Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.4s

Alternatives: 13

Speedup: 1.0×

• 34.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 67.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-199}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))))
   (if (<= y -1.15e+44)
     t_1
     (if (<= y -4e-199)
       t_2
       (if (<= y 4.2e-257) (* x (+ z 1.0)) (if (<= y 6.5e+36) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -1.15e+44) {
		tmp = t_1;
	} else if (y <= -4e-199) {
		tmp = t_2;
	} else if (y <= 4.2e-257) {
		tmp = x * (z + 1.0);
	} else if (y <= 6.5e+36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    if (y <= (-1.15d+44)) then
        tmp = t_1
    else if (y <= (-4d-199)) then
        tmp = t_2
    else if (y <= 4.2d-257) then
        tmp = x * (z + 1.0d0)
    else if (y <= 6.5d+36) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -1.15e+44) {
		tmp = t_1;
	} else if (y <= -4e-199) {
		tmp = t_2;
	} else if (y <= 4.2e-257) {
		tmp = x * (z + 1.0);
	} else if (y <= 6.5e+36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	tmp = 0
	if y <= -1.15e+44:
		tmp = t_1
	elif y <= -4e-199:
		tmp = t_2
	elif y <= 4.2e-257:
		tmp = x * (z + 1.0)
	elif y <= 6.5e+36:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (y <= -1.15e+44)
		tmp = t_1;
	elseif (y <= -4e-199)
		tmp = t_2;
	elseif (y <= 4.2e-257)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 6.5e+36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	tmp = 0.0;
	if (y <= -1.15e+44)
		tmp = t_1;
	elseif (y <= -4e-199)
		tmp = t_2;
	elseif (y <= 4.2e-257)
		tmp = x * (z + 1.0);
	elseif (y <= 6.5e+36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+44], t$95$1, If[LessEqual[y, -4e-199], t$95$2, If[LessEqual[y, 4.2e-257], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+36], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000002e44 or 6.4999999999999998e36 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 85.1%

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

   4. Taylor expanded in z around -inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. *-commutative 76.4%

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

      3. distribute-rgt-neg-in 76.4%

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

      4. mul-1-neg 76.4%

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

      5. unsub-neg 76.4%

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

      6. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

   7. Taylor expanded in y around -inf 83.7%

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

   if -1.15000000000000002e44 < y < -3.99999999999999993e-199 or 4.2000000000000002e-257 < y < 6.4999999999999998e36

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in z around inf 62.4%

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

   if -3.99999999999999993e-199 < y < 4.2000000000000002e-257

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in y around 0 90.5%

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

      1. +-commutative 90.5%

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

   8. Simplified 90.5%

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

Alternative 3: 45.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+114} \lor \neg \left(t \leq 4.5 \cdot 10^{+235}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.1e+35)
   (* y t)
   (if (<= t 7.5e+88)
     (* x (+ z 1.0))
     (if (or (<= t 8.2e+114) (not (<= t 4.5e+235))) (* y t) (* z (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.1e+35) {
		tmp = y * t;
	} else if (t <= 7.5e+88) {
		tmp = x * (z + 1.0);
	} else if ((t <= 8.2e+114) || !(t <= 4.5e+235)) {
		tmp = y * t;
	} else {
		tmp = 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 (t <= (-6.1d+35)) then
        tmp = y * t
    else if (t <= 7.5d+88) then
        tmp = x * (z + 1.0d0)
    else if ((t <= 8.2d+114) .or. (.not. (t <= 4.5d+235))) then
        tmp = y * t
    else
        tmp = z * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.1e+35) {
		tmp = y * t;
	} else if (t <= 7.5e+88) {
		tmp = x * (z + 1.0);
	} else if ((t <= 8.2e+114) || !(t <= 4.5e+235)) {
		tmp = y * t;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.1e+35:
		tmp = y * t
	elif t <= 7.5e+88:
		tmp = x * (z + 1.0)
	elif (t <= 8.2e+114) or not (t <= 4.5e+235):
		tmp = y * t
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.1e+35)
		tmp = Float64(y * t);
	elseif (t <= 7.5e+88)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((t <= 8.2e+114) || !(t <= 4.5e+235))
		tmp = Float64(y * t);
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.1e+35)
		tmp = y * t;
	elseif (t <= 7.5e+88)
		tmp = x * (z + 1.0);
	elseif ((t <= 8.2e+114) || ~((t <= 4.5e+235)))
		tmp = y * t;
	else
		tmp = z * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.1e+35], N[(y * t), $MachinePrecision], If[LessEqual[t, 7.5e+88], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 8.2e+114], N[Not[LessEqual[t, 4.5e+235]], $MachinePrecision]], N[(y * t), $MachinePrecision], N[(z * (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.09999999999999977e35 or 7.50000000000000031e88 < t < 8.2000000000000001e114 or 4.5e235 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.5%

