
	} else if (y <= 5e-21) {
		tmp = t_1;
	} else {
		tmp = x * -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) :: t_1
    real(8) :: tmp
    t_1 = t * -z
    if (y <= (-3.4d+56)) then
        tmp = t * y
    else if (y <= (-20.5d0)) then
        tmp = t_1
    else if (y <= (-1.1d-87)) then
        tmp = t * y
    else if (y <= (-1.8d-192)) then
        tmp = x
    else if (y <= 4d-194) then
        tmp = t_1
    else if (y <= 5.5d-76) then
        tmp = x
    else if (y <= 5d-21) then
        tmp = t_1
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (y <= -3.4e+56) {
		tmp = t * y;
	} else if (y <= -20.5) {
		tmp = t_1;
	} else if (y <= -1.1e-87) {
		tmp = t * y;
	} else if (y <= -1.8e-192) {
		tmp = x;
	} else if (y <= 4e-194) {
		tmp = t_1;
	} else if (y <= 5.5e-76) {
		tmp = x;
	} else if (y <= 5e-21) {
		tmp = t_1;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if y <= -3.4e+56:
		tmp = t * y
	elif y <= -20.5:
		tmp = t_1
	elif y <= -1.1e-87:
		tmp = t * y
	elif y <= -1.8e-192:
		tmp = x
	elif y <= 4e-194:
		tmp = t_1
	elif y <= 5.5e-76:
		tmp = x
	elif y <= 5e-21:
		tmp = t_1
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (y <= -3.4e+56)
		tmp = Float64(t * y);
	elseif (y <= -20.5)
		tmp = t_1;
	elseif (y <= -1.1e-87)
		tmp = Float64(t * y);
	elseif (y <= -1.8e-192)
		tmp = x;
	elseif (y <= 4e-194)
		tmp = t_1;
	elseif (y <= 5.5e-76)
		tmp = x;
	elseif (y <= 5e-21)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (y <= -3.4e+56)
		tmp = t * y;
	elseif (y <= -20.5)
		tmp = t_1;
	elseif (y <= -1.1e-87)
		tmp = t * y;
	elseif (y <= -1.8e-192)
		tmp = x;
	elseif (y <= 4e-194)
		tmp = t_1;
	elseif (y <= 5.5e-76)
		tmp = x;
	elseif (y <= 5e-21)
		tmp = t_1;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[y, -3.4e+56], N[(t * y), $MachinePrecision], If[LessEqual[y, -20.5], t$95$1, If[LessEqual[y, -1.1e-87], N[(t * y), $MachinePrecision], If[LessEqual[y, -1.8e-192], x, If[LessEqual[y, 4e-194], t$95$1, If[LessEqual[y, 5.5e-76], x, If[LessEqual[y, 5e-21], t$95$1, N[(x * (-y)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.40000000000000001e56 or -20.5 < y < -1.09999999999999994e-87

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 68.0%

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

   3. Taylor expanded in y around inf 59.3%

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

   if -3.40000000000000001e56 < y < -20.5 or -1.7999999999999999e-192 < y < 4.00000000000000007e-194 or 5.50000000000000014e-76 < y < 4.99999999999999973e-21

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.8%

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

   3. Taylor expanded in z around inf 54.8%

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

      1. associate-*r* 54.8%

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

      2. mul-1-neg 54.8%

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

   5. Simplified 54.8%

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

   if -1.09999999999999994e-87 < y < -1.7999999999999999e-192 or 4.00000000000000007e-194 < y < 5.50000000000000014e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 67.3%

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

   3. Taylor expanded in x around inf 39.4%

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

   if 4.99999999999999973e-21 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.5%

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

      1. *-commutative 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in x around inf 47.4%

