Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.1s

Alternatives: 18

Speedup: 1.0×

• 34.1% 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: 72.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+65} \lor \neg \left(t \leq -4800000000000 \lor \neg \left(t \leq -3.35 \cdot 10^{-100}\right) \land t \leq 1.75 \cdot 10^{-39}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.05e+65)
         (not
          (or (<= t -4800000000000.0)
              (and (not (<= t -3.35e-100)) (<= t 1.75e-39)))))
   (* (- y z) t)
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e+65) || !((t <= -4800000000000.0) || (!(t <= -3.35e-100) && (t <= 1.75e-39)))) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 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 ((t <= (-1.05d+65)) .or. (.not. (t <= (-4800000000000.0d0)) .or. (.not. (t <= (-3.35d-100))) .and. (t <= 1.75d-39))) then
        tmp = (y - z) * t
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e+65) || !((t <= -4800000000000.0) || (!(t <= -3.35e-100) && (t <= 1.75e-39)))) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.05e+65) or not ((t <= -4800000000000.0) or (not (t <= -3.35e-100) and (t <= 1.75e-39))):
		tmp = (y - z) * t
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.05e+65) || !((t <= -4800000000000.0) || (!(t <= -3.35e-100) && (t <= 1.75e-39))))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.05e+65) || ~(((t <= -4800000000000.0) || (~((t <= -3.35e-100)) && (t <= 1.75e-39)))))
		tmp = (y - z) * t;
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.05e+65], N[Not[Or[LessEqual[t, -4800000000000.0], And[N[Not[LessEqual[t, -3.35e-100]], $MachinePrecision], LessEqual[t, 1.75e-39]]]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999996e65 or -4.8e12 < t < -3.34999999999999986e-100 or 1.75e-39 < t

   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. Taylor expanded in t around inf 87.4%

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

   6. Taylor expanded in t around inf 81.6%

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

   if -1.04999999999999996e65 < t < -4.8e12 or -3.34999999999999986e-100 < t < 1.75e-39

   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 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+65} \lor \neg \left(t \leq -4800000000000 \lor \neg \left(t \leq -3.35 \cdot 10^{-100}\right) \land t \leq 1.75 \cdot 10^{-39}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+28}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 6000000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -7.8e+87)
     t_1
     (if (<= y -2e+28)
       (* (- y z) t)
       (if (<= y -8e-61)
         (* x (+ z 1.0))
         (if (<= y 6000000000.0) (- x (* z t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -7.8e+87) {
		tmp = t_1;
	} else if (y <= -2e+28) {
		tmp = (y - z) * t;
	} else if (y <= -8e-61) {
		tmp = x * (z + 1.0);
	} else if (y <= 6000000000.0) {
		tmp = x - (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 = y * (t - x)
    if (y <= (-7.8d+87)) then
        tmp = t_1
    else if (y <= (-2d+28)) then
        tmp = (y - z) * t
    else if (y <= (-8d-61)) then
        tmp = x * (z + 1.0d0)
    else if (y <= 6000000000.0d0) then
        tmp = x - (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 = y * (t - x);
	double tmp;
	if (y <= -7.8e+87) {
		tmp = t_1;
	} else if (y <= -2e+28) {
		tmp = (y - z) * t;
	} else if (y <= -8e-61) {
		tmp = x * (z + 1.0);
	} else if (y <= 6000000000.0) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -7.8e+87:
		tmp = t_1
	elif y <= -2e+28:
		tmp = (y - z) * t
	elif y <= -8e-61:
		tmp = x * (z + 1.0)
	elif y <= 6000000000.0:
		tmp = x - (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -7.8e+87)
		tmp = t_1;
	elseif (y <= -2e+28)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= -8e-61)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 6000000000.0)
		tmp = Float64(x - Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -7.8e+87)
		tmp = t_1;
	elseif (y <= -2e+28)
		tmp = (y - z) * t;
	elseif (y <= -8e-61)
		tmp = x * (z + 1.0);
	elseif (y <= 6000000000.0)
		tmp = x - (z * t);
	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]}, If[LessEqual[y, -7.8e+87], t$95$1, If[LessEqual[y, -2e+28], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -8e-61], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6000000000.0], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.80000000000000039e87 or 6e9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.0%

