Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Alternatives: 13

Speedup: 1.0×

• 34.8% 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. Final simplification 100.0%

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

Alternative 2: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \left(z - y\right)\\ t_2 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-199}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* t (- z y)))) (t_2 (+ x (* y (- t x)))))
   (if (<= y -4.4e+101)
     t_2
     (if (<= y -2.2e-174)
       t_1
       (if (<= y -1.1e-199)
         (+ x (* x z))
         (if (<= y -3.6e-242)
           t_1
           (if (<= y -1.95e-275)
             (* x (+ z 1.0))
             (if (<= y 5.3e+133) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (t * (z - y));
	double t_2 = x + (y * (t - x));
	double tmp;
	if (y <= -4.4e+101) {
		tmp = t_2;
	} else if (y <= -2.2e-174) {
		tmp = t_1;
	} else if (y <= -1.1e-199) {
		tmp = x + (x * z);
	} else if (y <= -3.6e-242) {
		tmp = t_1;
	} else if (y <= -1.95e-275) {
		tmp = x * (z + 1.0);
	} else if (y <= 5.3e+133) {
		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) :: tmp
    t_1 = x - (t * (z - y))
    t_2 = x + (y * (t - x))
    if (y <= (-4.4d+101)) then
        tmp = t_2
    else if (y <= (-2.2d-174)) then
        tmp = t_1
    else if (y <= (-1.1d-199)) then
        tmp = x + (x * z)
    else if (y <= (-3.6d-242)) then
        tmp = t_1
    else if (y <= (-1.95d-275)) then
        tmp = x * (z + 1.0d0)
    else if (y <= 5.3d+133) 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 - (t * (z - y));
	double t_2 = x + (y * (t - x));
	double tmp;
	if (y <= -4.4e+101) {
		tmp = t_2;
	} else if (y <= -2.2e-174) {
		tmp = t_1;
	} else if (y <= -1.1e-199) {
		tmp = x + (x * z);
	} else if (y <= -3.6e-242) {
		tmp = t_1;
	} else if (y <= -1.95e-275) {
		tmp = x * (z + 1.0);
	} else if (y <= 5.3e+133) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (t * (z - y))
	t_2 = x + (y * (t - x))
	tmp = 0
	if y <= -4.4e+101:
		tmp = t_2
	elif y <= -2.2e-174:
		tmp = t_1
	elif y <= -1.1e-199:
		tmp = x + (x * z)
	elif y <= -3.6e-242:
		tmp = t_1
	elif y <= -1.95e-275:
		tmp = x * (z + 1.0)
	elif y <= 5.3e+133:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(t * Float64(z - y)))
	t_2 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (y <= -4.4e+101)
		tmp = t_2;
	elseif (y <= -2.2e-174)
		tmp = t_1;
	elseif (y <= -1.1e-199)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= -3.6e-242)
		tmp = t_1;
	elseif (y <= -1.95e-275)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 5.3e+133)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (t * (z - y));
	t_2 = x + (y * (t - x));
	tmp = 0.0;
	if (y <= -4.4e+101)
		tmp = t_2;
	elseif (y <= -2.2e-174)
		tmp = t_1;
	elseif (y <= -1.1e-199)
		tmp = x + (x * z);
	elseif (y <= -3.6e-242)
		tmp = t_1;
	elseif (y <= -1.95e-275)
		tmp = x * (z + 1.0);
	elseif (y <= 5.3e+133)
		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[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+101], t$95$2, If[LessEqual[y, -2.2e-174], t$95$1, If[LessEqual[y, -1.1e-199], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.6e-242], t$95$1, If[LessEqual[y, -1.95e-275], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e+133], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4000000000000001e101 or 5.29999999999999997e133 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 88.0%

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

   if -4.4000000000000001e101 < y < -2.20000000000000022e-174 or -1.0999999999999999e-199 < y < -3.60000000000000014e-242 or -1.94999999999999986e-275 < y < 5.29999999999999997e133

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.3%

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

   if -2.20000000000000022e-174 < y < -1.0999999999999999e-199

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*r/ 85.2%

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

   3. Applied egg-rr 85.2%

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

      1. associate-/l* 99.5%

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

      2. difference-of-squares 99.5%

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

      3. associate-/r* 99.7%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{\frac{y + z}{y + z}}{y - z}}} \]