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

      1. +-commutative 47.4%

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

      2. distribute-rgt1-in 47.4%

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

      3. associate-*r* 47.4%

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

      4. mul-1-neg 47.4%

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

      5. unsub-neg 47.4%

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

   7. Simplified 47.4%

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

   8. Taylor expanded in y around inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. distribute-rgt-neg-out 44.8%

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

   10. Simplified 44.8%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+56}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq -20.5:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-87}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y - z\right)\\ t_2 := x + x \cdot z\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- y z))) (t_2 (+ x (* x z))))
   (if (<= t -6.8e-101)
     t_1
     (if (<= t -1.7e-189)
       t_2
       (if (<= t -7.1e-205) (* x (- y)) (if (<= t 5.1e-110) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y - z);
	double t_2 = x + (x * z);
	double tmp;
	if (t <= -6.8e-101) {
		tmp = t_1;
	} else if (t <= -1.7e-189) {
		tmp = t_2;
	} else if (t <= -7.1e-205) {
		tmp = x * -y;
	} else if (t <= 5.1e-110) {
		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 = t * (y - z)
    t_2 = x + (x * z)
    if (t <= (-6.8d-101)) then
        tmp = t_1
    else if (t <= (-1.7d-189)) then
        tmp = t_2
    else if (t <= (-7.1d-205)) then
        tmp = x * -y
    else if (t <= 5.1d-110) 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 = t * (y - z);
	double t_2 = x + (x * z);
	double tmp;
	if (t <= -6.8e-101) {
		tmp = t_1;
	} else if (t <= -1.7e-189) {
		tmp = t_2;
	} else if (t <= -7.1e-205) {
		tmp = x * -y;
	} else if (t <= 5.1e-110) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y - z)
	t_2 = x + (x * z)
	tmp = 0
	if t <= -6.8e-101:
		tmp = t_1
	elif t <= -1.7e-189:
		tmp = t_2
	elif t <= -7.1e-205:
		tmp = x * -y
	elif t <= 5.1e-110:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y - z))
	t_2 = Float64(x + Float64(x * z))
	tmp = 0.0
	if (t <= -6.8e-101)
		tmp = t_1;
	elseif (t <= -1.7e-189)
		tmp = t_2;
	elseif (t <= -7.1e-205)
		tmp = Float64(x * Float64(-y));
	elseif (t <= 5.1e-110)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y - z);
	t_2 = x + (x * z);
	tmp = 0.0;
	if (t <= -6.8e-101)
		tmp = t_1;
	elseif (t <= -1.7e-189)
		tmp = t_2;
	elseif (t <= -7.1e-205)
		tmp = x * -y;
	elseif (t <= 5.1e-110)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-101], t$95$1, If[LessEqual[t, -1.7e-189], t$95$2, If[LessEqual[t, -7.1e-205], N[(x * (-y)), $MachinePrecision], If[LessEqual[t, 5.1e-110], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.79999999999999978e-101 or 5.1000000000000002e-110 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.7%

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

   3. Taylor expanded in y around 0 77.0%

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

   4. Taylor expanded in t around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

   6. Simplified 72.2%

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

   if -6.79999999999999978e-101 < t < -1.7000000000000001e-189 or -7.1000000000000003e-205 < t < 5.1000000000000002e-110

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. distribute-lft-neg-out 60.8%

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

      3. *-commutative 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in t around 0 56.9%

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

   if -1.7000000000000001e-189 < t < -7.1000000000000003e-205

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 90.6%

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

      1. +-commutative 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. associate-*r* 90.6%

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

      4. mul-1-neg 90.6%

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

      5. unsub-neg 90.6%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in y around inf 90.6%

