Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 12

Speedup: 1.0×

• 34.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 52.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ t_2 := x - z \cdot t\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-147}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))) (t_2 (- x (* z t))))
   (if (<= y -8.2e+66)
     t_1
     (if (<= y -1.35e-60)
       t_2
       (if (<= y -6e-147)
         (+ x (* z x))
         (if (<= y -1.9e-292)
           t_2
           (if (<= y 5e-200)
             (* x (+ z 1.0))
             (if (<= y 5.5e+65)
               t_2
               (if (<= y 1.05e+223) t_1 (+ x (* y t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -8.2e+66) {
		tmp = t_1;
	} else if (y <= -1.35e-60) {
		tmp = t_2;
	} else if (y <= -6e-147) {
		tmp = x + (z * x);
	} else if (y <= -1.9e-292) {
		tmp = t_2;
	} else if (y <= 5e-200) {
		tmp = x * (z + 1.0);
	} else if (y <= 5.5e+65) {
		tmp = t_2;
	} else if (y <= 1.05e+223) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * -x
    t_2 = x - (z * t)
    if (y <= (-8.2d+66)) then
        tmp = t_1
    else if (y <= (-1.35d-60)) then
        tmp = t_2
    else if (y <= (-6d-147)) then
        tmp = x + (z * x)
    else if (y <= (-1.9d-292)) then
        tmp = t_2
    else if (y <= 5d-200) then
        tmp = x * (z + 1.0d0)
    else if (y <= 5.5d+65) then
        tmp = t_2
    else if (y <= 1.05d+223) then
        tmp = t_1
    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 t_1 = y * -x;
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -8.2e+66) {
		tmp = t_1;
	} else if (y <= -1.35e-60) {
		tmp = t_2;
	} else if (y <= -6e-147) {
		tmp = x + (z * x);
	} else if (y <= -1.9e-292) {
		tmp = t_2;
	} else if (y <= 5e-200) {
		tmp = x * (z + 1.0);
	} else if (y <= 5.5e+65) {
		tmp = t_2;
	} else if (y <= 1.05e+223) {
		tmp = t_1;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	t_2 = x - (z * t)
	tmp = 0
	if y <= -8.2e+66:
		tmp = t_1
	elif y <= -1.35e-60:
		tmp = t_2
	elif y <= -6e-147:
		tmp = x + (z * x)
	elif y <= -1.9e-292:
		tmp = t_2
	elif y <= 5e-200:
		tmp = x * (z + 1.0)
	elif y <= 5.5e+65:
		tmp = t_2
	elif y <= 1.05e+223:
		tmp = t_1
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	t_2 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -8.2e+66)
		tmp = t_1;
	elseif (y <= -1.35e-60)
		tmp = t_2;
	elseif (y <= -6e-147)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= -1.9e-292)
		tmp = t_2;
	elseif (y <= 5e-200)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 5.5e+65)
		tmp = t_2;
	elseif (y <= 1.05e+223)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	t_2 = x - (z * t);
	tmp = 0.0;
	if (y <= -8.2e+66)
		tmp = t_1;
	elseif (y <= -1.35e-60)
		tmp = t_2;
	elseif (y <= -6e-147)
		tmp = x + (z * x);
	elseif (y <= -1.9e-292)
		tmp = t_2;
	elseif (y <= 5e-200)
		tmp = x * (z + 1.0);
	elseif (y <= 5.5e+65)
		tmp = t_2;
	elseif (y <= 1.05e+223)
		tmp = t_1;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+66], t$95$1, If[LessEqual[y, -1.35e-60], t$95$2, If[LessEqual[y, -6e-147], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-292], t$95$2, If[LessEqual[y, 5e-200], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+65], t$95$2, If[LessEqual[y, 1.05e+223], t$95$1, N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.19999999999999989e66 or 5.4999999999999996e65 < y < 1.04999999999999995e223

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. distribute-rgt-neg-in 67.9%

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

      3. +-commutative 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in y around inf 55.7%

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

   if -8.19999999999999989e66 < y < -1.35e-60 or -6.0000000000000004e-147 < y < -1.9000000000000001e-292 or 4.99999999999999991e-200 < y < 5.4999999999999996e65