      4. *-inverses 99.7%

         \[\leadsto x + \frac{t - x}{\frac{\color{blue}{1}}{y - z}} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]

   6. Taylor expanded in y around 0 99.7%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{-1}{z}}} \]

   7. Taylor expanded in t around 0 100.0%

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

   if -3.60000000000000014e-242 < y < -1.94999999999999986e-275

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around -inf 89.4%

      \[\leadsto \color{blue}{\left(1 + z\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+101}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-199}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-242}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+133}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 3: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -x \cdot y\\ \mathbf{if}\;y \leq -0.037:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-275}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 7:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x y))))
   (if (<= y -0.037)
     t_1
     (if (<= y -1.95e-227)
       x
       (if (<= y -1.95e-275) (* x z) (if (<= y 7.0) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -(x * y);
	double tmp;
	if (y <= -0.037) {
		tmp = t_1;
	} else if (y <= -1.95e-227) {
		tmp = x;
	} else if (y <= -1.95e-275) {
		tmp = x * z;
	} else if (y <= 7.0) {
		tmp = x;
	} 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 <= (-0.037d0)) then
        tmp = t_1
    else if (y <= (-1.95d-227)) then
        tmp = x
    else if (y <= (-1.95d-275)) then
        tmp = x * z
    else if (y <= 7.0d0) then
        tmp = x
    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 <= -0.037) {
		tmp = t_1;
	} else if (y <= -1.95e-227) {
		tmp = x;
	} else if (y <= -1.95e-275) {
		tmp = x * z;
	} else if (y <= 7.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -(x * y)
	tmp = 0
	if y <= -0.037:
		tmp = t_1
	elif y <= -1.95e-227:
		tmp = x
	elif y <= -1.95e-275:
		tmp = x * z
	elif y <= 7.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(x * y))
	tmp = 0.0
	if (y <= -0.037)
		tmp = t_1;
	elseif (y <= -1.95e-227)
		tmp = x;
	elseif (y <= -1.95e-275)
		tmp = Float64(x * z);
	elseif (y <= 7.0)
		tmp = x;
	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 <= -0.037)
		tmp = t_1;
	elseif (y <= -1.95e-227)
		tmp = x;
	elseif (y <= -1.95e-275)
		tmp = x * z;
	elseif (y <= 7.0)
		tmp = x;
	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, -0.037], t$95$1, If[LessEqual[y, -1.95e-227], x, If[LessEqual[y, -1.95e-275], N[(x * z), $MachinePrecision], If[LessEqual[y, 7.0], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0369999999999999982 or 7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. mul-1-neg 46.7%

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

      3. unsub-neg 46.7%

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

      4. distribute-lft-out-- 46.7%

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

      5. *-rgt-identity 46.7%

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

   4. Simplified 46.7%

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

   5. Taylor expanded in z around 0 43.5%

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

   6. Taylor expanded in y around inf 37.8%

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

      1. mul-1-neg 37.8%

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

      2. distribute-rgt-neg-out 37.8%

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

   8. Simplified 37.8%

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

   if -0.0369999999999999982 < y < -1.95e-227 or -1.94999999999999986e-275 < y < 7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. mul-1-neg 91.3%

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

      3. unsub-neg 91.3%

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

      4. *-commutative 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in z around 0 39.8%

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

   if -1.95e-227 < y < -1.94999999999999986e-275

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. distribute-lft-out-- 70.1%

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

      5. *-rgt-identity 70.1%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in z around inf 55.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.037:\\ \;\;\;\;-x \cdot y\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-275}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 7:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-x \cdot y\\ \end{array} \]

Alternative 4: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+54} \lor \neg \left(x \leq 4.45 \cdot 10^{+55}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.32e+54) (not (<= x 4.45e+55)))
   (+ x (* x (- z y)))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.32e+54) || !(x <= 4.45e+55)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.32d+54)) .or. (.not. (x <= 4.45d+55))) then
        tmp = x + (x * (z - y))
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.32e+54) || !(x <= 4.45e+55)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.32e+54) or not (x <= 4.45e+55):
		tmp = x + (x * (z - y))
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.32e+54) || !(x <= 4.45e+55))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.32e+54) || ~((x <= 4.45e+55)))
		tmp = x + (x * (z - y));
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.32e+54], N[Not[LessEqual[x, 4.45e+55]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3200000000000001e54 or 4.4500000000000001e55 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.7%