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

      1. mul-1-neg 90.6%

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

      2. distribute-rgt-neg-out 90.6%

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

   10. Simplified 90.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-189}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;t \leq -7.1 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-110}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 4: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y - z\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-189}:\\ \;\;\;\;x + t \cdot y\\ \mathbf{elif}\;t \leq -3.75 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-108}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- y z))))
   (if (<= t -9e-99)
     t_1
     (if (<= t -2.4e-189)
       (+ x (* t y))
       (if (<= t -3.75e-205)
         (* x (- y))
         (if (<= t 6.4e-108) (+ x (* x z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y - z);
	double tmp;
	if (t <= -9e-99) {
		tmp = t_1;
	} else if (t <= -2.4e-189) {
		tmp = x + (t * y);
	} else if (t <= -3.75e-205) {
		tmp = x * -y;
	} else if (t <= 6.4e-108) {
		tmp = x + (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 = t * (y - z)
    if (t <= (-9d-99)) then
        tmp = t_1
    else if (t <= (-2.4d-189)) then
        tmp = x + (t * y)
    else if (t <= (-3.75d-205)) then
        tmp = x * -y
    else if (t <= 6.4d-108) then
        tmp = x + (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 = t * (y - z);
	double tmp;
	if (t <= -9e-99) {
		tmp = t_1;
	} else if (t <= -2.4e-189) {
		tmp = x + (t * y);
	} else if (t <= -3.75e-205) {
		tmp = x * -y;
	} else if (t <= 6.4e-108) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y - z)
	tmp = 0
	if t <= -9e-99:
		tmp = t_1
	elif t <= -2.4e-189:
		tmp = x + (t * y)
	elif t <= -3.75e-205:
		tmp = x * -y
	elif t <= 6.4e-108:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y - z))
	tmp = 0.0
	if (t <= -9e-99)
		tmp = t_1;
	elseif (t <= -2.4e-189)
		tmp = Float64(x + Float64(t * y));
	elseif (t <= -3.75e-205)
		tmp = Float64(x * Float64(-y));
	elseif (t <= 6.4e-108)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y - z);
	tmp = 0.0;
	if (t <= -9e-99)
		tmp = t_1;
	elseif (t <= -2.4e-189)
		tmp = x + (t * y);
	elseif (t <= -3.75e-205)
		tmp = x * -y;
	elseif (t <= 6.4e-108)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e-99], t$95$1, If[LessEqual[t, -2.4e-189], N[(x + N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.75e-205], N[(x * (-y)), $MachinePrecision], If[LessEqual[t, 6.4e-108], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.0000000000000006e-99 or 6.3999999999999999e-108 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.7%

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

   3. Taylor expanded in y around 0 77.0%

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

   4. Taylor expanded in t around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

   6. Simplified 72.2%

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

   if -9.0000000000000006e-99 < t < -2.3999999999999998e-189

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 68.4%

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

   3. Taylor expanded in z around 0 68.3%

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

   if -2.3999999999999998e-189 < t < -3.7499999999999998e-205

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 90.6%

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

      1. +-commutative 90.6%

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

      2. distribute-rgt1-in 90.6%

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

      3. associate-*r* 90.6%

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

      4. mul-1-neg 90.6%

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

      5. unsub-neg 90.6%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in y around inf 90.6%

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

      1. mul-1-neg 90.6%

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

      2. distribute-rgt-neg-out 90.6%

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

   10. Simplified 90.6%

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

   if -3.7499999999999998e-205 < t < 6.3999999999999999e-108

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-lft-neg-out 58.8%

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

      3. *-commutative 58.8%

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

   4. Simplified 58.8%

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

   5. Taylor expanded in t around 0 54.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-189}:\\ \;\;\;\;x + t \cdot y\\ \mathbf{elif}\;t \leq -3.75 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-108}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 5: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(y - z\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-233}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-108}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* t (- y z)))))
   (if (<= t -1.4e-187)
     t_1
     (if (<= t 1.1e-233)
       (- x (* x y))
       (if (<= t 5.8e-108) (+ x (* x z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (t * (y - z));
	double tmp;
	if (t <= -1.4e-187) {
		tmp = t_1;
	} else if (t <= 1.1e-233) {
		tmp = x - (x * y);
	} else if (t <= 5.8e-108) {
		tmp = x + (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 + (t * (y - z))
    if (t <= (-1.4d-187)) then
        tmp = t_1
    else if (t <= 1.1d-233) then
        tmp = x - (x * y)
    else if (t <= 5.8d-108) then
        tmp = x + (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 + (t * (y - z));
	double tmp;
	if (t <= -1.4e-187) {
		tmp = t_1;
	} else if (t <= 1.1e-233) {
		tmp = x - (x * y);
	} else if (t <= 5.8e-108) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (t * (y - z))
	tmp = 0
	if t <= -1.4e-187:
		tmp = t_1
	elif t <= 1.1e-233:
		tmp = x - (x * y)
	elif t <= 5.8e-108:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(t * Float64(y - z)))
	tmp = 0.0
	if (t <= -1.4e-187)
		tmp = t_1;
	elseif (t <= 1.1e-233)
		tmp = Float64(x - Float64(x * y));
	elseif (t <= 5.8e-108)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (t * (y - z));
	tmp = 0.0;
	if (t <= -1.4e-187)
		tmp = t_1;
	elseif (t <= 1.1e-233)
		tmp = x - (x * y);
	elseif (t <= 5.8e-108)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-187], t$95$1, If[LessEqual[t, 1.1e-233], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-108], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4e-187 or 5.8000000000000002e-108 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.4%

