Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.7s

Alternatives: 16

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. Final simplification 100.0%

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

Alternative 2: 38.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-224}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-56}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+52} \lor \neg \left(z \leq 1.92 \cdot 10^{+146}\right) \land z \leq 1.2 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -6.8e-12)
     t_1
     (if (<= z 4.4e-280)
       x
       (if (<= z 1.45e-224)
         (* y t)
         (if (<= z 8.5e-217)
           x
           (if (<= z 9.5e-56)
             (* y t)
             (if (or (<= z 3.9e+52)
                     (and (not (<= z 1.92e+146)) (<= z 1.2e+229)))
               t_1
               (* z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -6.8e-12) {
		tmp = t_1;
	} else if (z <= 4.4e-280) {
		tmp = x;
	} else if (z <= 1.45e-224) {
		tmp = y * t;
	} else if (z <= 8.5e-217) {
		tmp = x;
	} else if (z <= 9.5e-56) {
		tmp = y * t;
	} else if ((z <= 3.9e+52) || (!(z <= 1.92e+146) && (z <= 1.2e+229))) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-6.8d-12)) then
        tmp = t_1
    else if (z <= 4.4d-280) then
        tmp = x
    else if (z <= 1.45d-224) then
        tmp = y * t
    else if (z <= 8.5d-217) then
        tmp = x
    else if (z <= 9.5d-56) then
        tmp = y * t
    else if ((z <= 3.9d+52) .or. (.not. (z <= 1.92d+146)) .and. (z <= 1.2d+229)) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -6.8e-12) {
		tmp = t_1;
	} else if (z <= 4.4e-280) {
		tmp = x;
	} else if (z <= 1.45e-224) {
		tmp = y * t;
	} else if (z <= 8.5e-217) {
		tmp = x;
	} else if (z <= 9.5e-56) {
		tmp = y * t;
	} else if ((z <= 3.9e+52) || (!(z <= 1.92e+146) && (z <= 1.2e+229))) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -6.8e-12:
		tmp = t_1
	elif z <= 4.4e-280:
		tmp = x
	elif z <= 1.45e-224:
		tmp = y * t
	elif z <= 8.5e-217:
		tmp = x
	elif z <= 9.5e-56:
		tmp = y * t
	elif (z <= 3.9e+52) or (not (z <= 1.92e+146) and (z <= 1.2e+229)):
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -6.8e-12)
		tmp = t_1;
	elseif (z <= 4.4e-280)
		tmp = x;
	elseif (z <= 1.45e-224)
		tmp = Float64(y * t);
	elseif (z <= 8.5e-217)
		tmp = x;
	elseif (z <= 9.5e-56)
		tmp = Float64(y * t);
	elseif ((z <= 3.9e+52) || (!(z <= 1.92e+146) && (z <= 1.2e+229)))
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -6.8e-12)
		tmp = t_1;
	elseif (z <= 4.4e-280)
		tmp = x;
	elseif (z <= 1.45e-224)
		tmp = y * t;
	elseif (z <= 8.5e-217)
		tmp = x;
	elseif (z <= 9.5e-56)
		tmp = y * t;
	elseif ((z <= 3.9e+52) || (~((z <= 1.92e+146)) && (z <= 1.2e+229)))
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -6.8e-12], t$95$1, If[LessEqual[z, 4.4e-280], x, If[LessEqual[z, 1.45e-224], N[(y * t), $MachinePrecision], If[LessEqual[z, 8.5e-217], x, If[LessEqual[z, 9.5e-56], N[(y * t), $MachinePrecision], If[Or[LessEqual[z, 3.9e+52], And[N[Not[LessEqual[z, 1.92e+146]], $MachinePrecision], LessEqual[z, 1.2e+229]]], t$95$1, N[(z * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.8000000000000001e-12 or 9.4999999999999991e-56 < z < 3.9e52 or 1.91999999999999993e146 < z < 1.2e229

   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 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in z around inf 73.7%

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

   7. Taylor expanded in x around 0 52.7%

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

      1. mul-1-neg 52.7%

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

      2. distribute-rgt-neg-in 52.7%

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

   9. Simplified 52.7%

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

   if -6.8000000000000001e-12 < z < 4.4000000000000002e-280 or 1.45e-224 < z < 8.4999999999999994e-217

   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 93.1%

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

      1. *-commutative 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in y around 0 54.8%

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

   if 4.4000000000000002e-280 < z < 1.45e-224 or 8.4999999999999994e-217 < z < 9.4999999999999991e-56