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

      1. *-commutative 90.7%

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

      2. mul-1-neg 90.7%

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

      3. unsub-neg 90.7%

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

      4. distribute-lft-out-- 90.7%

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

      5. *-rgt-identity 90.7%

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

   4. Simplified 90.7%

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

   if -1.3200000000000001e54 < x < 4.4500000000000001e55

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+54} \lor \neg \left(x \leq 4.45 \cdot 10^{+55}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]

Alternative 5: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -62000000000 \lor \neg \left(y \leq 2 \cdot 10^{+18}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -62000000000.0) (not (<= y 2e+18)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -62000000000.0) || !(y <= 2e+18)) {
		tmp = x + (y * (t - x));
	} 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 <= (-62000000000.0d0)) .or. (.not. (y <= 2d+18))) then
        tmp = x + (y * (t - x))
    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 <= -62000000000.0) || !(y <= 2e+18)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -62000000000.0) or not (y <= 2e+18):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -62000000000.0) || !(y <= 2e+18))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	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 <= -62000000000.0) || ~((y <= 2e+18)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -62000000000.0], N[Not[LessEqual[y, 2e+18]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2e10 or 2e18 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 82.7%

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

   if -6.2e10 < y < 2e18

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.4%

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

      1. +-commutative 90.4%

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

      2. mul-1-neg 90.4%

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

      3. unsub-neg 90.4%

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

      4. *-commutative 90.4%

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

   4. Simplified 90.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -62000000000 \lor \neg \left(y \leq 2 \cdot 10^{+18}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 6: 68.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+244}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+56}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.45e+244)
   (- x (* x y))
   (if (<= x 1.3e+56) (- x (* t (- z y))) (* x (+ z 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e+244) {
		tmp = x - (x * y);
	} else if (x <= 1.3e+56) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.45d+244)) then
        tmp = x - (x * y)
    else if (x <= 1.3d+56) then
        tmp = x - (t * (z - y))
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e+244) {
		tmp = x - (x * y);
	} else if (x <= 1.3e+56) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.45e+244:
		tmp = x - (x * y)
	elif x <= 1.3e+56:
		tmp = x - (t * (z - y))
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.45e+244)
		tmp = Float64(x - Float64(x * y));
	elseif (x <= 1.3e+56)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.45e+244)
		tmp = x - (x * y);
	elseif (x <= 1.3e+56)
		tmp = x - (t * (z - y));
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.45e+244], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+56], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4500000000000001e244

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-lft-out-- 100.0%

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

      5. *-rgt-identity 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 83.3%

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

   if -1.4500000000000001e244 < x < 1.30000000000000005e56

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.2%

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

   if 1.30000000000000005e56 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.3%

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

      1. +-commutative 72.3%

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

      2. mul-1-neg 72.3%

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

      3. unsub-neg 72.3%

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

      4. *-commutative 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in x around -inf 67.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+244}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+56}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 7: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -130 \lor \neg \left(y \leq 130000000\right):\\ \;\;\;\;-x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -130.0) (not (<= y 130000000.0))) (- (* x y)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -130.0) || !(y <= 130000000.0)) {
		tmp = -(x * y);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-130.0d0)) .or. (.not. (y <= 130000000.0d0))) then
        tmp = -(x * y)
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -130.0) || !(y <= 130000000.0)) {
		tmp = -(x * y);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -130.0) or not (y <= 130000000.0):
		tmp = -(x * y)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -130.0) || !(y <= 130000000.0))
		tmp = Float64(-Float64(x * y));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -130.0) || ~((y <= 130000000.0)))
		tmp = -(x * y);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -130.0], N[Not[LessEqual[y, 130000000.0]], $MachinePrecision]], (-N[(x * y), $MachinePrecision]), N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -130 or 1.3e8 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 46.3%

