Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.4s

Alternatives: 17

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: 46.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(z + 1\right)\\ t_3 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+204}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+76}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-297}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+118}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (+ z 1.0))) (t_3 (* y (- x))))
   (if (<= y -3.9e+204)
     (* y t)
     (if (<= y -6.8e+76)
       t_3
       (if (<= y -3e+29)
         t_1
         (if (<= y 9e-297)
           t_2
           (if (<= y 2.9e-77)
             t_1
             (if (<= y 3.6e+53) t_2 (if (<= y 2.9e+118) t_3 (* y t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * (z + 1.0);
	double t_3 = y * -x;
	double tmp;
	if (y <= -3.9e+204) {
		tmp = y * t;
	} else if (y <= -6.8e+76) {
		tmp = t_3;
	} else if (y <= -3e+29) {
		tmp = t_1;
	} else if (y <= 9e-297) {
		tmp = t_2;
	} else if (y <= 2.9e-77) {
		tmp = t_1;
	} else if (y <= 3.6e+53) {
		tmp = t_2;
	} else if (y <= 2.9e+118) {
		tmp = t_3;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x * (z + 1.0d0)
    t_3 = y * -x
    if (y <= (-3.9d+204)) then
        tmp = y * t
    else if (y <= (-6.8d+76)) then
        tmp = t_3
    else if (y <= (-3d+29)) then
        tmp = t_1
    else if (y <= 9d-297) then
        tmp = t_2
    else if (y <= 2.9d-77) then
        tmp = t_1
    else if (y <= 3.6d+53) then
        tmp = t_2
    else if (y <= 2.9d+118) then
        tmp = t_3
    else
        tmp = y * t
    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 t_2 = x * (z + 1.0);
	double t_3 = y * -x;
	double tmp;
	if (y <= -3.9e+204) {
		tmp = y * t;
	} else if (y <= -6.8e+76) {
		tmp = t_3;
	} else if (y <= -3e+29) {
		tmp = t_1;
	} else if (y <= 9e-297) {
		tmp = t_2;
	} else if (y <= 2.9e-77) {
		tmp = t_1;
	} else if (y <= 3.6e+53) {
		tmp = t_2;
	} else if (y <= 2.9e+118) {
		tmp = t_3;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x * (z + 1.0)
	t_3 = y * -x
	tmp = 0
	if y <= -3.9e+204:
		tmp = y * t
	elif y <= -6.8e+76:
		tmp = t_3
	elif y <= -3e+29:
		tmp = t_1
	elif y <= 9e-297:
		tmp = t_2
	elif y <= 2.9e-77:
		tmp = t_1
	elif y <= 3.6e+53:
		tmp = t_2
	elif y <= 2.9e+118:
		tmp = t_3
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x * Float64(z + 1.0))
	t_3 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -3.9e+204)
		tmp = Float64(y * t);
	elseif (y <= -6.8e+76)
		tmp = t_3;
	elseif (y <= -3e+29)
		tmp = t_1;
	elseif (y <= 9e-297)
		tmp = t_2;
	elseif (y <= 2.9e-77)
		tmp = t_1;
	elseif (y <= 3.6e+53)
		tmp = t_2;
	elseif (y <= 2.9e+118)
		tmp = t_3;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x * (z + 1.0);
	t_3 = y * -x;
	tmp = 0.0;
	if (y <= -3.9e+204)
		tmp = y * t;
	elseif (y <= -6.8e+76)
		tmp = t_3;
	elseif (y <= -3e+29)
		tmp = t_1;
	elseif (y <= 9e-297)
		tmp = t_2;
	elseif (y <= 2.9e-77)
		tmp = t_1;
	elseif (y <= 3.6e+53)
		tmp = t_2;
	elseif (y <= 2.9e+118)
		tmp = t_3;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -3.9e+204], N[(y * t), $MachinePrecision], If[LessEqual[y, -6.8e+76], t$95$3, If[LessEqual[y, -3e+29], t$95$1, If[LessEqual[y, 9e-297], t$95$2, If[LessEqual[y, 2.9e-77], t$95$1, If[LessEqual[y, 3.6e+53], t$95$2, If[LessEqual[y, 2.9e+118], t$95$3, N[(y * t), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.90000000000000017e204 or 2.90000000000000016e118 < 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 87.1%