   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 95.5%

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

      1. *-commutative 95.5%

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

   5. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      2. sub-neg 95.5%

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

      3. distribute-lft-in 91.0%

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

   7. Applied egg-rr 91.0%

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

      1. associate-+r+ 91.0%

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

      2. distribute-rgt-neg-out 91.0%

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

      3. unsub-neg 91.0%

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

      4. *-commutative 91.0%

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

   9. Applied egg-rr 91.0%

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

   10. Taylor expanded in x around 0 61.6%

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

   if 3.9e52 < z < 1.91999999999999993e146 or 1.2e229 < 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 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in z around inf 85.2%

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

   7. Taylor expanded in x around inf 71.0%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-224}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-56}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+52} \lor \neg \left(z \leq 1.92 \cdot 10^{+146}\right) \land z \leq 1.2 \cdot 10^{+229}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-278}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-233}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-213}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-116}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+228}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (- 1.0 y))))
   (if (<= z -1.3e+91)
     t_1
     (if (<= z 4.2e-278)
       t_2
       (if (<= z 2.1e-233)
         (* y t)
         (if (<= z 2.45e-213)
           t_2
           (if (<= z 2.7e-116)
             (* y t)
             (if (<= z 2e+51)
               t_2
               (if (<= z 1.45e+148)
                 (* x (+ z 1.0))
                 (if (<= z 4.6e+228) t_1 (* z x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -1.3e+91) {
		tmp = t_1;
	} else if (z <= 4.2e-278) {
		tmp = t_2;
	} else if (z <= 2.1e-233) {
		tmp = y * t;
	} else if (z <= 2.45e-213) {
		tmp = t_2;
	} else if (z <= 2.7e-116) {
		tmp = y * t;
	} else if (z <= 2e+51) {
		tmp = t_2;
	} else if (z <= 1.45e+148) {
		tmp = x * (z + 1.0);
	} else if (z <= 4.6e+228) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x * (1.0d0 - y)
    if (z <= (-1.3d+91)) then
        tmp = t_1
    else if (z <= 4.2d-278) then
        tmp = t_2
    else if (z <= 2.1d-233) then
        tmp = y * t
    else if (z <= 2.45d-213) then
        tmp = t_2
    else if (z <= 2.7d-116) then
        tmp = y * t
    else if (z <= 2d+51) then
        tmp = t_2
    else if (z <= 1.45d+148) then
        tmp = x * (z + 1.0d0)
    else if (z <= 4.6d+228) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -1.3e+91) {
		tmp = t_1;
	} else if (z <= 4.2e-278) {
		tmp = t_2;
	} else if (z <= 2.1e-233) {
		tmp = y * t;
	} else if (z <= 2.45e-213) {
		tmp = t_2;
	} else if (z <= 2.7e-116) {
		tmp = y * t;
	} else if (z <= 2e+51) {
		tmp = t_2;
	} else if (z <= 1.45e+148) {
		tmp = x * (z + 1.0);
	} else if (z <= 4.6e+228) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x * (1.0 - y)
	tmp = 0
	if z <= -1.3e+91:
		tmp = t_1
	elif z <= 4.2e-278:
		tmp = t_2
	elif z <= 2.1e-233:
		tmp = y * t
	elif z <= 2.45e-213:
		tmp = t_2
	elif z <= 2.7e-116:
		tmp = y * t
	elif z <= 2e+51:
		tmp = t_2
	elif z <= 1.45e+148:
		tmp = x * (z + 1.0)
	elif z <= 4.6e+228:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.3e+91)
		tmp = t_1;
	elseif (z <= 4.2e-278)
		tmp = t_2;
	elseif (z <= 2.1e-233)
		tmp = Float64(y * t);
	elseif (z <= 2.45e-213)
		tmp = t_2;
	elseif (z <= 2.7e-116)
		tmp = Float64(y * t);
	elseif (z <= 2e+51)
		tmp = t_2;
	elseif (z <= 1.45e+148)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (z <= 4.6e+228)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.3e+91)
		tmp = t_1;
	elseif (z <= 4.2e-278)
		tmp = t_2;
	elseif (z <= 2.1e-233)
		tmp = y * t;
	elseif (z <= 2.45e-213)
		tmp = t_2;
	elseif (z <= 2.7e-116)
		tmp = y * t;
	elseif (z <= 2e+51)
		tmp = t_2;
	elseif (z <= 1.45e+148)
		tmp = x * (z + 1.0);
	elseif (z <= 4.6e+228)
		tmp = t_1;
	else
		tmp = z * x;
	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[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+91], t$95$1, If[LessEqual[z, 4.2e-278], t$95$2, If[LessEqual[z, 2.1e-233], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.45e-213], t$95$2, If[LessEqual[z, 2.7e-116], N[(y * t), $MachinePrecision], If[LessEqual[z, 2e+51], t$95$2, If[LessEqual[z, 1.45e+148], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+228], t$95$1, N[(z * x), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.3e91 or 1.45e148 < z < 4.60000000000000026e228