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.0%

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

      1. +-commutative 85.0%

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

      2. mul-1-neg 85.0%

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

      3. unsub-neg 85.0%

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

      4. *-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in t around inf 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if -1.35e-60 < y < -6.0000000000000004e-147

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 93.0%

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

      3. associate-*r/ 86.4%

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

   3. Applied egg-rr 86.4%

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

      1. associate-/l* 93.0%

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

      2. difference-of-squares 93.0%

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

      3. associate-/r* 100.0%

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

      4. *-inverses 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

   7. Taylor expanded in t around 0 92.9%

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

   if -1.9000000000000001e-292 < y < 4.99999999999999991e-200

   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 86.9%

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

   if 1.04999999999999995e223 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 71.3%

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

   3. Taylor expanded in z around 0 71.3%

      \[\leadsto \color{blue}{y \cdot t + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-60}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-147}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-292}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 3: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ t_2 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-145}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-290}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))) (t_2 (+ x (* y (- t x)))))
   (if (<= y -8.5e+66)
     t_2
     (if (<= y -1.05e-60)
       t_1
       (if (<= y -1.25e-145)
         (+ x (* z x))
         (if (<= y -8.2e-290)
           (- x (* z t))
           (if (<= y 2.6e-200)
             (* x (+ z 1.0))
             (if (<= y 2.5e+62) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double t_2 = x + (y * (t - x));
	double tmp;
	if (y <= -8.5e+66) {
		tmp = t_2;
	} else if (y <= -1.05e-60) {
		tmp = t_1;
	} else if (y <= -1.25e-145) {
		tmp = x + (z * x);
	} else if (y <= -8.2e-290) {
		tmp = x - (z * t);
	} else if (y <= 2.6e-200) {
		tmp = x * (z + 1.0);
	} else if (y <= 2.5e+62) {
		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 + ((y - z) * t)
    t_2 = x + (y * (t - x))
    if (y <= (-8.5d+66)) then
        tmp = t_2
    else if (y <= (-1.05d-60)) then
        tmp = t_1
    else if (y <= (-1.25d-145)) then
        tmp = x + (z * x)
    else if (y <= (-8.2d-290)) then
        tmp = x - (z * t)
    else if (y <= 2.6d-200) then
        tmp = x * (z + 1.0d0)
    else if (y <= 2.5d+62) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double t_2 = x + (y * (t - x));
	double tmp;
	if (y <= -8.5e+66) {
		tmp = t_2;
	} else if (y <= -1.05e-60) {
		tmp = t_1;
	} else if (y <= -1.25e-145) {
		tmp = x + (z * x);
	} else if (y <= -8.2e-290) {
		tmp = x - (z * t);
	} else if (y <= 2.6e-200) {
		tmp = x * (z + 1.0);
	} else if (y <= 2.5e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - z) * t)
	t_2 = x + (y * (t - x))
	tmp = 0
	if y <= -8.5e+66:
		tmp = t_2
	elif y <= -1.05e-60:
		tmp = t_1
	elif y <= -1.25e-145:
		tmp = x + (z * x)
	elif y <= -8.2e-290:
		tmp = x - (z * t)
	elif y <= 2.6e-200:
		tmp = x * (z + 1.0)
	elif y <= 2.5e+62:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - z) * t))
	t_2 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (y <= -8.5e+66)
		tmp = t_2;
	elseif (y <= -1.05e-60)
		tmp = t_1;
	elseif (y <= -1.25e-145)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= -8.2e-290)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 2.6e-200)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 2.5e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - z) * t);
	t_2 = x + (y * (t - x));
	tmp = 0.0;
	if (y <= -8.5e+66)
		tmp = t_2;
	elseif (y <= -1.05e-60)
		tmp = t_1;
	elseif (y <= -1.25e-145)
		tmp = x + (z * x);
	elseif (y <= -8.2e-290)
		tmp = x - (z * t);
	elseif (y <= 2.6e-200)
		tmp = x * (z + 1.0);
	elseif (y <= 2.5e+62)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+66], t$95$2, If[LessEqual[y, -1.05e-60], t$95$1, If[LessEqual[y, -1.25e-145], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-290], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-200], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+62], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.5000000000000004e66 or 2.50000000000000014e62 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.6%