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

      1. +-commutative 90.0%

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

      2. associate--l+ 90.0%

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

      3. +-commutative 90.0%

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

      4. mul-1-neg 90.0%

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

      5. unsub-neg 90.0%

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

      6. div-sub 90.0%

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

      7. unsub-neg 90.0%

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

      8. mul-1-neg 90.0%

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

      9. +-commutative 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in y around inf 88.9%

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

   if -7.80000000000000039e87 < y < -1.99999999999999992e28

   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. Taylor expanded in t around inf 88.5%

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

   6. Taylor expanded in t around inf 88.5%

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

   if -1.99999999999999992e28 < y < -8.0000000000000003e-61

   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 85.1%

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

      1. mul-1-neg 85.1%

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

      2. unsub-neg 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in y around 0 71.0%

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

      1. +-commutative 71.0%

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

   8. Simplified 71.0%

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

   if -8.0000000000000003e-61 < y < 6e9

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 83.6%

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

   4. Taylor expanded in y around 0 74.2%

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

      1. mul-1-neg 74.2%

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

      2. unsub-neg 74.2%

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

   6. Simplified 74.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+28}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 6000000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 880000000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.35e+88)
     t_1
     (if (<= y -4.8e+27)
       (* (- y z) t)
       (if (<= y 4.3e-297)
         (* x (+ z 1.0))
         (if (<= y 880000000000.0) (* z (- x t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1.35e+88) {
		tmp = t_1;
	} else if (y <= -4.8e+27) {
		tmp = (y - z) * t;
	} else if (y <= 4.3e-297) {
		tmp = x * (z + 1.0);
	} else if (y <= 880000000000.0) {
		tmp = z * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-1.35d+88)) then
        tmp = t_1
    else if (y <= (-4.8d+27)) then
        tmp = (y - z) * t
    else if (y <= 4.3d-297) then
        tmp = x * (z + 1.0d0)
    else if (y <= 880000000000.0d0) then
        tmp = z * (x - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1.35e+88) {
		tmp = t_1;
	} else if (y <= -4.8e+27) {
		tmp = (y - z) * t;
	} else if (y <= 4.3e-297) {
		tmp = x * (z + 1.0);
	} else if (y <= 880000000000.0) {
		tmp = z * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -1.35e+88:
		tmp = t_1
	elif y <= -4.8e+27:
		tmp = (y - z) * t
	elif y <= 4.3e-297:
		tmp = x * (z + 1.0)
	elif y <= 880000000000.0:
		tmp = z * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -1.35e+88)
		tmp = t_1;
	elseif (y <= -4.8e+27)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 4.3e-297)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 880000000000.0)
		tmp = Float64(z * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -1.35e+88)
		tmp = t_1;
	elseif (y <= -4.8e+27)
		tmp = (y - z) * t;
	elseif (y <= 4.3e-297)
		tmp = x * (z + 1.0);
	elseif (y <= 880000000000.0)
		tmp = z * (x - t);
	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]}, If[LessEqual[y, -1.35e+88], t$95$1, If[LessEqual[y, -4.8e+27], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 4.3e-297], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 880000000000.0], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35000000000000008e88 or 8.8e11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.0%

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

      1. +-commutative 90.0%

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

      2. associate--l+ 90.0%

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

      3. +-commutative 90.0%

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

      4. mul-1-neg 90.0%

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

      5. unsub-neg 90.0%

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

      6. div-sub 90.0%

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

      7. unsub-neg 90.0%

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

      8. mul-1-neg 90.0%

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

      9. +-commutative 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in y around inf 88.9%

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

   if -1.35000000000000008e88 < y < -4.79999999999999995e27

   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. Taylor expanded in t around inf 88.5%

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

   6. Taylor expanded in t around inf 88.5%

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

   if -4.79999999999999995e27 < y < 4.3000000000000003e-297

   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 68.8%

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

      1. mul-1-neg 68.8%

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

      2. unsub-neg 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in y around 0 64.7%