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

   if -1.4e-187 < t < 1.1e-233

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in x around inf 69.6%

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

      1. +-commutative 69.6%

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

      2. distribute-rgt1-in 69.6%

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

      3. associate-*r* 69.6%

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

      4. mul-1-neg 69.6%

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

      5. unsub-neg 69.6%

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

   7. Simplified 69.6%

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

   if 1.1e-233 < t < 5.8000000000000002e-108

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 69.1%

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

      1. mul-1-neg 69.1%

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

      2. distribute-lft-neg-out 69.1%

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

      3. *-commutative 69.1%

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

   4. Simplified 69.1%

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

   5. Taylor expanded in t around 0 62.0%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-187}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-233}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-108}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 6: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(y - z\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-234}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-82}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* t (- y z)))))
   (if (<= t -2.1e-187)
     t_1
     (if (<= t 9.5e-234)
       (- x (* x y))
       (if (<= t 3.4e-82) (+ x (* z (- x t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (t * (y - z));
	double tmp;
	if (t <= -2.1e-187) {
		tmp = t_1;
	} else if (t <= 9.5e-234) {
		tmp = x - (x * y);
	} else if (t <= 3.4e-82) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y - z))
    if (t <= (-2.1d-187)) then
        tmp = t_1
    else if (t <= 9.5d-234) then
        tmp = x - (x * y)
    else if (t <= 3.4d-82) then
        tmp = x + (z * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (t * (y - z));
	double tmp;
	if (t <= -2.1e-187) {
		tmp = t_1;
	} else if (t <= 9.5e-234) {
		tmp = x - (x * y);
	} else if (t <= 3.4e-82) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (t * (y - z))
	tmp = 0
	if t <= -2.1e-187:
		tmp = t_1
	elif t <= 9.5e-234:
		tmp = x - (x * y)
	elif t <= 3.4e-82:
		tmp = x + (z * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(t * Float64(y - z)))
	tmp = 0.0
	if (t <= -2.1e-187)
		tmp = t_1;
	elseif (t <= 9.5e-234)
		tmp = Float64(x - Float64(x * y));
	elseif (t <= 3.4e-82)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (t * (y - z));
	tmp = 0.0;
	if (t <= -2.1e-187)
		tmp = t_1;
	elseif (t <= 9.5e-234)
		tmp = x - (x * y);
	elseif (t <= 3.4e-82)
		tmp = x + (z * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e-187], t$95$1, If[LessEqual[t, 9.5e-234], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-82], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.09999999999999992e-187 or 3.39999999999999975e-82 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.2%

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

   if -2.09999999999999992e-187 < t < 9.4999999999999999e-234

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in x around inf 69.6%

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

      1. +-commutative 69.6%

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

      2. distribute-rgt1-in 69.6%

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

      3. associate-*r* 69.6%

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

      4. mul-1-neg 69.6%

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

      5. unsub-neg 69.6%

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

   7. Simplified 69.6%

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

   if 9.4999999999999999e-234 < t < 3.39999999999999975e-82

   1. Initial program 99.9%

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

      1. flip-- 86.9%

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

      2. associate-*r/ 83.6%

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

   3. Applied egg-rr 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-*l/ 86.9%

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

      3. difference-of-squares 86.8%

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

      4. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. distribute-rgt-neg-in 68.9%