   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 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in z around inf 89.7%

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

   7. Taylor expanded in x around 0 61.5%

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

      1. mul-1-neg 61.5%

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

      2. distribute-rgt-neg-in 61.5%

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

   9. Simplified 61.5%

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

   if -1.3e91 < z < 4.20000000000000027e-278 or 2.0999999999999999e-233 < z < 2.4499999999999999e-213 or 2.7e-116 < z < 2e51

   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 65.3%

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

      1. mul-1-neg 65.3%

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

      2. unsub-neg 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in z around 0 63.2%

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

   if 4.20000000000000027e-278 < z < 2.0999999999999999e-233 or 2.4499999999999999e-213 < z < 2.7e-116

   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 94.4%

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

      1. *-commutative 94.4%

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

   5. Simplified 94.4%

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

      1. *-commutative 94.4%

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

      2. sub-neg 94.4%

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

      3. distribute-lft-in 88.8%

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

   7. Applied egg-rr 88.8%

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

      1. associate-+r+ 88.8%

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

      2. distribute-rgt-neg-out 88.8%

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

      3. unsub-neg 88.8%

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

      4. *-commutative 88.8%

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

   9. Applied egg-rr 88.8%

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

   10. Taylor expanded in x around 0 68.2%

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

   if 2e51 < z < 1.45e148

   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 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unsub-neg 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in y around 0 59.2%

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

      1. +-commutative 59.2%

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

   8. Simplified 59.2%

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

   if 4.60000000000000026e228 < 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 93.3%

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

      1. mul-1-neg 93.3%

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

      2. unsub-neg 93.3%

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

   5. Simplified 93.3%

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

   6. Taylor expanded in z around inf 93.3%

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

   7. Taylor expanded in x around inf 86.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-233}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-116}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+228}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-182}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.00162:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+216} \lor \neg \left(y \leq 9 \cdot 10^{+257}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -2.15e+41)
     t_1
     (if (<= y 7e-182)
       t_2
       (if (<= y 8.2e-126)
         (* z (- t))
         (if (<= y 0.00162)
           t_2
           (if (or (<= y 3e+216) (not (<= y 9e+257))) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -2.15e+41) {
		tmp = t_1;
	} else if (y <= 7e-182) {
		tmp = t_2;
	} else if (y <= 8.2e-126) {
		tmp = z * -t;
	} else if (y <= 0.00162) {
		tmp = t_2;
	} else if ((y <= 3e+216) || !(y <= 9e+257)) {
		tmp = y * 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) :: t_2
    real(8) :: tmp
    t_1 = y * -x
    t_2 = x * (z + 1.0d0)
    if (y <= (-2.15d+41)) then
        tmp = t_1
    else if (y <= 7d-182) then
        tmp = t_2
    else if (y <= 8.2d-126) then
        tmp = z * -t
    else if (y <= 0.00162d0) then
        tmp = t_2
    else if ((y <= 3d+216) .or. (.not. (y <= 9d+257))) then
        tmp = y * 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 * -x;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -2.15e+41) {
		tmp = t_1;
	} else if (y <= 7e-182) {
		tmp = t_2;
	} else if (y <= 8.2e-126) {
		tmp = z * -t;
	} else if (y <= 0.00162) {
		tmp = t_2;
	} else if ((y <= 3e+216) || !(y <= 9e+257)) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -2.15e+41:
		tmp = t_1
	elif y <= 7e-182:
		tmp = t_2
	elif y <= 8.2e-126:
		tmp = z * -t
	elif y <= 0.00162:
		tmp = t_2
	elif (y <= 3e+216) or not (y <= 9e+257):
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -2.15e+41)
		tmp = t_1;
	elseif (y <= 7e-182)
		tmp = t_2;
	elseif (y <= 8.2e-126)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 0.00162)
		tmp = t_2;
	elseif ((y <= 3e+216) || !(y <= 9e+257))
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -2.15e+41)
		tmp = t_1;
	elseif (y <= 7e-182)
		tmp = t_2;
	elseif (y <= 8.2e-126)
		tmp = z * -t;
	elseif (y <= 0.00162)
		tmp = t_2;
	elseif ((y <= 3e+216) || ~((y <= 9e+257)))
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e+41], t$95$1, If[LessEqual[y, 7e-182], t$95$2, If[LessEqual[y, 8.2e-126], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 0.00162], t$95$2, If[Or[LessEqual[y, 3e+216], N[Not[LessEqual[y, 9e+257]], $MachinePrecision]], N[(y * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.15000000000000012e41 or 2.9999999999999998e216 < y < 8.9999999999999999e257