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

      1. associate--l+ 87.1%

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

      2. +-commutative 87.1%

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

      3. mul-1-neg 87.1%

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

      4. unsub-neg 87.1%

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

      5. div-sub 87.1%

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

      6. unsub-neg 87.1%

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

      7. mul-1-neg 87.1%

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

      8. mul-1-neg 87.1%

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

      9. distribute-rgt-neg-in 87.1%

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

      10. sub-neg 87.1%

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

      11. +-commutative 87.1%

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

      12. distribute-neg-in 87.1%

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

      13. remove-double-neg 87.1%

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

      14. sub-neg 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in t around inf 63.8%

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

      1. neg-mul-1 63.8%

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

      2. sub-neg 63.8%

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

   8. Simplified 63.8%

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

   9. Taylor expanded in z around 0 57.6%

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

   if -3.90000000000000017e204 < y < -6.7999999999999994e76 or 3.6e53 < y < 2.90000000000000016e118

   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 72.7%

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

      1. mul-1-neg 72.7%

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

      2. unsub-neg 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in y around inf 66.8%

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

      1. mul-1-neg 66.8%

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

   8. Simplified 66.8%

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

   if -6.7999999999999994e76 < y < -2.9999999999999999e29 or 8.99999999999999951e-297 < y < 2.8999999999999999e-77

   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 68.6%

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

      1. associate--l+ 68.6%

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

      2. +-commutative 68.6%

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

      3. mul-1-neg 68.6%

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

      4. unsub-neg 68.6%

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

      5. div-sub 73.0%

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

      6. unsub-neg 73.0%

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

      7. mul-1-neg 73.0%

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

      8. mul-1-neg 73.0%

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

      9. distribute-rgt-neg-in 73.0%

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

      10. sub-neg 73.0%

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

      11. +-commutative 73.0%

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

      12. distribute-neg-in 73.0%

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

      13. remove-double-neg 73.0%

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

      14. sub-neg 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in t around inf 46.8%

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

      1. neg-mul-1 46.8%

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

      2. sub-neg 46.8%

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

   8. Simplified 46.8%

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

   9. Taylor expanded in y around 0 58.2%

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

       1. associate-*r* 58.2%

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

       2. mul-1-neg 58.2%

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

   11. Simplified 58.2%

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

   if -2.9999999999999999e29 < y < 8.99999999999999951e-297 or 2.8999999999999999e-77 < y < 3.6e53

   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 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in y around 0 60.0%

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

      1. +-commutative 60.0%

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

   8. Simplified 60.0%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+204}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -28500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-297}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 470000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -28500.0)
     t_1
     (if (<= y 8.2e-297)
       t_2
       (if (<= y 6.2e-77) (* z (- t)) (if (<= y 470000000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -28500.0) {
		tmp = t_1;
	} else if (y <= 8.2e-297) {
		tmp = t_2;
	} else if (y <= 6.2e-77) {
		tmp = z * -t;
	} else if (y <= 470000000000.0) {
		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 = x * (z + 1.0d0)
    if (y <= (-28500.0d0)) then
        tmp = t_1
    else if (y <= 8.2d-297) then
        tmp = t_2
    else if (y <= 6.2d-77) then
        tmp = z * -t
    else if (y <= 470000000000.0d0) 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 = x * (z + 1.0);
	double tmp;
	if (y <= -28500.0) {
		tmp = t_1;
	} else if (y <= 8.2e-297) {
		tmp = t_2;
	} else if (y <= 6.2e-77) {
		tmp = z * -t;
	} else if (y <= 470000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -28500.0:
		tmp = t_1
	elif y <= 8.2e-297:
		tmp = t_2
	elif y <= 6.2e-77:
		tmp = z * -t
	elif y <= 470000000000.0:
		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(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -28500.0)
		tmp = t_1;
	elseif (y <= 8.2e-297)
		tmp = t_2;
	elseif (y <= 6.2e-77)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 470000000000.0)
		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 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -28500.0)
		tmp = t_1;
	elseif (y <= 8.2e-297)
		tmp = t_2;
	elseif (y <= 6.2e-77)
		tmp = z * -t;
	elseif (y <= 470000000000.0)
		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[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -28500.0], t$95$1, If[LessEqual[y, 8.2e-297], t$95$2, If[LessEqual[y, 6.2e-77], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 470000000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -28500 or 4.7e11 < 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 91.7%