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

      3. sub-neg 68.9%

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

      4. +-commutative 68.9%

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

      5. distribute-neg-in 68.9%

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

      6. remove-double-neg 68.9%

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

      7. sub-neg 68.9%

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

   8. Simplified 68.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-187}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-234}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-82}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 7: 53.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y - z\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- y z))))
   (if (<= t -2.3e-146)
     t_1
     (if (<= t -6e-189) x (if (<= t 2.9e-58) (* x (- y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y - z);
	double tmp;
	if (t <= -2.3e-146) {
		tmp = t_1;
	} else if (t <= -6e-189) {
		tmp = x;
	} else if (t <= 2.9e-58) {
		tmp = x * -y;
	} 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 = t * (y - z)
    if (t <= (-2.3d-146)) then
        tmp = t_1
    else if (t <= (-6d-189)) then
        tmp = x
    else if (t <= 2.9d-58) then
        tmp = x * -y
    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 = t * (y - z);
	double tmp;
	if (t <= -2.3e-146) {
		tmp = t_1;
	} else if (t <= -6e-189) {
		tmp = x;
	} else if (t <= 2.9e-58) {
		tmp = x * -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y - z)
	tmp = 0
	if t <= -2.3e-146:
		tmp = t_1
	elif t <= -6e-189:
		tmp = x
	elif t <= 2.9e-58:
		tmp = x * -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y - z))
	tmp = 0.0
	if (t <= -2.3e-146)
		tmp = t_1;
	elseif (t <= -6e-189)
		tmp = x;
	elseif (t <= 2.9e-58)
		tmp = Float64(x * Float64(-y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y - z);
	tmp = 0.0;
	if (t <= -2.3e-146)
		tmp = t_1;
	elseif (t <= -6e-189)
		tmp = x;
	elseif (t <= 2.9e-58)
		tmp = x * -y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e-146], t$95$1, If[LessEqual[t, -6e-189], x, If[LessEqual[t, 2.9e-58], N[(x * (-y)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3000000000000001e-146 or 2.8999999999999999e-58 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.6%

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

   3. Taylor expanded in y around 0 77.8%

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

   4. Taylor expanded in t around inf 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

   6. Simplified 72.9%

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

   if -2.3000000000000001e-146 < t < -6e-189

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.1%

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

   3. Taylor expanded in x around inf 56.4%

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

   if -6e-189 < t < 2.8999999999999999e-58

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 66.1%

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

      1. *-commutative 66.1%

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

   4. Simplified 66.1%

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

   5. Taylor expanded in x around inf 57.6%

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

      1. +-commutative 57.6%

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

      2. distribute-rgt1-in 57.6%

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

      3. associate-*r* 57.6%

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

      4. mul-1-neg 57.6%

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

      5. unsub-neg 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in y around inf 39.9%

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

      1. mul-1-neg 39.9%

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

      2. distribute-rgt-neg-out 39.9%

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

   10. Simplified 39.9%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-146}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-189}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 8: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+60} \lor \neg \left(y \leq 1.02 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+60) (not (<= y 1.02e-8)))
   (+ x (* (- t x) y))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+60) || !(y <= 1.02e-8)) {
		tmp = x + ((t - x) * y);
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.9d+60)) .or. (.not. (y <= 1.02d-8))) then
        tmp = x + ((t - x) * y)
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+60) || !(y <= 1.02e-8)) {
		tmp = x + ((t - x) * y);
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e+60) or not (y <= 1.02e-8):
		tmp = x + ((t - x) * y)
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e+60) || !(y <= 1.02e-8))
		tmp = Float64(x + Float64(Float64(t - x) * y));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.9e+60) || ~((y <= 1.02e-8)))
		tmp = x + ((t - x) * y);
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e+60], N[Not[LessEqual[y, 1.02e-8]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000005e60 or 1.02000000000000003e-8 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.4%

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

      1. *-commutative 86.4%

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

   4. Simplified 86.4%

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

   if -1.90000000000000005e60 < y < 1.02000000000000003e-8

   1. Initial program 100.0%

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

      1. flip-- 72.7%

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

      2. associate-*r/ 69.0%

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

   3. Applied egg-rr 69.0%

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

      1. *-commutative 69.0%

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

      2. associate-*l/ 72.7%

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

      3. difference-of-squares 75.1%

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

      4. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 88.7%

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

      1. mul-1-neg 88.7%

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

      2. distribute-rgt-neg-in 88.7%

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

      3. sub-neg 88.7%

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

      4. +-commutative 88.7%

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

      5. distribute-neg-in 88.7%

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

      6. remove-double-neg 88.7%

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

      7. sub-neg 88.7%

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

   8. Simplified 88.7%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+60} \lor \neg \left(y \leq 1.02 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 62.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.1)
   (- x (* x y))
   (if (<= x 5.8e+108) (* t (- y z)) (+ x (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.1) {
		tmp = x - (x * y);
	} else if (x <= 5.8e+108) {
		tmp = t * (y - z);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.1d0)) then
        tmp = x - (x * y)
    else if (x <= 5.8d+108) then
        tmp = t * (y - z)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.1) {
		tmp = x - (x * y);
	} else if (x <= 5.8e+108) {
		tmp = t * (y - z);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.1:
		tmp = x - (x * y)
	elif x <= 5.8e+108:
		tmp = t * (y - z)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.1)
		tmp = Float64(x - Float64(x * y));
	elseif (x <= 5.8e+108)
		tmp = Float64(t * Float64(y - z));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.1)
		tmp = x - (x * y);
	elseif (x <= 5.8e+108)
		tmp = t * (y - z);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.1], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+108], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.10000000000000009