   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 57.8%

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

      1. mul-1-neg 57.8%

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

      2. unsub-neg 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in z around 0 50.0%

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

   7. Taylor expanded in y around inf 50.0%

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

      1. mul-1-neg 50.0%

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

      2. distribute-rgt-neg-out 50.0%

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

   9. Simplified 50.0%

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

   if -2.15000000000000012e41 < y < 6.99999999999999966e-182 or 8.1999999999999995e-126 < y < 0.0016199999999999999

   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 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in y around 0 65.9%

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

      1. +-commutative 65.9%

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

   8. Simplified 65.9%

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

   if 6.99999999999999966e-182 < y < 8.1999999999999995e-126

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

   7. Taylor expanded in x around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-in 83.4%

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

   9. Simplified 83.4%

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

   if 0.0016199999999999999 < y < 2.9999999999999998e216 or 8.9999999999999999e257 < 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 80.5%

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

      1. *-commutative 80.5%

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

   5. Simplified 80.5%

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

      1. *-commutative 80.5%

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

      2. sub-neg 80.5%

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

      3. distribute-lft-in 77.2%

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

   7. Applied egg-rr 77.2%

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

      1. associate-+r+ 77.2%

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

      2. distribute-rgt-neg-out 77.2%

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

      3. unsub-neg 77.2%

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

      4. *-commutative 77.2%

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

   9. Applied egg-rr 77.2%

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

   10. Taylor expanded in x around 0 55.8%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-182}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.00162:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+216} \lor \neg \left(y \leq 9 \cdot 10^{+257}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7200000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))))
   (if (<= z -7200000000000.0)
     t_2
     (if (<= z 4.7e-278)
       (* x (- 1.0 y))
       (if (<= z 4.5e-224)
         t_1
         (if (<= z 2.2e-218) x (if (<= z 7e-46) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (z <= -7200000000000.0) {
		tmp = t_2;
	} else if (z <= 4.7e-278) {
		tmp = x * (1.0 - y);
	} else if (z <= 4.5e-224) {
		tmp = t_1;
	} else if (z <= 2.2e-218) {
		tmp = x;
	} else if (z <= 7e-46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    if (z <= (-7200000000000.0d0)) then
        tmp = t_2
    else if (z <= 4.7d-278) then
        tmp = x * (1.0d0 - y)
    else if (z <= 4.5d-224) then
        tmp = t_1
    else if (z <= 2.2d-218) then
        tmp = x
    else if (z <= 7d-46) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (z <= -7200000000000.0) {
		tmp = t_2;
	} else if (z <= 4.7e-278) {
		tmp = x * (1.0 - y);
	} else if (z <= 4.5e-224) {
		tmp = t_1;
	} else if (z <= 2.2e-218) {
		tmp = x;
	} else if (z <= 7e-46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	tmp = 0
	if z <= -7200000000000.0:
		tmp = t_2
	elif z <= 4.7e-278:
		tmp = x * (1.0 - y)
	elif z <= 4.5e-224:
		tmp = t_1
	elif z <= 2.2e-218:
		tmp = x
	elif z <= 7e-46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -7200000000000.0)
		tmp = t_2;
	elseif (z <= 4.7e-278)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 4.5e-224)
		tmp = t_1;
	elseif (z <= 2.2e-218)
		tmp = x;
	elseif (z <= 7e-46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	tmp = 0.0;
	if (z <= -7200000000000.0)
		tmp = t_2;
	elseif (z <= 4.7e-278)
		tmp = x * (1.0 - y);
	elseif (z <= 4.5e-224)
		tmp = t_1;
	elseif (z <= 2.2e-218)
		tmp = x;
	elseif (z <= 7e-46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7200000000000.0], t$95$2, If[LessEqual[z, 4.7e-278], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-224], t$95$1, If[LessEqual[z, 2.2e-218], x, If[LessEqual[z, 7e-46], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.2e12 or 7.0000000000000004e-46 < 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 80.1%