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

   4. Taylor expanded in z around -inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. *-commutative 80.9%

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

      3. distribute-rgt-neg-in 80.9%

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

      4. mul-1-neg 80.9%

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

      5. unsub-neg 80.9%

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

      6. associate-/l* 78.7%

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

   6. Simplified 78.7%

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

   7. Taylor expanded in y around -inf 68.2%

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

   8. Taylor expanded in t around inf 65.3%

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

      1. *-commutative 65.3%

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

   10. Simplified 65.3%

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

   if -6.09999999999999977e35 < t < 7.50000000000000031e88

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.8%

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

      1. mul-1-neg 77.8%

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

      2. unsub-neg 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in y around 0 56.3%

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

      1. +-commutative 56.3%

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

   8. Simplified 56.3%

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

   if 8.2000000000000001e114 < t < 4.5e235

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-rgt-neg-in 56.4%

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

   8. Simplified 56.4%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+114} \lor \neg \left(t \leq 4.5 \cdot 10^{+235}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 33.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+145}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-96}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-304}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.08e+145)
   (* z x)
   (if (<= x -2.3e-96)
     (* y t)
     (if (<= x -2e-304) (* z (- t)) (if (<= x 2.2e+48) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.08e+145) {
		tmp = z * x;
	} else if (x <= -2.3e-96) {
		tmp = y * t;
	} else if (x <= -2e-304) {
		tmp = z * -t;
	} else if (x <= 2.2e+48) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.08d+145)) then
        tmp = z * x
    else if (x <= (-2.3d-96)) then
        tmp = y * t
    else if (x <= (-2d-304)) then
        tmp = z * -t
    else if (x <= 2.2d+48) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.08e+145) {
		tmp = z * x;
	} else if (x <= -2.3e-96) {
		tmp = y * t;
	} else if (x <= -2e-304) {
		tmp = z * -t;
	} else if (x <= 2.2e+48) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.08e+145:
		tmp = z * x
	elif x <= -2.3e-96:
		tmp = y * t
	elif x <= -2e-304:
		tmp = z * -t
	elif x <= 2.2e+48:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.08e+145)
		tmp = Float64(z * x);
	elseif (x <= -2.3e-96)
		tmp = Float64(y * t);
	elseif (x <= -2e-304)
		tmp = Float64(z * Float64(-t));
	elseif (x <= 2.2e+48)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.08e+145)
		tmp = z * x;
	elseif (x <= -2.3e-96)
		tmp = y * t;
	elseif (x <= -2e-304)
		tmp = z * -t;
	elseif (x <= 2.2e+48)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.08e+145], N[(z * x), $MachinePrecision], If[LessEqual[x, -2.3e-96], N[(y * t), $MachinePrecision], If[LessEqual[x, -2e-304], N[(z * (-t)), $MachinePrecision], If[LessEqual[x, 2.2e+48], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.08000000000000006e145 or 2.1999999999999999e48 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.4%

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

      1. mul-1-neg 88.4%

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

      2. unsub-neg 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in z around inf 44.8%

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

      1. *-commutative 44.8%

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

   8. Simplified 44.8%

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

   if -1.08000000000000006e145 < x < -2.3e-96 or -1.99999999999999994e-304 < x < 2.1999999999999999e48

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 88.8%

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

   4. Taylor expanded in z around -inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. *-commutative 83.5%

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

      3. distribute-rgt-neg-in 83.5%

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

      4. mul-1-neg 83.5%

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

      5. unsub-neg 83.5%

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

      6. associate-/l* 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in y around -inf 61.6%

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

   8. Taylor expanded in t around inf 45.8%

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

      1. *-commutative 45.8%

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

   10. Simplified 45.8%

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

   if -2.3e-96 < x < -1.99999999999999994e-304

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in x around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. distribute-rgt-neg-in 62.4%

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

   8. Simplified 62.4%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+145}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-96}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-304}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-32}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.85e-31)
   (* x (- 1.0 y))
   (if (<= x -1.1e-305)
     (* z (- t))
     (if (<= x 1.1e-32) (* y t) (* x (+ z 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.85e-31) {
		tmp = x * (1.0 - y);
	} else if (x <= -1.1e-305) {
		tmp = z * -t;
	} else if (x <= 1.1e-32) {
		tmp = 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 <= (-1.85d-31)) then
        tmp = x * (1.0d0 - y)
    else if (x <= (-1.1d-305)) then
        tmp = z * -t
    else if (x <= 1.1d-32) then
        tmp = 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 <= -1.85e-31) {
		tmp = x * (1.0 - y);
	} else if (x <= -1.1e-305) {
		tmp = z * -t;
	} else if (x <= 1.1e-32) {
		tmp = y * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.85e-31:
		tmp = x * (1.0 - y)
	elif x <= -1.1e-305:
		tmp = z * -t
	elif x <= 1.1e-32:
		tmp = y * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.85e-31)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= -1.1e-305)
		tmp = Float64(z * Float64(-t));
	elseif (x <= 1.1e-32)
		tmp = 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 <= -1.85e-31)
		tmp = x * (1.0 - y);
	elseif (x <= -1.1e-305)
		tmp = z * -t;
	elseif (x <= 1.1e-32)
		tmp = y * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.85e-31], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.1e-305], N[(z * (-t)), $MachinePrecision], If[LessEqual[x, 1.1e-32], N[(y * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8499999999999999e-31