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

      1. +-commutative 64.7%

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

   8. Simplified 64.7%

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

   if 4.3000000000000003e-297 < y < 8.8e11

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   6. Taylor expanded in z around inf 66.2%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 880000000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -7.7 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* (- y z) t)))
   (if (<= y -7.7e+87)
     t_1
     (if (<= y -7.2e+27)
       t_2
       (if (<= y 2.5e-296) (* x (+ z 1.0)) (if (<= y 1.45e+14) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (y <= -7.7e+87) {
		tmp = t_1;
	} else if (y <= -7.2e+27) {
		tmp = t_2;
	} else if (y <= 2.5e-296) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.45e+14) {
		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 = (y - z) * t
    if (y <= (-7.7d+87)) then
        tmp = t_1
    else if (y <= (-7.2d+27)) then
        tmp = t_2
    else if (y <= 2.5d-296) then
        tmp = x * (z + 1.0d0)
    else if (y <= 1.45d+14) 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 = (y - z) * t;
	double tmp;
	if (y <= -7.7e+87) {
		tmp = t_1;
	} else if (y <= -7.2e+27) {
		tmp = t_2;
	} else if (y <= 2.5e-296) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.45e+14) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = (y - z) * t
	tmp = 0
	if y <= -7.7e+87:
		tmp = t_1
	elif y <= -7.2e+27:
		tmp = t_2
	elif y <= 2.5e-296:
		tmp = x * (z + 1.0)
	elif y <= 1.45e+14:
		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(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -7.7e+87)
		tmp = t_1;
	elseif (y <= -7.2e+27)
		tmp = t_2;
	elseif (y <= 2.5e-296)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 1.45e+14)
		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 = (y - z) * t;
	tmp = 0.0;
	if (y <= -7.7e+87)
		tmp = t_1;
	elseif (y <= -7.2e+27)
		tmp = t_2;
	elseif (y <= 2.5e-296)
		tmp = x * (z + 1.0);
	elseif (y <= 1.45e+14)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -7.7e+87], t$95$1, If[LessEqual[y, -7.2e+27], t$95$2, If[LessEqual[y, 2.5e-296], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+14], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.70000000000000031e87 or 1.45e14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.0%

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

      1. +-commutative 90.0%

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

      2. associate--l+ 90.0%

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

      3. +-commutative 90.0%

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

      4. mul-1-neg 90.0%

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

      5. unsub-neg 90.0%

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

      6. div-sub 90.0%

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

      7. unsub-neg 90.0%

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

      8. mul-1-neg 90.0%

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

      9. +-commutative 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in y around inf 88.9%

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

   if -7.70000000000000031e87 < y < -7.19999999999999966e27 or 2.50000000000000015e-296 < y < 1.45e14

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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. Taylor expanded in t around inf 84.1%

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

   6. Taylor expanded in t around inf 62.9%

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

   if -7.19999999999999966e27 < y < 2.50000000000000015e-296

   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 68.8%

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

      1. mul-1-neg 68.8%

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

      2. unsub-neg 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in y around 0 64.7%

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

      1. +-commutative 64.7%

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

   8. Simplified 64.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+27}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+14}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-277}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -1.2e+63)
     t_1
     (if (<= z 1.25e-277) (* y t) (if (<= z 2e-17) x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.2e+63) {
		tmp = t_1;
	} else if (z <= 1.25e-277) {
		tmp = y * t;
	} else if (z <= 2e-17) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-1.2d+63)) then
        tmp = t_1
    else if (z <= 1.25d-277) then
        tmp = y * t
    else if (z <= 2d-17) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.2e+63) {
		tmp = t_1;
	} else if (z <= 1.25e-277) {
		tmp = y * t;
	} else if (z <= 2e-17) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -1.2e+63:
		tmp = t_1
	elif z <= 1.25e-277:
		tmp = y * t
	elif z <= 2e-17:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -1.2e+63)
		tmp = t_1;
	elseif (z <= 1.25e-277)
		tmp = Float64(y * t);
	elseif (z <= 2e-17)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -1.2e+63)
		tmp = t_1;
	elseif (z <= 1.25e-277)
		tmp = y * t;
	elseif (z <= 2e-17)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -1.2e+63], t$95$1, If[LessEqual[z, 1.25e-277], N[(y * t), $MachinePrecision], If[LessEqual[z, 2e-17], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e63 or 2.00000000000000014e-17 < z

   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. Taylor expanded in t around inf 58.0%

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

   6. Taylor expanded in z around inf 48.2%

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

      1. associate-*r* 48.2%

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

      2. mul-1-neg 48.2%

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

   8. Simplified 48.2%

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

   if -1.2e63 < z < 1.25e-277

   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 83.8%

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

      1. +-commutative 83.8%

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

      2. associate--l+ 83.8%

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

      3. +-commutative 83.8%

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

      4. mul-1-neg 83.8%

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

      5. unsub-neg 83.8%

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

      6. div-sub 85.4%

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

      7. unsub-neg 85.4%

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

      8. mul-1-neg 85.4%

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

      9. +-commutative 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in t around inf 49.1%