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

   if -8.5000000000000004e66 < y < -1.04999999999999996e-60 or 2.5999999999999999e-200 < y < 2.50000000000000014e62

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.6%

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

   if -1.04999999999999996e-60 < y < -1.2499999999999999e-145

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 93.0%

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

      3. associate-*r/ 86.4%

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

   3. Applied egg-rr 86.4%

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

      1. associate-/l* 93.0%

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

      2. difference-of-squares 93.0%

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

      3. associate-/r* 100.0%

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

      4. *-inverses 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

   7. Taylor expanded in t around 0 92.9%

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

   if -1.2499999999999999e-145 < y < -8.2000000000000005e-290

   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 t around inf 83.7%

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

      1. *-commutative 83.7%

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

   7. Simplified 83.7%

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

   if -8.2000000000000005e-290 < y < 2.5999999999999999e-200

   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 86.9%

      \[\leadsto \color{blue}{\left(1 + z\right) \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+66}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-60}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-145}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-290}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 35.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+124}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= z -1.95e+124)
     (* z x)
     (if (<= z -2.5e-8)
       t_1
       (if (<= z -1.2e-196)
         x
         (if (<= z 4.6e-300) t_1 (if (<= z 1.0) x (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (z <= -1.95e+124) {
		tmp = z * x;
	} else if (z <= -2.5e-8) {
		tmp = t_1;
	} else if (z <= -1.2e-196) {
		tmp = x;
	} else if (z <= 4.6e-300) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (z <= (-1.95d+124)) then
        tmp = z * x
    else if (z <= (-2.5d-8)) then
        tmp = t_1
    else if (z <= (-1.2d-196)) then
        tmp = x
    else if (z <= 4.6d-300) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (z <= -1.95e+124) {
		tmp = z * x;
	} else if (z <= -2.5e-8) {
		tmp = t_1;
	} else if (z <= -1.2e-196) {
		tmp = x;
	} else if (z <= 4.6e-300) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if z <= -1.95e+124:
		tmp = z * x
	elif z <= -2.5e-8:
		tmp = t_1
	elif z <= -1.2e-196:
		tmp = x
	elif z <= 4.6e-300:
		tmp = t_1
	elif z <= 1.0:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (z <= -1.95e+124)
		tmp = Float64(z * x);
	elseif (z <= -2.5e-8)
		tmp = t_1;
	elseif (z <= -1.2e-196)
		tmp = x;
	elseif (z <= 4.6e-300)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (z <= -1.95e+124)
		tmp = z * x;
	elseif (z <= -2.5e-8)
		tmp = t_1;
	elseif (z <= -1.2e-196)
		tmp = x;
	elseif (z <= 4.6e-300)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[z, -1.95e+124], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.5e-8], t$95$1, If[LessEqual[z, -1.2e-196], x, If[LessEqual[z, 4.6e-300], t$95$1, If[LessEqual[z, 1.0], x, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e124 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. distribute-rgt-neg-in 57.5%

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

      3. +-commutative 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in z around inf 49.4%

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

   if -1.95e124 < z < -2.4999999999999999e-8 or -1.2000000000000001e-196 < z < 4.60000000000000002e-300

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. distribute-rgt-neg-in 57.2%

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

      3. +-commutative 57.2%

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

   4. Simplified 57.2%

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

   5. Taylor expanded in y around inf 42.6%

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

   if -2.4999999999999999e-8 < z < -1.2000000000000001e-196 or 4.60000000000000002e-300 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.7%