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around 0 58.9%

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

   if -1.8499999999999999e-31 < x < -1.09999999999999998e-305

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in x around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. distribute-rgt-neg-in 60.2%

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

   8. Simplified 60.2%

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

   if -1.09999999999999998e-305 < x < 1.1e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 81.9%

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

   4. Taylor expanded in z around -inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. *-commutative 70.2%

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

      3. distribute-rgt-neg-in 70.2%

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

      4. mul-1-neg 70.2%

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

      5. unsub-neg 70.2%

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

      6. associate-/l* 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in y around -inf 63.0%

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

   8. Taylor expanded in t around inf 57.9%

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

      1. *-commutative 57.9%

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

   10. Simplified 57.9%

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

   if 1.1e-32 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in y around 0 58.7%

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

      1. +-commutative 58.7%

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

   8. Simplified 58.7%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-32}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-306}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+46}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2e-35)
   (* x (- y))
   (if (<= x -4.8e-306) (* z (- t)) (if (<= x 8e+46) (* y t) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2e-35) {
		tmp = x * -y;
	} else if (x <= -4.8e-306) {
		tmp = z * -t;
	} else if (x <= 8e+46) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2d-35)) then
        tmp = x * -y
    else if (x <= (-4.8d-306)) then
        tmp = z * -t
    else if (x <= 8d+46) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2e-35) {
		tmp = x * -y;
	} else if (x <= -4.8e-306) {
		tmp = z * -t;
	} else if (x <= 8e+46) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2e-35:
		tmp = x * -y
	elif x <= -4.8e-306:
		tmp = z * -t
	elif x <= 8e+46:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2e-35)
		tmp = Float64(x * Float64(-y));
	elseif (x <= -4.8e-306)
		tmp = Float64(z * Float64(-t));
	elseif (x <= 8e+46)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2e-35)
		tmp = x * -y;
	elseif (x <= -4.8e-306)
		tmp = z * -t;
	elseif (x <= 8e+46)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2e-35], N[(x * (-y)), $MachinePrecision], If[LessEqual[x, -4.8e-306], N[(z * (-t)), $MachinePrecision], If[LessEqual[x, 8e+46], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.00000000000000002e-35

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in y around inf 39.2%

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

      1. mul-1-neg 39.2%

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

      2. distribute-lft-neg-out 39.2%

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

      3. *-commutative 39.2%

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

   8. Simplified 39.2%

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

   if -2.00000000000000002e-35 < x < -4.7999999999999999e-306

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in x around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. distribute-rgt-neg-in 60.2%

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

   8. Simplified 60.2%

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

   if -4.7999999999999999e-306 < x < 7.9999999999999999e46

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 85.2%

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

   4. Taylor expanded in z around -inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. *-commutative 76.3%

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

      3. distribute-rgt-neg-in 76.3%

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

      4. mul-1-neg 76.3%

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

      5. unsub-neg 76.3%

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

      6. associate-/l* 73.8%

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

   6. Simplified 73.8%

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

   7. Taylor expanded in y around -inf 62.2%

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

   8. Taylor expanded in t around inf 49.7%

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

      1. *-commutative 49.7%

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

   10. Simplified 49.7%

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

   if 7.9999999999999999e46 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. unsub-neg 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in z around inf 48.9%

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

      1. *-commutative 48.9%

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

   8. Simplified 48.9%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-306}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+46}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+24} \lor \neg \left(z \leq 1.05 \cdot 10^{+56}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.5e+24) (not (<= z 1.05e+56)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+24) || !(z <= 1.05e+56)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.5d+24)) .or. (.not. (z <= 1.05d+56))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.5e+24) || !(z <= 1.05e+56)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.5e+24) or not (z <= 1.05e+56):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.5e+24) || !(z <= 1.05e+56))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.5e+24) || ~((z <= 1.05e+56)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.5e+24], N[Not[LessEqual[z, 1.05e+56]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000014e24 or 1.05000000000000009e56 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in z around inf 86.5%