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

      1. *-commutative 46.3%

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

      2. mul-1-neg 46.3%

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

      3. unsub-neg 46.3%

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

      4. distribute-lft-out-- 46.3%

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

      5. *-rgt-identity 46.3%

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

   4. Simplified 46.3%

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

   5. Taylor expanded in z around 0 43.0%

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

   6. Taylor expanded in y around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. distribute-rgt-neg-out 38.1%

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

   8. Simplified 38.1%

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

   if -130 < y < 1.3e8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.5%

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

      1. +-commutative 91.5%

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

      2. mul-1-neg 91.5%

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

      3. unsub-neg 91.5%

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

      4. *-commutative 91.5%

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

   4. Simplified 91.5%

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

   5. Taylor expanded in x around -inf 58.8%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -130 \lor \neg \left(y \leq 130000000\right):\\ \;\;\;\;-x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 8: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+53} \lor \neg \left(x \leq 7.1 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.2e+53) (not (<= x 7.1e+55))) (* x (+ z 1.0)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e+53) || !(x <= 7.1e+55)) {
		tmp = x * (z + 1.0);
	} 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 ((x <= (-4.2d+53)) .or. (.not. (x <= 7.1d+55))) then
        tmp = x * (z + 1.0d0)
    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 ((x <= -4.2e+53) || !(x <= 7.1e+55)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.2e+53) or not (x <= 7.1e+55):
		tmp = x * (z + 1.0)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.2e+53) || !(x <= 7.1e+55))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.2e+53) || ~((x <= 7.1e+55)))
		tmp = x * (z + 1.0);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.2e+53], N[Not[LessEqual[x, 7.1e+55]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000004e53 or 7.1e55 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. mul-1-neg 72.4%

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

      3. unsub-neg 72.4%

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

      4. *-commutative 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in x around -inf 65.2%

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

   if -4.2000000000000004e53 < x < 7.1e55

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.9%

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

   3. Taylor expanded in y around inf 49.1%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+53} \lor \neg \left(x \leq 7.1 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 9: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+53}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{+55}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.05e+53)
   (+ x (* x z))
   (if (<= x 1.76e+55) (+ x (* y t)) (* x (+ z 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.05e+53) {
		tmp = x + (x * z);
	} else if (x <= 1.76e+55) {
		tmp = x + (y * t);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.05d+53)) then
        tmp = x + (x * z)
    else if (x <= 1.76d+55) then
        tmp = x + (y * t)
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.05e+53) {
		tmp = x + (x * z);
	} else if (x <= 1.76e+55) {
		tmp = x + (y * t);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.05e+53:
		tmp = x + (x * z)
	elif x <= 1.76e+55:
		tmp = x + (y * t)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.05e+53)
		tmp = Float64(x + Float64(x * z));
	elseif (x <= 1.76e+55)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.05e+53)
		tmp = x + (x * z);
	elseif (x <= 1.76e+55)
		tmp = x + (y * t);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.05e+53], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.76e+55], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0500000000000001e53

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 91.4%

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

      3. associate-*r/ 83.4%

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

   3. Applied egg-rr 83.4%

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

      1. associate-/l* 91.3%

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

      2. difference-of-squares 93.7%

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

      3. associate-/r* 99.9%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{\frac{y + z}{y + z}}{y - z}}} \]

      4. *-inverses 99.9%

         \[\leadsto x + \frac{t - x}{\frac{\color{blue}{1}}{y - z}} \]

   5. Simplified 99.9%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]

   6. Taylor expanded in y around 0 72.4%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{-1}{z}}} \]

   7. Taylor expanded in t around 0 62.4%

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

   if -3.0500000000000001e53 < x < 1.75999999999999992e55

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.9%

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

   3. Taylor expanded in y around inf 49.1%

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

   if 1.75999999999999992e55 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.3%