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

      1. associate--l+ 91.7%

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

      2. +-commutative 91.7%

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

      3. mul-1-neg 91.7%

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

      4. unsub-neg 91.7%

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

      5. div-sub 91.7%

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

      6. unsub-neg 91.7%

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

      7. mul-1-neg 91.7%

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

      8. mul-1-neg 91.7%

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

      9. distribute-rgt-neg-in 91.7%

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

      10. sub-neg 91.7%

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

      11. +-commutative 91.7%

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

      12. distribute-neg-in 91.7%

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

      13. remove-double-neg 91.7%

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

      14. sub-neg 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in y around inf 81.6%

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

   if -28500 < y < 8.2000000000000004e-297 or 6.20000000000000016e-77 < y < 4.7e11

   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 65.0%

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

      1. mul-1-neg 65.0%

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

      2. unsub-neg 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in y around 0 63.9%

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

      1. +-commutative 63.9%

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

   8. Simplified 63.9%

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

   if 8.2000000000000004e-297 < y < 6.20000000000000016e-77

   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 62.5%

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

      1. associate--l+ 62.5%

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

      2. +-commutative 62.5%

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

      3. mul-1-neg 62.5%

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

      4. unsub-neg 62.5%

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

      5. div-sub 67.6%

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

      6. unsub-neg 67.6%

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

      7. mul-1-neg 67.6%

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

      8. mul-1-neg 67.6%

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

      9. distribute-rgt-neg-in 67.6%

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

      10. sub-neg 67.6%

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

      11. +-commutative 67.6%

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

      12. distribute-neg-in 67.6%

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

      13. remove-double-neg 67.6%

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

      14. sub-neg 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 39.0%

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

      1. neg-mul-1 39.0%

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

      2. sub-neg 39.0%

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

   8. Simplified 39.0%

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

   9. Taylor expanded in y around 0 57.9%

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

       1. associate-*r* 57.9%

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

       2. mul-1-neg 57.9%

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

   11. Simplified 57.9%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -28500:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 470000000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq 5500000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -5.8e+27)
     t_1
     (if (<= y -3.5e-63)
       (* x (+ (- z y) 1.0))
       (if (<= y 5500000000.0) (- 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 <= -5.8e+27) {
		tmp = t_1;
	} else if (y <= -3.5e-63) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= 5500000000.0) {
		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 <= (-5.8d+27)) then
        tmp = t_1
    else if (y <= (-3.5d-63)) then
        tmp = x * ((z - y) + 1.0d0)
    else if (y <= 5500000000.0d0) 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 <= -5.8e+27) {
		tmp = t_1;
	} else if (y <= -3.5e-63) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= 5500000000.0) {
		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 <= -5.8e+27:
		tmp = t_1
	elif y <= -3.5e-63:
		tmp = x * ((z - y) + 1.0)
	elif y <= 5500000000.0:
		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 <= -5.8e+27)
		tmp = t_1;
	elseif (y <= -3.5e-63)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (y <= 5500000000.0)
		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 <= -5.8e+27)
		tmp = t_1;
	elseif (y <= -3.5e-63)
		tmp = x * ((z - y) + 1.0);
	elseif (y <= 5500000000.0)
		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, -5.8e+27], t$95$1, If[LessEqual[y, -3.5e-63], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5500000000.0], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000002e27 or 5.5e9 < 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 91.2%

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

      1. associate--l+ 91.2%

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

      2. +-commutative 91.2%

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

      3. mul-1-neg 91.2%

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

      4. unsub-neg 91.2%

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

      5. div-sub 91.2%

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

      6. unsub-neg 91.2%

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

      7. mul-1-neg 91.2%

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

      8. mul-1-neg 91.2%

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

      9. distribute-rgt-neg-in 91.2%

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

      10. sub-neg 91.2%

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

      11. +-commutative 91.2%

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

      12. distribute-neg-in 91.2%

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

      13. remove-double-neg 91.2%

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

      14. sub-neg 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in y around inf 83.6%