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

   3. Taylor expanded in x around inf 43.0%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+124}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 5: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+91}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))))
   (if (<= x -6.8e+166)
     t_1
     (if (<= x -4.2e+111)
       (* x (- 1.0 y))
       (if (<= x 2.6e+91) (+ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double tmp;
	if (x <= -6.8e+166) {
		tmp = t_1;
	} else if (x <= -4.2e+111) {
		tmp = x * (1.0 - y);
	} else if (x <= 2.6e+91) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    if (x <= (-6.8d+166)) then
        tmp = t_1
    else if (x <= (-4.2d+111)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 2.6d+91) then
        tmp = x + ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double tmp;
	if (x <= -6.8e+166) {
		tmp = t_1;
	} else if (x <= -4.2e+111) {
		tmp = x * (1.0 - y);
	} else if (x <= 2.6e+91) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	tmp = 0
	if x <= -6.8e+166:
		tmp = t_1
	elif x <= -4.2e+111:
		tmp = x * (1.0 - y)
	elif x <= 2.6e+91:
		tmp = x + ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (x <= -6.8e+166)
		tmp = t_1;
	elseif (x <= -4.2e+111)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 2.6e+91)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	tmp = 0.0;
	if (x <= -6.8e+166)
		tmp = t_1;
	elseif (x <= -4.2e+111)
		tmp = x * (1.0 - y);
	elseif (x <= 2.6e+91)
		tmp = x + ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+166], t$95$1, If[LessEqual[x, -4.2e+111], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+91], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8000000000000001e166 or 2.6e91 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.6%

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

      1. +-commutative 71.6%

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

      2. mul-1-neg 71.6%

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

      3. unsub-neg 71.6%

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

      4. *-commutative 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in x around -inf 66.6%

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

   if -6.8000000000000001e166 < x < -4.1999999999999999e111

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

   if -4.1999999999999999e111 < x < 2.6e91

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+166}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+91}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 6: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2800:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+222}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -2.2e+123)
     t_1
     (if (<= y 2800.0)
       (* x (+ z 1.0))
       (if (<= y 8.2e+222) t_1 (+ x (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -2.2e+123) {
		tmp = t_1;
	} else if (y <= 2800.0) {
		tmp = x * (z + 1.0);
	} else if (y <= 8.2e+222) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (y <= (-2.2d+123)) then
        tmp = t_1
    else if (y <= 2800.0d0) then
        tmp = x * (z + 1.0d0)
    else if (y <= 8.2d+222) then
        tmp = t_1
    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 t_1 = y * -x;
	double tmp;
	if (y <= -2.2e+123) {
		tmp = t_1;
	} else if (y <= 2800.0) {
		tmp = x * (z + 1.0);
	} else if (y <= 8.2e+222) {
		tmp = t_1;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -2.2e+123:
		tmp = t_1
	elif y <= 2800.0:
		tmp = x * (z + 1.0)
	elif y <= 8.2e+222:
		tmp = t_1
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -2.2e+123)
		tmp = t_1;
	elseif (y <= 2800.0)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 8.2e+222)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -2.2e+123)
		tmp = t_1;
	elseif (y <= 2800.0)
		tmp = x * (z + 1.0);
	elseif (y <= 8.2e+222)
		tmp = t_1;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -2.2e+123], t$95$1, If[LessEqual[y, 2800.0], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+222], t$95$1, N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.19999999999999992e123 or 2800 < y < 8.19999999999999974e222

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. distribute-rgt-neg-in 62.0%

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

      3. +-commutative 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in y around inf 53.0%

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

   if -2.19999999999999992e123 < y < 2800

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

      4. *-commutative 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in x around -inf 61.7%

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

   if 8.19999999999999974e222 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 71.3%

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

   3. Taylor expanded in z around 0 71.3%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2800:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 7: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2800:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -2.5e+124)
     t_1
     (if (<= y 2800.0)
       (+ x (* z x))
       (if (<= y 1.25e+223) t_1 (+ x (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -2.5e+124) {
		tmp = t_1;
	} else if (y <= 2800.0) {
		tmp = x + (z * x);
	} else if (y <= 1.25e+223) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (y <= (-2.5d+124)) then
        tmp = t_1
    else if (y <= 2800.0d0) then
        tmp = x + (z * x)
    else if (y <= 1.25d+223) then
        tmp = t_1
    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 t_1 = y * -x;
	double tmp;
	if (y <= -2.5e+124) {
		tmp = t_1;
	} else if (y <= 2800.0) {
		tmp = x + (z * x);
	} else if (y <= 1.25e+223) {
		tmp = t_1;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -2.5e+124:
		tmp = t_1
	elif y <= 2800.0:
		tmp = x + (z * x)
	elif y <= 1.25e+223:
		tmp = t_1
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -2.5e+124)
		tmp = t_1;
	elseif (y <= 2800.0)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 1.25e+223)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -2.5e+124)
		tmp = t_1;
	elseif (y <= 2800.0)
		tmp = x + (z * x);
	elseif (y <= 1.25e+223)
		tmp = t_1;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -2.5e+124], t$95$1, If[LessEqual[y, 2800.0], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+223], t$95$1, N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999998e124 or 2800 < y < 1.24999999999999996e223