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

      1. mul-1-neg 80.1%

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

      2. unsub-neg 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in z around inf 78.6%

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

   if -7.2e12 < z < 4.6999999999999997e-278

   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 69.3%

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

      1. mul-1-neg 69.3%

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

      2. unsub-neg 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around 0 69.2%

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

   if 4.6999999999999997e-278 < z < 4.5000000000000004e-224 or 2.20000000000000007e-218 < z < 7.0000000000000004e-46

   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 95.6%

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

      1. *-commutative 95.6%

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

   5. Simplified 95.6%

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

      1. *-commutative 95.6%

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

      2. sub-neg 95.6%

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

      3. distribute-lft-in 91.2%

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

   7. Applied egg-rr 91.2%

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

      1. associate-+r+ 91.2%

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

      2. distribute-rgt-neg-out 91.2%

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

      3. unsub-neg 91.2%

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

      4. *-commutative 91.2%

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

   9. Applied egg-rr 91.2%

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

   10. Taylor expanded in y around inf 83.4%

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

   if 4.5000000000000004e-224 < z < 2.20000000000000007e-218

   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 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7200000000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -29000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-231}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -29000000.0)
   (* z x)
   (if (<= z 3.8e-280)
     x
     (if (<= z 1.8e-231)
       (* y t)
       (if (<= z 8e-216) x (if (<= z 7.5e+52) (* y t) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -29000000.0) {
		tmp = z * x;
	} else if (z <= 3.8e-280) {
		tmp = x;
	} else if (z <= 1.8e-231) {
		tmp = y * t;
	} else if (z <= 8e-216) {
		tmp = x;
	} else if (z <= 7.5e+52) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-29000000.0d0)) then
        tmp = z * x
    else if (z <= 3.8d-280) then
        tmp = x
    else if (z <= 1.8d-231) then
        tmp = y * t
    else if (z <= 8d-216) then
        tmp = x
    else if (z <= 7.5d+52) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -29000000.0) {
		tmp = z * x;
	} else if (z <= 3.8e-280) {
		tmp = x;
	} else if (z <= 1.8e-231) {
		tmp = y * t;
	} else if (z <= 8e-216) {
		tmp = x;
	} else if (z <= 7.5e+52) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -29000000.0:
		tmp = z * x
	elif z <= 3.8e-280:
		tmp = x
	elif z <= 1.8e-231:
		tmp = y * t
	elif z <= 8e-216:
		tmp = x
	elif z <= 7.5e+52:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -29000000.0)
		tmp = Float64(z * x);
	elseif (z <= 3.8e-280)
		tmp = x;
	elseif (z <= 1.8e-231)
		tmp = Float64(y * t);
	elseif (z <= 8e-216)
		tmp = x;
	elseif (z <= 7.5e+52)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -29000000.0)
		tmp = z * x;
	elseif (z <= 3.8e-280)
		tmp = x;
	elseif (z <= 1.8e-231)
		tmp = y * t;
	elseif (z <= 8e-216)
		tmp = x;
	elseif (z <= 7.5e+52)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -29000000.0], N[(z * x), $MachinePrecision], If[LessEqual[z, 3.8e-280], x, If[LessEqual[z, 1.8e-231], N[(y * t), $MachinePrecision], If[LessEqual[z, 8e-216], x, If[LessEqual[z, 7.5e+52], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e7 or 7.49999999999999995e52 < 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 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in z around inf 82.6%

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

   7. Taylor expanded in x around inf 49.3%

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

   if -2.9e7 < z < 3.8000000000000001e-280 or 1.79999999999999987e-231 < z < 8.0000000000000003e-216

   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 92.3%

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

      1. *-commutative 92.3%

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

   5. Simplified 92.3%

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

   6. Taylor expanded in y around 0 53.7%

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

   if 3.8000000000000001e-280 < z < 1.79999999999999987e-231 or 8.0000000000000003e-216 < z < 7.49999999999999995e52