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

   if -5.8000000000000002e27 < y < -3.50000000000000003e-63

   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%

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

   if -3.50000000000000003e-63 < y < 5.5e9

   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 3 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq 5500000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 7500000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.4e+70)
     t_1
     (if (<= y -2.65e-114)
       (* z (- x t))
       (if (<= y 7500000000.0) (- 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 <= -1.4e+70) {
		tmp = t_1;
	} else if (y <= -2.65e-114) {
		tmp = z * (x - t);
	} else if (y <= 7500000000.0) {
		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 <= (-1.4d+70)) then
        tmp = t_1
    else if (y <= (-2.65d-114)) then
        tmp = z * (x - t)
    else if (y <= 7500000000.0d0) 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 <= -1.4e+70) {
		tmp = t_1;
	} else if (y <= -2.65e-114) {
		tmp = z * (x - t);
	} else if (y <= 7500000000.0) {
		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 <= -1.4e+70:
		tmp = t_1
	elif y <= -2.65e-114:
		tmp = z * (x - t)
	elif y <= 7500000000.0:
		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 <= -1.4e+70)
		tmp = t_1;
	elseif (y <= -2.65e-114)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= 7500000000.0)
		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 <= -1.4e+70)
		tmp = t_1;
	elseif (y <= -2.65e-114)
		tmp = z * (x - t);
	elseif (y <= 7500000000.0)
		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, -1.4e+70], t$95$1, If[LessEqual[y, -2.65e-114], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7500000000.0], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999995e70 or 7.5e9 < 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. associate--l+ 90.2%

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

      2. +-commutative 90.2%

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

      3. mul-1-neg 90.2%

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

      4. unsub-neg 90.2%

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

      5. div-sub 90.2%

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

      6. unsub-neg 90.2%

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

      7. mul-1-neg 90.2%

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

      8. mul-1-neg 90.2%

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

      9. distribute-rgt-neg-in 90.2%

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

      10. sub-neg 90.2%

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

      11. +-commutative 90.2%

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

      12. distribute-neg-in 90.2%

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

      13. remove-double-neg 90.2%

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

      14. sub-neg 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in y around inf 89.1%

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

   if -1.39999999999999995e70 < y < -2.64999999999999986e-114

   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 69.5%

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

      1. mul-1-neg 69.5%

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

      2. unsub-neg 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in z around inf 55.9%

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

   if -2.64999999999999986e-114 < y < 7.5e9

   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 84.1%

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

   4. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

   6. Simplified 75.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 7500000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -850:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 12500000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -850.0)
     t_1
     (if (<= y 3e-297)
       (* x (+ z 1.0))
       (if (<= y 12500000000.0) (* 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 <= -850.0) {
		tmp = t_1;
	} else if (y <= 3e-297) {
		tmp = x * (z + 1.0);
	} else if (y <= 12500000000.0) {
		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 <= (-850.0d0)) then
        tmp = t_1
    else if (y <= 3d-297) then
        tmp = x * (z + 1.0d0)
    else if (y <= 12500000000.0d0) 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 <= -850.0) {
		tmp = t_1;
	} else if (y <= 3e-297) {
		tmp = x * (z + 1.0);
	} else if (y <= 12500000000.0) {
		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 <= -850.0:
		tmp = t_1
	elif y <= 3e-297:
		tmp = x * (z + 1.0)
	elif y <= 12500000000.0:
		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 <= -850.0)
		tmp = t_1;
	elseif (y <= 3e-297)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 12500000000.0)
		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 <= -850.0)
		tmp = t_1;
	elseif (y <= 3e-297)
		tmp = x * (z + 1.0);
	elseif (y <= 12500000000.0)
		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, -850.0], t$95$1, If[LessEqual[y, 3e-297], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 12500000000.0], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -850 or 1.25e10 < 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 91.7%