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

      1. neg-mul-1 49.1%

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

      2. sub-neg 49.1%

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

   8. Simplified 49.1%

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

   9. Taylor expanded in z around 0 46.2%

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

   if 1.25e-277 < z < 2.00000000000000014e-17

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 77.7%

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

   4. Taylor expanded in x around inf 46.7%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-277}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+50}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-279}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e+50)
   (* z x)
   (if (<= z 6.8e-279) (* y t) (if (<= z 6.5e-14) x (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e+50) {
		tmp = z * x;
	} else if (z <= 6.8e-279) {
		tmp = y * t;
	} else if (z <= 6.5e-14) {
		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 <= (-6d+50)) then
        tmp = z * x
    else if (z <= 6.8d-279) then
        tmp = y * t
    else if (z <= 6.5d-14) 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 <= -6e+50) {
		tmp = z * x;
	} else if (z <= 6.8e-279) {
		tmp = y * t;
	} else if (z <= 6.5e-14) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6e+50:
		tmp = z * x
	elif z <= 6.8e-279:
		tmp = y * t
	elif z <= 6.5e-14:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e+50)
		tmp = Float64(z * x);
	elseif (z <= 6.8e-279)
		tmp = Float64(y * t);
	elseif (z <= 6.5e-14)
		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 <= -6e+50)
		tmp = z * x;
	elseif (z <= 6.8e-279)
		tmp = y * t;
	elseif (z <= 6.5e-14)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e+50], N[(z * x), $MachinePrecision], If[LessEqual[z, 6.8e-279], N[(y * t), $MachinePrecision], If[LessEqual[z, 6.5e-14], x, N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.9999999999999996e50 or 6.5000000000000001e-14 < 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 50.1%

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

      1. mul-1-neg 50.1%

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

      2. unsub-neg 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around inf 35.5%

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

   if -5.9999999999999996e50 < z < 6.8000000000000003e-279

   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 84.7%

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

      1. +-commutative 84.7%

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

      2. associate--l+ 84.7%

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

      3. +-commutative 84.7%

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

      4. mul-1-neg 84.7%

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

      5. unsub-neg 84.7%

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

      6. div-sub 85.1%

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

      7. unsub-neg 85.1%

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

      8. mul-1-neg 85.1%

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

      9. +-commutative 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in t around inf 49.0%

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

      1. neg-mul-1 49.0%

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

      2. sub-neg 49.0%

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

   8. Simplified 49.0%

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

   9. Taylor expanded in z around 0 46.0%

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

   if 6.8000000000000003e-279 < z < 6.5000000000000001e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 77.7%

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

   4. Taylor expanded in x around inf 46.7%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+50}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-279}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+70} \lor \neg \left(y \leq 1.08 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e+70) (not (<= y 1.08e+15)))
   (* y (- t x))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+70) || !(y <= 1.08e+15)) {
		tmp = 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 <= (-1.3d+70)) .or. (.not. (y <= 1.08d+15))) then
        tmp = 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 <= -1.3e+70) || !(y <= 1.08e+15)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.3e+70) or not (y <= 1.08e+15):
		tmp = y * (t - x)
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.3e+70) || !(y <= 1.08e+15))
		tmp = 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 <= -1.3e+70) || ~((y <= 1.08e+15)))
		tmp = y * (t - x);
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.3e+70], N[Not[LessEqual[y, 1.08e+15]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e70 or 1.08e15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.2%

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

      1. +-commutative 90.2%

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

      2. associate--l+ 90.2%

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

      3. +-commutative 90.2%

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

      4. mul-1-neg 90.2%

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

      5. unsub-neg 90.2%

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

      6. div-sub 90.2%

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

      7. unsub-neg 90.2%

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

      8. mul-1-neg 90.2%

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

      9. +-commutative 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in y around inf 89.1%

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

   if -1.3e70 < y < 1.08e15

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. unsub-neg 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+70} \lor \neg \left(y \leq 1.08 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.22 \cdot 10^{-100} \lor \neg \left(t \leq 4.9 \cdot 10^{-54}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.22e-100) (not (<= t 4.9e-54)))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.22e-100) || !(t <= 4.9e-54)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 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 ((t <= (-2.22d-100)) .or. (.not. (t <= 4.9d-54))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.22e-100) || !(t <= 4.9e-54)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.22e-100) or not (t <= 4.9e-54):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.22e-100) || !(t <= 4.9e-54))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.22e-100) || ~((t <= 4.9e-54)))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.22e-100], N[Not[LessEqual[t, 4.9e-54]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2199999999999999e-100 or 4.90000000000000021e-54 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 84.6%