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

   if -7.50000000000000014e24 < z < 1.05000000000000009e56

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.2%

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

      1. *-commutative 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+24} \lor \neg \left(z \leq 1.05 \cdot 10^{+56}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+24} \lor \neg \left(z \leq 53000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e+24) (not (<= z 53000000000.0)))
   (* z (- x t))
   (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+24) || !(z <= 53000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.5d+24)) .or. (.not. (z <= 53000000000.0d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+24) || !(z <= 53000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e+24) or not (z <= 53000000000.0):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e+24) || !(z <= 53000000000.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e+24) || ~((z <= 53000000000.0)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e+24], N[Not[LessEqual[z, 53000000000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000002e24 or 5.3e10 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. unsub-neg 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in z around inf 83.3%

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

   if -5.5000000000000002e24 < z < 5.3e10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in t around inf 72.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+24} \lor \neg \left(z \leq 53000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-9} \lor \neg \left(y \leq 80000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.2e-9) (not (<= y 80000.0))) (* y (- t x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e-9) || !(y <= 80000.0)) {
		tmp = y * (t - 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 <= (-7.2d-9)) .or. (.not. (y <= 80000.0d0))) then
        tmp = y * (t - 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 <= -7.2e-9) || !(y <= 80000.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.2e-9) or not (y <= 80000.0):
		tmp = y * (t - x)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.2e-9) || !(y <= 80000.0))
		tmp = Float64(y * Float64(t - 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 <= -7.2e-9) || ~((y <= 80000.0)))
		tmp = y * (t - x);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.2e-9], N[Not[LessEqual[y, 80000.0]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e-9 or 8e4 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.4%

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

   4. Taylor expanded in z around -inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. *-commutative 79.4%

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

      3. distribute-rgt-neg-in 79.4%

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

      4. mul-1-neg 79.4%

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

      5. unsub-neg 79.4%

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

      6. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

   7. Taylor expanded in y around -inf 76.6%

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

   if -7.2e-9 < y < 8e4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in y around 0 57.1%

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

      1. +-commutative 57.1%

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

   8. Simplified 57.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-9} \lor \neg \left(y \leq 80000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+37} \lor \neg \left(z \leq 46000000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.1e+37) (not (<= z 46000000000.0))) (* z x) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e+37) || !(z <= 46000000000.0)) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.1d+37)) .or. (.not. (z <= 46000000000.0d0))) then
        tmp = z * x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e+37) || !(z <= 46000000000.0)) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.1e+37) or not (z <= 46000000000.0):
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.1e+37) || !(z <= 46000000000.0))
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.1e+37) || ~((z <= 46000000000.0)))
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.1e+37], N[Not[LessEqual[z, 46000000000.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e37 or 4.6e10 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. unsub-neg 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in z around inf 45.2%

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

      1. *-commutative 45.2%

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

   8. Simplified 45.2%

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

   if -1.1e37 < z < 4.6e10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.6%

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

   4. Taylor expanded in z around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. *-commutative 80.0%

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

      3. distribute-rgt-neg-in 80.0%

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

      4. mul-1-neg 80.0%

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

      5. unsub-neg 80.0%

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

      6. associate-/l* 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in y around -inf 60.5%

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

   8. Taylor expanded in t around inf 43.2%

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

      1. *-commutative 43.2%

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

   10. Simplified 43.2%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+37} \lor \neg \left(z \leq 46000000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-10} \lor \neg \left(y \leq 5.6 \cdot 10^{-101}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e-10) (not (<= y 5.6e-101))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-10) || !(y <= 5.6e-101)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.5d-10)) .or. (.not. (y <= 5.6d-101))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-10) || !(y <= 5.6e-101)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5e-10) or not (y <= 5.6e-101):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5e-10) || !(y <= 5.6e-101))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.5e-10) || ~((y <= 5.6e-101)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.5e-10], N[Not[LessEqual[y, 5.6e-101]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999998e-10 or 5.59999999999999978e-101 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.3%

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

   4. Taylor expanded in z around -inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. *-commutative 81.3%

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

      3. distribute-rgt-neg-in 81.3%

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

      4. mul-1-neg 81.3%

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

      5. unsub-neg 81.3%

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

      6. associate-/l* 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in y around -inf 69.3%

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

   8. Taylor expanded in t around inf 44.5%

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

      1. *-commutative 44.5%

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

   10. Simplified 44.5%

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

   if -3.4999999999999998e-10 < y < 5.59999999999999978e-101

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 44.3%

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

      1. *-commutative 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in y around 0 38.2%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-10} \lor \neg \left(y \leq 5.6 \cdot 10^{-101}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 13: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 61.6%

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

   1. *-commutative 61.6%

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

5. Simplified 61.6%

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

6. Taylor expanded in y around 0 17.3%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Developer Target 1: 96.3% 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 2024170 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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