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

      1. associate--l+ 91.7%

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

      2. +-commutative 91.7%

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

      3. mul-1-neg 91.7%

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

      4. unsub-neg 91.7%

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

      5. div-sub 91.7%

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

      6. unsub-neg 91.7%

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

      7. mul-1-neg 91.7%

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

      8. mul-1-neg 91.7%

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

      9. distribute-rgt-neg-in 91.7%

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

      10. sub-neg 91.7%

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

      11. +-commutative 91.7%

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

      12. distribute-neg-in 91.7%

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

      13. remove-double-neg 91.7%

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

      14. sub-neg 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in y around inf 81.6%

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

   if -850 < y < 2.99999999999999995e-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 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in y around 0 66.7%

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

      1. +-commutative 66.7%

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

   8. Simplified 66.7%

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

   if 2.99999999999999995e-297 < y < 1.25e10

   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 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 49.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -4.6e+65)
     t_1
     (if (<= z -4.2e-54) (* y t) (if (<= z 7e+57) (* x (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -4.6e+65) {
		tmp = t_1;
	} else if (z <= -4.2e-54) {
		tmp = y * t;
	} else if (z <= 7e+57) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-4.6d+65)) then
        tmp = t_1
    else if (z <= (-4.2d-54)) then
        tmp = y * t
    else if (z <= 7d+57) then
        tmp = x * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -4.6e+65) {
		tmp = t_1;
	} else if (z <= -4.2e-54) {
		tmp = y * t;
	} else if (z <= 7e+57) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -4.6e+65:
		tmp = t_1
	elif z <= -4.2e-54:
		tmp = y * t
	elif z <= 7e+57:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -4.6e+65)
		tmp = t_1;
	elseif (z <= -4.2e-54)
		tmp = Float64(y * t);
	elseif (z <= 7e+57)
		tmp = Float64(x * Float64(1.0 - y));
	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 <= -4.6e+65)
		tmp = t_1;
	elseif (z <= -4.2e-54)
		tmp = y * t;
	elseif (z <= 7e+57)
		tmp = x * (1.0 - y);
	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, -4.6e+65], t$95$1, If[LessEqual[z, -4.2e-54], N[(y * t), $MachinePrecision], If[LessEqual[z, 7e+57], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e65 or 6.9999999999999995e57 < 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 inf 73.8%

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

      1. associate--l+ 73.8%

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

      2. +-commutative 73.8%

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

      3. mul-1-neg 73.8%

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

      4. unsub-neg 73.8%

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

      5. div-sub 77.4%

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

      6. unsub-neg 77.4%

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

      7. mul-1-neg 77.4%

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

      8. mul-1-neg 77.4%

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

      9. distribute-rgt-neg-in 77.4%

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

      10. sub-neg 77.4%

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

      11. +-commutative 77.4%

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

      12. distribute-neg-in 77.4%

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

      13. remove-double-neg 77.4%

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

      14. sub-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in t around inf 50.1%

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

      1. neg-mul-1 50.1%

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

      2. sub-neg 50.1%

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

   8. Simplified 50.1%

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

   9. Taylor expanded in y around 0 51.4%

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

       1. associate-*r* 51.4%

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

       2. mul-1-neg 51.4%

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

   11. Simplified 51.4%

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

   if -4.6e65 < z < -4.2e-54

   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 76.7%

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

      1. associate--l+ 76.7%

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

      2. +-commutative 76.7%

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

      3. mul-1-neg 76.7%

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

      4. unsub-neg 76.7%

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

      5. div-sub 81.8%

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

      6. unsub-neg 81.8%

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

      7. mul-1-neg 81.8%

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

      8. mul-1-neg 81.8%

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

      9. distribute-rgt-neg-in 81.8%

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

      10. sub-neg 81.8%

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

      11. +-commutative 81.8%

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

      12. distribute-neg-in 81.8%

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

      13. remove-double-neg 81.8%

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

      14. sub-neg 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in t around inf 58.8%