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

   if -2.2199999999999999e-100 < t < 4.90000000000000021e-54

   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 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.22 \cdot 10^{-100} \lor \neg \left(t \leq 4.9 \cdot 10^{-54}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+51} \lor \neg \left(z \leq 4 \cdot 10^{+44}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02e+51) (not (<= z 4e+44)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e+51) || !(z <= 4e+44)) {
		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 <= (-1.02d+51)) .or. (.not. (z <= 4d+44))) 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 <= -1.02e+51) || !(z <= 4e+44)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.02e+51) or not (z <= 4e+44):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.02e+51) || !(z <= 4e+44))
		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 <= -1.02e+51) || ~((z <= 4e+44)))
		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, -1.02e+51], N[Not[LessEqual[z, 4e+44]], $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 < -1.02e51 or 4.0000000000000004e44 < 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 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in z around inf 81.6%

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

   if -1.02e51 < z < 4.0000000000000004e44

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 88.6%

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

      1. *-commutative 88.6%

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

   5. Simplified 88.6%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+51} \lor \neg \left(z \leq 4 \cdot 10^{+44}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+51} \lor \neg \left(z \leq 2.1 \cdot 10^{-15}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5e+51) (not (<= z 2.1e-15))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e+51) || !(z <= 2.1e-15)) {
		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 <= (-5d+51)) .or. (.not. (z <= 2.1d-15))) 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 <= -5e+51) || !(z <= 2.1e-15)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5e+51) or not (z <= 2.1e-15):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5e+51) || !(z <= 2.1e-15))
		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 <= -5e+51) || ~((z <= 2.1e-15)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5e+51], N[Not[LessEqual[z, 2.1e-15]], $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 < -5e51 or 2.09999999999999981e-15 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. unsub-neg 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in z around inf 77.2%

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

   if -5e51 < z < 2.09999999999999981e-15

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 78.6%

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

   4. Taylor expanded in y around inf 70.9%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+51} \lor \neg \left(z \leq 2.1 \cdot 10^{-15}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.22 \cdot 10^{-100} \lor \neg \left(t \leq 3.7 \cdot 10^{-61}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.22e-100) (not (<= t 3.7e-61)))
   (* (- y z) t)
   (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.22e-100) || !(t <= 3.7e-61)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.22d-100)) .or. (.not. (t <= 3.7d-61))) then
        tmp = (y - z) * t
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.22e-100) || !(t <= 3.7e-61)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.22e-100) or not (t <= 3.7e-61):
		tmp = (y - z) * t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.22e-100) || !(t <= 3.7e-61))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.22e-100) || ~((t <= 3.7e-61)))
		tmp = (y - z) * t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.22e-100], N[Not[LessEqual[t, 3.7e-61]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2199999999999999e-100 or 3.7e-61 < t

   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. Taylor expanded in t around inf 84.1%

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

   6. Taylor expanded in t around inf 75.1%

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

   if -2.2199999999999999e-100 < t < 3.7e-61

   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 86.8%

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

      1. mul-1-neg 86.8%

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

      2. unsub-neg 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around 0 62.6%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.22 \cdot 10^{-100} \lor \neg \left(t \leq 3.7 \cdot 10^{-61}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-100} \lor \neg \left(t \leq 7.4 \cdot 10^{-38}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e-100) (not (<= t 7.4e-38))) (* (- y z) t) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-100) || !(t <= 7.4e-38)) {
		tmp = (y - z) * 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 ((t <= (-3.2d-100)) .or. (.not. (t <= 7.4d-38))) then
        tmp = (y - z) * 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 ((t <= -3.2e-100) || !(t <= 7.4e-38)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.2e-100) or not (t <= 7.4e-38):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e-100) || !(t <= 7.4e-38))
		tmp = Float64(Float64(y - z) * 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 ((t <= -3.2e-100) || ~((t <= 7.4e-38)))
		tmp = (y - z) * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e-100], N[Not[LessEqual[t, 7.4e-38]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.20000000000000017e-100 or 7.4e-38 < t

   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. Taylor expanded in t around inf 84.4%