   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 82.2%

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

      1. *-commutative 82.2%

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

   5. Simplified 82.2%

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

      1. *-commutative 82.2%

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

      2. sub-neg 82.2%

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

      3. distribute-lft-in 79.1%

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

   7. Applied egg-rr 79.1%

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

      1. associate-+r+ 79.1%

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

      2. distribute-rgt-neg-out 79.1%

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

      3. unsub-neg 79.1%

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

      4. *-commutative 79.1%

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

   9. Applied egg-rr 79.1%

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

   10. Taylor expanded in x around 0 48.8%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -29000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-231}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -16:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.00102:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -16.0)
     t_1
     (if (<= y 4.6e-180)
       t_2
       (if (<= y 4.3e-135) (* z (- t)) (if (<= y 0.00102) 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 <= -16.0) {
		tmp = t_1;
	} else if (y <= 4.6e-180) {
		tmp = t_2;
	} else if (y <= 4.3e-135) {
		tmp = z * -t;
	} else if (y <= 0.00102) {
		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 <= (-16.0d0)) then
        tmp = t_1
    else if (y <= 4.6d-180) then
        tmp = t_2
    else if (y <= 4.3d-135) then
        tmp = z * -t
    else if (y <= 0.00102d0) 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 <= -16.0) {
		tmp = t_1;
	} else if (y <= 4.6e-180) {
		tmp = t_2;
	} else if (y <= 4.3e-135) {
		tmp = z * -t;
	} else if (y <= 0.00102) {
		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 <= -16.0:
		tmp = t_1
	elif y <= 4.6e-180:
		tmp = t_2
	elif y <= 4.3e-135:
		tmp = z * -t
	elif y <= 0.00102:
		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 <= -16.0)
		tmp = t_1;
	elseif (y <= 4.6e-180)
		tmp = t_2;
	elseif (y <= 4.3e-135)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 0.00102)
		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 <= -16.0)
		tmp = t_1;
	elseif (y <= 4.6e-180)
		tmp = t_2;
	elseif (y <= 4.3e-135)
		tmp = z * -t;
	elseif (y <= 0.00102)
		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, -16.0], t$95$1, If[LessEqual[y, 4.6e-180], t$95$2, If[LessEqual[y, 4.3e-135], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 0.00102], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -16 or 0.00102 < y

   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 81.7%

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

      1. *-commutative 81.7%

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

   5. Simplified 81.7%

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

      1. *-commutative 81.7%

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

      2. sub-neg 81.7%

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

      3. distribute-lft-in 76.6%

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

   7. Applied egg-rr 76.6%

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

      1. associate-+r+ 76.6%

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

      2. distribute-rgt-neg-out 76.6%

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

      3. unsub-neg 76.6%

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

      4. *-commutative 76.6%

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

   9. Applied egg-rr 76.6%

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

   10. Taylor expanded in y around inf 81.1%

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

   if -16 < y < 4.59999999999999992e-180 or 4.29999999999999999e-135 < y < 0.00102

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around 0 68.0%

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

      1. +-commutative 68.0%

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

   8. Simplified 68.0%

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

   if 4.59999999999999992e-180 < y < 4.29999999999999999e-135

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

   7. Taylor expanded in x around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-in 83.4%

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

   9. Simplified 83.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -16:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-180}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.00102:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-50}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+50}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -7.2e+33)
     t_1
     (if (<= z 4.2e-50)
       (- x (* y (- x t)))
       (if (<= z 2.3e+50) (+ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.2e+33) {
		tmp = t_1;
	} else if (z <= 4.2e-50) {
		tmp = x - (y * (x - t));
	} else if (z <= 2.3e+50) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-7.2d+33)) then
        tmp = t_1
    else if (z <= 4.2d-50) then
        tmp = x - (y * (x - t))
    else if (z <= 2.3d+50) then
        tmp = x + ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.2e+33) {
		tmp = t_1;
	} else if (z <= 4.2e-50) {
		tmp = x - (y * (x - t));
	} else if (z <= 2.3e+50) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -7.2e+33:
		tmp = t_1
	elif z <= 4.2e-50:
		tmp = x - (y * (x - t))
	elif z <= 2.3e+50:
		tmp = x + ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -7.2e+33)
		tmp = t_1;
	elseif (z <= 4.2e-50)
		tmp = Float64(x - Float64(y * Float64(x - t)));
	elseif (z <= 2.3e+50)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -7.2e+33)
		tmp = t_1;
	elseif (z <= 4.2e-50)
		tmp = x - (y * (x - t));
	elseif (z <= 2.3e+50)
		tmp = x + ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+33], t$95$1, If[LessEqual[z, 4.2e-50], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+50], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000005e33 or 2.29999999999999997e50 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in z around inf 86.4%