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

      1. neg-mul-1 58.8%

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

      2. sub-neg 58.8%

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

   8. Simplified 58.8%

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

   9. Taylor expanded in z around 0 58.3%

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

   if -4.2e-54 < z < 6.9999999999999995e57

   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 60.9%

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

      1. mul-1-neg 60.9%

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

      2. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in z around 0 58.3%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-276}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -3.4e+60)
     t_1
     (if (<= z 3.8e-276) (* y t) (if (<= z 2.5e-23) x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -3.4e+60) {
		tmp = t_1;
	} else if (z <= 3.8e-276) {
		tmp = y * t;
	} else if (z <= 2.5e-23) {
		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 <= (-3.4d+60)) then
        tmp = t_1
    else if (z <= 3.8d-276) then
        tmp = y * t
    else if (z <= 2.5d-23) 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 <= -3.4e+60) {
		tmp = t_1;
	} else if (z <= 3.8e-276) {
		tmp = y * t;
	} else if (z <= 2.5e-23) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -3.4e+60:
		tmp = t_1
	elif z <= 3.8e-276:
		tmp = y * t
	elif z <= 2.5e-23:
		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 <= -3.4e+60)
		tmp = t_1;
	elseif (z <= 3.8e-276)
		tmp = Float64(y * t);
	elseif (z <= 2.5e-23)
		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 <= -3.4e+60)
		tmp = t_1;
	elseif (z <= 3.8e-276)
		tmp = y * t;
	elseif (z <= 2.5e-23)
		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, -3.4e+60], t$95$1, If[LessEqual[z, 3.8e-276], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.5e-23], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4e60 or 2.5000000000000001e-23 < 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 inf 75.2%

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

      1. associate--l+ 75.2%

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

      2. +-commutative 75.2%

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

      3. mul-1-neg 75.2%

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

      4. unsub-neg 75.2%

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

      5. div-sub 78.5%

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

      6. unsub-neg 78.5%

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

      7. mul-1-neg 78.5%

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

      8. mul-1-neg 78.5%

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

      9. distribute-rgt-neg-in 78.5%

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

      10. sub-neg 78.5%

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

      11. +-commutative 78.5%

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

      12. distribute-neg-in 78.5%

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

      13. remove-double-neg 78.5%

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

      14. sub-neg 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in t around inf 48.0%

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

      1. neg-mul-1 48.0%

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

      2. sub-neg 48.0%

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

   8. Simplified 48.0%

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

   9. Taylor expanded in y around 0 48.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot z\right)} \]
   10. 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%

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

   11. Simplified 48.2%

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

   if -3.4e60 < z < 3.8e-276

   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. associate--l+ 83.8%

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

      2. +-commutative 83.8%

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

      3. mul-1-neg 83.8%

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

      4. unsub-neg 83.8%

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

      5. div-sub 85.4%

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

      6. unsub-neg 85.4%

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

      7. mul-1-neg 85.4%

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

      8. mul-1-neg 85.4%

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

      9. distribute-rgt-neg-in 85.4%

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

      10. sub-neg 85.4%

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

      11. +-commutative 85.4%

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

      12. distribute-neg-in 85.4%

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

      13. remove-double-neg 85.4%

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

      14. sub-neg 85.4%

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

   5. Simplified 85.4%

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

   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 3.8e-276 < z < 2.5000000000000001e-23

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-276}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+51}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-276}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e+51)
   (* z x)
   (if (<= z 5.1e-276) (* 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 <= -5.8e+51) {
		tmp = z * x;
	} else if (z <= 5.1e-276) {
		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 <= (-5.8d+51)) then
        tmp = z * x
    else if (z <= 5.1d-276) 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 <= -5.8e+51) {
		tmp = z * x;
	} else if (z <= 5.1e-276) {
		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 <= -5.8e+51:
		tmp = z * x
	elif z <= 5.1e-276:
		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 <= -5.8e+51)
		tmp = Float64(z * x);
	elseif (z <= 5.1e-276)
		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 <= -5.8e+51)
		tmp = z * x;
	elseif (z <= 5.1e-276)
		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, -5.8e+51], N[(z * x), $MachinePrecision], If[LessEqual[z, 5.1e-276], 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 < -5.7999999999999997e51 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 -5.7999999999999997e51 < z < 5.09999999999999968e-276