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

   6. Taylor expanded in t around inf 75.9%

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

   if -3.20000000000000017e-100 < t < 7.4e-38

   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 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 56.8%

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

      1. +-commutative 56.8%

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

   8. Simplified 56.8%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-100} \lor \neg \left(t \leq 7.4 \cdot 10^{-38}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+149}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+32}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.1e+149) (* z x) (if (<= x 1.25e+32) (* (- y z) t) (* y (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.1e+149) {
		tmp = z * x;
	} else if (x <= 1.25e+32) {
		tmp = (y - z) * t;
	} else {
		tmp = y * -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 <= (-4.1d+149)) then
        tmp = z * x
    else if (x <= 1.25d+32) then
        tmp = (y - z) * t
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.1e+149) {
		tmp = z * x;
	} else if (x <= 1.25e+32) {
		tmp = (y - z) * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.1e+149:
		tmp = z * x
	elif x <= 1.25e+32:
		tmp = (y - z) * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.1e+149)
		tmp = Float64(z * x);
	elseif (x <= 1.25e+32)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.1e+149)
		tmp = z * x;
	elseif (x <= 1.25e+32)
		tmp = (y - z) * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.1e+149], N[(z * x), $MachinePrecision], If[LessEqual[x, 1.25e+32], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.0999999999999996e149

   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 97.5%

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

      1. mul-1-neg 97.5%

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

      2. unsub-neg 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around inf 42.5%

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

   if -4.0999999999999996e149 < x < 1.2499999999999999e32

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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. Taylor expanded in t around inf 80.5%

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

   6. Taylor expanded in t around inf 68.2%

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

   if 1.2499999999999999e32 < 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 92.8%

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

      1. mul-1-neg 92.8%

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

      2. unsub-neg 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in y around inf 47.4%

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

      1. neg-mul-1 47.4%

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

   8. Simplified 47.4%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+149}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+32}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+91}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+20}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.65e+91) (* z x) (if (<= x 1.45e+20) (* y t) (* y (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.65e+91) {
		tmp = z * x;
	} else if (x <= 1.45e+20) {
		tmp = y * t;
	} else {
		tmp = y * -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 <= (-2.65d+91)) then
        tmp = z * x
    else if (x <= 1.45d+20) then
        tmp = y * t
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.65e+91) {
		tmp = z * x;
	} else if (x <= 1.45e+20) {
		tmp = y * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.65e+91:
		tmp = z * x
	elif x <= 1.45e+20:
		tmp = y * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.65e+91)
		tmp = Float64(z * x);
	elseif (x <= 1.45e+20)
		tmp = Float64(y * t);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.65e+91)
		tmp = z * x;
	elseif (x <= 1.45e+20)
		tmp = y * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.65e+91], N[(z * x), $MachinePrecision], If[LessEqual[x, 1.45e+20], N[(y * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.64999999999999998e91

   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 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in z around inf 41.3%

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

   if -2.64999999999999998e91 < x < 1.45e20

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 86.4%

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

      1. +-commutative 86.4%

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

      2. associate--l+ 86.4%

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

      3. +-commutative 86.4%

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

      4. mul-1-neg 86.4%

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

      5. unsub-neg 86.4%

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

      6. div-sub 86.4%

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

      7. unsub-neg 86.4%

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

      8. mul-1-neg 86.4%

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

      9. +-commutative 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in t around inf 58.6%

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

      1. neg-mul-1 58.6%

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

      2. sub-neg 58.6%

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

   8. Simplified 58.6%

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

   9. Taylor expanded in z around 0 39.1%

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

   if 1.45e20 < 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 91.1%

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

      1. mul-1-neg 91.1%

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

      2. unsub-neg 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in y around inf 44.5%

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

      1. neg-mul-1 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+91}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+20}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 6.5 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 6.5e-14))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 6.5e-14)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 6.5d-14))) then
        tmp = z * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 6.5e-14)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 6.5e-14):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 6.5e-14))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 6.5e-14)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 6.5e-14]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 6.5000000000000001e-14 < 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 49.8%

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

      1. mul-1-neg 49.8%

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

      2. unsub-neg 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in z around inf 34.5%

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

   if -1 < z < 6.5000000000000001e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 79.0%

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

   4. Taylor expanded in x around inf 37.0%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 6.5 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 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 18: 17.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 68.4%

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

4. Taylor expanded in x around inf 19.3%

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

Developer Target 1: 96.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024123 
(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))))