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

   if -7.2000000000000005e33 < z < 4.2000000000000002e-50

   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 92.3%

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

      1. *-commutative 92.3%

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

   5. Simplified 92.3%

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

   if 4.2000000000000002e-50 < z < 2.29999999999999997e50

   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 78.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-50}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+50}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -2500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 4.05 \cdot 10^{-10}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -2500.0)
     t_1
     (if (<= y -4.4e-231)
       (* x (+ z 1.0))
       (if (<= y 4.05e-10) (- 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 <= -2500.0) {
		tmp = t_1;
	} else if (y <= -4.4e-231) {
		tmp = x * (z + 1.0);
	} else if (y <= 4.05e-10) {
		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 <= (-2500.0d0)) then
        tmp = t_1
    else if (y <= (-4.4d-231)) then
        tmp = x * (z + 1.0d0)
    else if (y <= 4.05d-10) 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 <= -2500.0) {
		tmp = t_1;
	} else if (y <= -4.4e-231) {
		tmp = x * (z + 1.0);
	} else if (y <= 4.05e-10) {
		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 <= -2500.0:
		tmp = t_1
	elif y <= -4.4e-231:
		tmp = x * (z + 1.0)
	elif y <= 4.05e-10:
		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 <= -2500.0)
		tmp = t_1;
	elseif (y <= -4.4e-231)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 4.05e-10)
		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 <= -2500.0)
		tmp = t_1;
	elseif (y <= -4.4e-231)
		tmp = x * (z + 1.0);
	elseif (y <= 4.05e-10)
		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, -2500.0], t$95$1, If[LessEqual[y, -4.4e-231], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.05e-10], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2500 or 4.04999999999999997e-10 < y

   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 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

      1. *-commutative 80.4%

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

      2. sub-neg 80.4%

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

      3. distribute-lft-in 75.4%

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

   7. Applied egg-rr 75.4%

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

      1. associate-+r+ 75.4%

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

      2. distribute-rgt-neg-out 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

   9. Applied egg-rr 75.4%

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

   10. Taylor expanded in y around inf 79.8%

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

   if -2500 < y < -4.40000000000000018e-231

   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 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in y around 0 76.3%

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

      1. +-commutative 76.3%

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

   8. Simplified 76.3%

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

   if -4.40000000000000018e-231 < y < 4.04999999999999997e-10

   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 95.4%

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

      1. mul-1-neg 95.4%

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

      2. unsub-neg 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in t around inf 80.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2500:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 4.05 \cdot 10^{-10}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -4.8e+19)
     t_1
     (if (<= y -6.8e-231)
       (* x (+ (- z y) 1.0))
       (if (<= y 1.9e-9) (- 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 <= -4.8e+19) {
		tmp = t_1;
	} else if (y <= -6.8e-231) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= 1.9e-9) {
		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 <= (-4.8d+19)) then
        tmp = t_1
    else if (y <= (-6.8d-231)) then
        tmp = x * ((z - y) + 1.0d0)
    else if (y <= 1.9d-9) 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 <= -4.8e+19) {
		tmp = t_1;
	} else if (y <= -6.8e-231) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= 1.9e-9) {
		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 <= -4.8e+19:
		tmp = t_1
	elif y <= -6.8e-231:
		tmp = x * ((z - y) + 1.0)
	elif y <= 1.9e-9:
		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 <= -4.8e+19)
		tmp = t_1;
	elseif (y <= -6.8e-231)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (y <= 1.9e-9)
		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 <= -4.8e+19)
		tmp = t_1;
	elseif (y <= -6.8e-231)
		tmp = x * ((z - y) + 1.0);
	elseif (y <= 1.9e-9)
		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, -4.8e+19], t$95$1, If[LessEqual[y, -6.8e-231], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-9], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8e19 or 1.90000000000000006e-9 < 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 79.9%

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

      1. *-commutative 79.9%

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

   5. Simplified 79.9%

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

      1. *-commutative 79.9%

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

      2. sub-neg 79.9%

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

      3. distribute-lft-in 74.8%

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

   7. Applied egg-rr 74.8%

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

      1. associate-+r+ 74.8%

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

      2. distribute-rgt-neg-out 74.8%

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

      3. unsub-neg 74.8%

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

      4. *-commutative 74.8%

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

   9. Applied egg-rr 74.8%

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

   10. Taylor expanded in y around inf 79.9%

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

   if -4.8e19 < y < -6.8e-231

   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 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   5. Simplified 78.4%