   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. associate--l+ 84.7%

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

      2. +-commutative 84.7%

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

      3. mul-1-neg 84.7%

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

      4. unsub-neg 84.7%

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

      5. div-sub 85.1%

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

      6. unsub-neg 85.1%

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

      7. mul-1-neg 85.1%

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

      8. mul-1-neg 85.1%

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

      9. distribute-rgt-neg-in 85.1%

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

      10. sub-neg 85.1%

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

      11. +-commutative 85.1%

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

      12. distribute-neg-in 85.1%

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

      13. remove-double-neg 85.1%

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

      14. sub-neg 85.1%

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

   5. Simplified 85.1%

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

   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 5.09999999999999968e-276 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+51}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-276}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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. associate--l+ 90.2%

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

      2. +-commutative 90.2%

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

      3. mul-1-neg 90.2%

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

      4. unsub-neg 90.2%

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

      5. div-sub 90.2%

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

      6. unsub-neg 90.2%

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

      7. mul-1-neg 90.2%

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

      8. mul-1-neg 90.2%

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

      9. distribute-rgt-neg-in 90.2%

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

      10. sub-neg 90.2%

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

      11. +-commutative 90.2%

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

      12. distribute-neg-in 90.2%

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

      13. remove-double-neg 90.2%

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

      14. sub-neg 90.2%

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

   5. Simplified 90.2%

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

   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 11: 80.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.22e-100) (not (<= t 4.9e-54)))
   (- x (* t (- z y)))
   (* 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 - (t * (z - y));
	} 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 - (t * (z - y))
    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 - (t * (z - y));
	} 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 - (t * (z - y))
	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(t * Float64(z - y)));
	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 - (t * (z - y));
	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[(t * N[(z - y), $MachinePrecision]), $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%

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

Alternative 12: 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 13: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+50} \lor \neg \left(z \leq 6.5 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e+50) (not (<= z 6.5e-14))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+50) || !(z <= 6.5e-14)) {
		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 <= (-6d+50)) .or. (.not. (z <= 6.5d-14))) 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 <= -6e+50) || !(z <= 6.5e-14)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e+50) or not (z <= 6.5e-14):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e+50) || !(z <= 6.5e-14))
		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 <= -6e+50) || ~((z <= 6.5e-14)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e+50], N[Not[LessEqual[z, 6.5e-14]], $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 < -5.9999999999999996e50 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 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 -5.9999999999999996e50 < 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 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+50} \lor \neg \left(z \leq 6.5 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+89}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+20}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.8e+89) (* z x) (if (<= x 1.9e+20) (* y t) (* y (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.8e+89) {
		tmp = z * x;
	} else if (x <= 1.9e+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 <= (-8.8d+89)) then
        tmp = z * x
    else if (x <= 1.9d+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 <= -8.8e+89) {
		tmp = z * x;
	} else if (x <= 1.9e+20) {
		tmp = y * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.8e+89:
		tmp = z * x
	elif x <= 1.9e+20:
		tmp = y * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.8e+89)
		tmp = Float64(z * x);
	elseif (x <= 1.9e+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 <= -8.8e+89)
		tmp = z * x;
	elseif (x <= 1.9e+20)
		tmp = y * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.8e+89], N[(z * x), $MachinePrecision], If[LessEqual[x, 1.9e+20], N[(y * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.8000000000000001e89

   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 -8.8000000000000001e89 < x < 1.9e20

   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. associate--l+ 86.4%

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

      2. +-commutative 86.4%

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

      3. mul-1-neg 86.4%

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

      4. unsub-neg 86.4%

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

      5. div-sub 86.4%

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

      6. unsub-neg 86.4%

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

      7. mul-1-neg 86.4%

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

      8. mul-1-neg 86.4%

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

      9. distribute-rgt-neg-in 86.4%

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

      10. sub-neg 86.4%

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

      11. +-commutative 86.4%

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

      12. distribute-neg-in 86.4%

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

      13. remove-double-neg 86.4%

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

      14. sub-neg 86.4%

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

   5. Simplified 86.4%

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

   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 1.9e20 < 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. mul-1-neg 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+89}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+20}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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 16: 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 17: 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))))