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

      1. +-commutative 72.3%

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

      2. mul-1-neg 72.3%

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

      3. unsub-neg 72.3%

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

      4. *-commutative 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in x around -inf 67.4%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+53}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{+55}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 10: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+38}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+55}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.15e+38)
   (- x (* x y))
   (if (<= x 6.2e+55) (+ x (* y t)) (* x (+ z 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e+38) {
		tmp = x - (x * y);
	} else if (x <= 6.2e+55) {
		tmp = x + (y * t);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.15d+38)) then
        tmp = x - (x * y)
    else if (x <= 6.2d+55) then
        tmp = x + (y * t)
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e+38) {
		tmp = x - (x * y);
	} else if (x <= 6.2e+55) {
		tmp = x + (y * t);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.15e+38:
		tmp = x - (x * y)
	elif x <= 6.2e+55:
		tmp = x + (y * t)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.15e+38)
		tmp = Float64(x - Float64(x * y));
	elseif (x <= 6.2e+55)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.15e+38)
		tmp = x - (x * y);
	elseif (x <= 6.2e+55)
		tmp = x + (y * t);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.15e+38], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+55], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1500000000000001e38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 85.4%

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

      1. *-commutative 85.4%

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

      2. mul-1-neg 85.4%

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

      3. unsub-neg 85.4%

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

      4. distribute-lft-out-- 85.4%

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

      5. *-rgt-identity 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in y around inf 63.3%

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

   if -1.1500000000000001e38 < x < 6.19999999999999987e55

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.3%

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

   3. Taylor expanded in y around inf 49.8%

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

   if 6.19999999999999987e55 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.3%

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

      1. +-commutative 72.3%

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

      2. mul-1-neg 72.3%

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

      3. unsub-neg 72.3%

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

      4. *-commutative 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in x around -inf 67.4%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+38}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+55}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 11: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+21}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+21) (* x z) (if (<= z 2.3e-9) (+ x (* y t)) (- x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+21) {
		tmp = x * z;
	} else if (z <= 2.3e-9) {
		tmp = x + (y * t);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1d+21)) then
        tmp = x * z
    else if (z <= 2.3d-9) then
        tmp = x + (y * t)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+21) {
		tmp = x * z;
	} else if (z <= 2.3e-9) {
		tmp = x + (y * t);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e+21:
		tmp = x * z
	elif z <= 2.3e-9:
		tmp = x + (y * t)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+21)
		tmp = Float64(x * z);
	elseif (z <= 2.3e-9)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e+21)
		tmp = x * z;
	elseif (z <= 2.3e-9)
		tmp = x + (y * t);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e+21], N[(x * z), $MachinePrecision], If[LessEqual[z, 2.3e-9], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e21

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

      4. distribute-lft-out-- 59.7%

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

      5. *-rgt-identity 59.7%

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

   4. Simplified 59.7%

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

   5. Taylor expanded in z around inf 44.0%

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

   if -1e21 < z < 2.2999999999999999e-9

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.5%

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

   3. Taylor expanded in y around inf 69.5%

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

   if 2.2999999999999999e-9 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. mul-1-neg 81.0%

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

      3. unsub-neg 81.0%

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

      4. *-commutative 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in t around inf 59.9%

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

      1. *-commutative 59.9%

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

   7. Simplified 59.9%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+21}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 12: 37.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0) (* x z) (if (<= z 2.15e-21) x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 2.15e-21) {
		tmp = x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 2.15d-21) then
        tmp = x
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 2.15e-21) {
		tmp = x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= 2.15e-21:
		tmp = x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 2.15e-21)
		tmp = x;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * z;
	elseif (z <= 2.15e-21)
		tmp = x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 2.15e-21], x, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 2.1499999999999999e-21 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 44.2%

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

      1. *-commutative 44.2%

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

      2. mul-1-neg 44.2%

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

      3. unsub-neg 44.2%

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

      4. distribute-lft-out-- 44.2%

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

      5. *-rgt-identity 44.2%

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

   4. Simplified 44.2%

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

   5. Taylor expanded in z around inf 33.6%

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

   if -1 < z < 2.1499999999999999e-21

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. *-commutative 47.6%

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

   4. Simplified 47.6%

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

   5. Taylor expanded in z around 0 39.2%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 13: 18.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 60.8%

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

   1. +-commutative 60.8%

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

   2. mul-1-neg 60.8%

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

   3. unsub-neg 60.8%

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

   4. *-commutative 60.8%

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

4. Simplified 60.8%

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

5. Taylor expanded in z around 0 20.7%

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

6. Final simplification 20.7%

   \[\leadsto x \]

Developer target: 96.1% 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 2023215 
(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))))