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

   if -6.8e-231 < y < 1.90000000000000006e-9

   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 95.4%

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

      1. mul-1-neg 95.4%

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

      2. unsub-neg 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in t around inf 80.8%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -10500000 \lor \neg \left(t \leq 6 \cdot 10^{-87}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -10500000.0) (not (<= t 6e-87)))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -10500000.0) || !(t <= 6e-87)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-10500000.0d0)) .or. (.not. (t <= 6d-87))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -10500000.0) || !(t <= 6e-87)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -10500000.0) or not (t <= 6e-87):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -10500000.0) || !(t <= 6e-87))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -10500000.0) || ~((t <= 6e-87)))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -10500000.0], N[Not[LessEqual[t, 6e-87]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e7 or 6.00000000000000033e-87 < 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 85.3%

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

   if -1.05e7 < t < 6.00000000000000033e-87

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

   5. Simplified 85.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -10500000 \lor \neg \left(t \leq 6 \cdot 10^{-87}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-99} \lor \neg \left(y \leq 0.00076\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e-99) (not (<= y 0.00076)))
   (- x (* y (- x t)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-99) || !(y <= 0.00076)) {
		tmp = x - (y * (x - t));
	} 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 <= (-1.15d-99)) .or. (.not. (y <= 0.00076d0))) then
        tmp = x - (y * (x - t))
    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 <= -1.15e-99) || !(y <= 0.00076)) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e-99) or not (y <= 0.00076):
		tmp = x - (y * (x - t))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e-99) || !(y <= 0.00076))
		tmp = Float64(x - Float64(y * Float64(x - t)));
	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 <= -1.15e-99) || ~((y <= 0.00076)))
		tmp = x - (y * (x - t));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e-99], N[Not[LessEqual[y, 0.00076]], $MachinePrecision]], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e-99 or 7.6000000000000004e-4 < y

   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 82.2%

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

      1. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   if -1.1499999999999999e-99 < y < 7.6000000000000004e-4

   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 95.7%

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

      1. mul-1-neg 95.7%

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

      2. unsub-neg 95.7%

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

   5. Simplified 95.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-99} \lor \neg \left(y \leq 0.00076\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+33} \lor \neg \left(z \leq 7 \cdot 10^{-46}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e+33) (not (<= z 7e-46))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+33) || !(z <= 7e-46)) {
		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 <= (-3.8d+33)) .or. (.not. (z <= 7d-46))) 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 <= -3.8e+33) || !(z <= 7e-46)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e+33) or not (z <= 7e-46):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e+33) || !(z <= 7e-46))
		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 <= -3.8e+33) || ~((z <= 7e-46)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e+33], N[Not[LessEqual[z, 7e-46]], $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 < -3.80000000000000002e33 or 7.0000000000000004e-46 < 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 82.5%

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

      1. mul-1-neg 82.5%

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

      2. unsub-neg 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in z around inf 80.9%

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

   if -3.80000000000000002e33 < z < 7.0000000000000004e-46

   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 92.3%

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

      1. *-commutative 92.3%

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

   5. Simplified 92.3%

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

   6. Taylor expanded in t around inf 73.4%

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

      1. *-commutative 73.4%

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

   8. Simplified 73.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+33} \lor \neg \left(z \leq 7 \cdot 10^{-46}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-13} \lor \neg \left(y \leq 1.15 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e-13) (not (<= y 1.15e-10))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-13) || !(y <= 1.15e-10)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.15d-13)) .or. (.not. (y <= 1.15d-10))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-13) || !(y <= 1.15e-10)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e-13) or not (y <= 1.15e-10):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e-13) || !(y <= 1.15e-10))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.15e-13) || ~((y <= 1.15e-10)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e-13], N[Not[LessEqual[y, 1.15e-10]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e-13 or 1.15000000000000004e-10 < y

   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 80.1%

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

      1. *-commutative 80.1%

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

   5. Simplified 80.1%

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

      1. *-commutative 80.1%

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

      2. sub-neg 80.1%

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

      3. distribute-lft-in 75.2%

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

   7. Applied egg-rr 75.2%

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

      1. associate-+r+ 75.2%

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

      2. distribute-rgt-neg-out 75.2%

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

      3. unsub-neg 75.2%

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

      4. *-commutative 75.2%

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

   9. Applied egg-rr 75.2%

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

   10. Taylor expanded in x around 0 46.5%

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

   if -1.1499999999999999e-13 < y < 1.15000000000000004e-10

   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 48.5%

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

      1. *-commutative 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in y around 0 42.0%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-13} \lor \neg \left(y \leq 1.15 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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. Final simplification 100.0%

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

Alternative 16: 17.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 63.7%

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

   1. *-commutative 63.7%

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

5. Simplified 63.7%

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

6. Taylor expanded in y around 0 23.5%

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

7. Final simplification 23.5%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 96.5% 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 2024055 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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