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 69.5%

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

      1. *-commutative 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in x around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. distribute-rgt1-in 63.2%

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

      3. associate-*r* 63.2%

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

      4. mul-1-neg 63.2%

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

      5. unsub-neg 63.2%

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

   7. Simplified 63.2%

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

   if -3.10000000000000009 < x < 5.80000000000000015e108

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.9%

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

   3. Taylor expanded in y around 0 77.1%

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

   4. Taylor expanded in t around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. mul-1-neg 71.6%

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

      3. unsub-neg 71.6%

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

   6. Simplified 71.6%

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

   if 5.80000000000000015e108 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. distribute-lft-neg-out 70.0%

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

      3. *-commutative 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in t around 0 64.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 11: 37.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-87}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e-87) (* t y) (if (<= y 5e-21) x (* x (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e-87) {
		tmp = t * y;
	} else if (y <= 5e-21) {
		tmp = x;
	} else {
		tmp = x * -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 (y <= (-6d-87)) then
        tmp = t * y
    else if (y <= 5d-21) then
        tmp = x
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e-87) {
		tmp = t * y;
	} else if (y <= 5e-21) {
		tmp = x;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6e-87:
		tmp = t * y
	elif y <= 5e-21:
		tmp = x
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6e-87)
		tmp = Float64(t * y);
	elseif (y <= 5e-21)
		tmp = x;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6e-87)
		tmp = t * y;
	elseif (y <= 5e-21)
		tmp = x;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6e-87], N[(t * y), $MachinePrecision], If[LessEqual[y, 5e-21], x, N[(x * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000033e-87

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 67.2%

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

   3. Taylor expanded in y around inf 52.5%

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

   if -6.00000000000000033e-87 < y < 4.99999999999999973e-21

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.4%

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

   3. Taylor expanded in x around inf 34.2%

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

   if 4.99999999999999973e-21 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.5%

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

      1. *-commutative 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in x around inf 47.4%

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

      1. +-commutative 47.4%

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

      2. distribute-rgt1-in 47.4%

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

      3. associate-*r* 47.4%

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

      4. mul-1-neg 47.4%

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

      5. unsub-neg 47.4%

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

   7. Simplified 47.4%

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

   8. Taylor expanded in y around inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. distribute-rgt-neg-out 44.8%

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

   10. Simplified 44.8%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-87}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 12: 37.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-87}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e-87) (* t y) (if (<= y 3.8e-24) x (* t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e-87) {
		tmp = t * y;
	} else if (y <= 3.8e-24) {
		tmp = x;
	} else {
		tmp = t * 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 (y <= (-6d-87)) then
        tmp = t * y
    else if (y <= 3.8d-24) then
        tmp = x
    else
        tmp = t * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e-87) {
		tmp = t * y;
	} else if (y <= 3.8e-24) {
		tmp = x;
	} else {
		tmp = t * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6e-87:
		tmp = t * y
	elif y <= 3.8e-24:
		tmp = x
	else:
		tmp = t * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6e-87)
		tmp = Float64(t * y);
	elseif (y <= 3.8e-24)
		tmp = x;
	else
		tmp = Float64(t * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6e-87)
		tmp = t * y;
	elseif (y <= 3.8e-24)
		tmp = x;
	else
		tmp = t * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6e-87], N[(t * y), $MachinePrecision], If[LessEqual[y, 3.8e-24], x, N[(t * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000033e-87 or 3.80000000000000026e-24 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 59.0%

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

   3. Taylor expanded in y around inf 47.0%

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

   if -6.00000000000000033e-87 < y < 3.80000000000000026e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.4%

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

   3. Taylor expanded in x around inf 34.2%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-87}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \]

Alternative 13: 18.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 66.6%

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

3. Taylor expanded in x around inf 16.2%

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

4. Final simplification 16.2%

   \[\leadsto x \]

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 2023253 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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