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. distribute-rgt-neg-in 62.0%

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

      3. +-commutative 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in y around inf 53.0%

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

   if -2.4999999999999998e124 < y < 2800

   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-- 85.5%

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

      3. associate-*r/ 79.4%

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

   3. Applied egg-rr 79.4%

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

      1. associate-/l* 85.3%

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

      2. difference-of-squares 85.3%

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

      3. associate-/r* 99.8%

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

      4. *-inverses 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 90.0%

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

   7. Taylor expanded in t around 0 61.8%

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

   if 1.24999999999999996e223 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 71.3%

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

   3. Taylor expanded in z around 0 71.3%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2800:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 8: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+117} \lor \neg \left(y \leq 8 \cdot 10^{+67}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.6e+117) (not (<= y 8e+67)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.6e+117) || !(y <= 8e+67)) {
		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 <= (-7.6d+117)) .or. (.not. (y <= 8d+67))) 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 <= -7.6e+117) || !(y <= 8e+67)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.6e+117) or not (y <= 8e+67):
		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 <= -7.6e+117) || !(y <= 8e+67))
		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 <= -7.6e+117) || ~((y <= 8e+67)))
		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, -7.6e+117], N[Not[LessEqual[y, 8e+67]], $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 < -7.6000000000000003e117 or 7.99999999999999986e67 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 89.8%

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

   if -7.6000000000000003e117 < y < 7.99999999999999986e67

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.9%

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

      1. +-commutative 87.9%

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

      2. mul-1-neg 87.9%

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

      3. unsub-neg 87.9%

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

      4. *-commutative 87.9%

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

   4. Simplified 87.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+117} \lor \neg \left(y \leq 8 \cdot 10^{+67}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 49.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+124} \lor \neg \left(y \leq 2850\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e+124) (not (<= y 2850.0))) (* y (- x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+124) || !(y <= 2850.0)) {
		tmp = y * -x;
	} 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 <= (-1.8d+124)) .or. (.not. (y <= 2850.0d0))) then
        tmp = y * -x
    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 <= -1.8e+124) || !(y <= 2850.0)) {
		tmp = y * -x;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e+124) or not (y <= 2850.0):
		tmp = y * -x
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e+124) || !(y <= 2850.0))
		tmp = Float64(y * Float64(-x));
	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 <= -1.8e+124) || ~((y <= 2850.0)))
		tmp = y * -x;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e+124], N[Not[LessEqual[y, 2850.0]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999993e124 or 2850 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. distribute-rgt-neg-in 56.0%

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

      3. +-commutative 56.0%

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

   4. Simplified 56.0%

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

   5. Taylor expanded in y around inf 48.7%

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

   if -1.79999999999999993e124 < y < 2850

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

      4. *-commutative 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in x around -inf 61.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+124} \lor \neg \left(y \leq 2850\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 11: 37.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e-8) (* z x) (if (<= z 1.0) x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e-8) {
		tmp = z * x;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.9d-8)) then
        tmp = z * x
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e-8) {
		tmp = z * x;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e-8:
		tmp = z * x
	elif z <= 1.0:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e-8)
		tmp = Float64(z * x);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.9e-8)
		tmp = z * x;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e-8], N[(z * x), $MachinePrecision], If[LessEqual[z, 1.0], x, N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000002e-8 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. distribute-rgt-neg-in 55.4%

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

      3. +-commutative 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in z around inf 43.6%

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

   if -2.9000000000000002e-8 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 71.6%

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

   3. Taylor expanded in x around inf 38.6%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-8}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 12: 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 60.8%

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

3. Taylor expanded in x around inf 19.5%

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

4. Final simplification 19.5%

   \[\leadsto x \]

Developer target: 96.0% 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 2023185 
(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))))