Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.8s

Alternatives: 16

Speedup: 1.0×

• 34.9% 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: 60.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* (- y z) t)))
   (if (<= x -3.4e+123)
     t_1
     (if (<= x -1e+21)
       t_2
       (if (<= x -1.45e-19)
         t_1
         (if (<= x 5.2e-59)
           t_2
           (if (<= x 3.1e+29)
             t_1
             (if (<= x 7.6e+57) t_2 (if (<= x 1.3e+87) (* z x) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = (y - z) * t;
	double tmp;
	if (x <= -3.4e+123) {
		tmp = t_1;
	} else if (x <= -1e+21) {
		tmp = t_2;
	} else if (x <= -1.45e-19) {
		tmp = t_1;
	} else if (x <= 5.2e-59) {
		tmp = t_2;
	} else if (x <= 3.1e+29) {
		tmp = t_1;
	} else if (x <= 7.6e+57) {
		tmp = t_2;
	} else if (x <= 1.3e+87) {
		tmp = z * 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) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = (y - z) * t
    if (x <= (-3.4d+123)) then
        tmp = t_1
    else if (x <= (-1d+21)) then
        tmp = t_2
    else if (x <= (-1.45d-19)) then
        tmp = t_1
    else if (x <= 5.2d-59) then
        tmp = t_2
    else if (x <= 3.1d+29) then
        tmp = t_1
    else if (x <= 7.6d+57) then
        tmp = t_2
    else if (x <= 1.3d+87) then
        tmp = z * 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 = x * (1.0 - y);
	double t_2 = (y - z) * t;
	double tmp;
	if (x <= -3.4e+123) {
		tmp = t_1;
	} else if (x <= -1e+21) {
		tmp = t_2;
	} else if (x <= -1.45e-19) {
		tmp = t_1;
	} else if (x <= 5.2e-59) {
		tmp = t_2;
	} else if (x <= 3.1e+29) {
		tmp = t_1;
	} else if (x <= 7.6e+57) {
		tmp = t_2;
	} else if (x <= 1.3e+87) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = (y - z) * t
	tmp = 0
	if x <= -3.4e+123:
		tmp = t_1
	elif x <= -1e+21:
		tmp = t_2
	elif x <= -1.45e-19:
		tmp = t_1
	elif x <= 5.2e-59:
		tmp = t_2
	elif x <= 3.1e+29:
		tmp = t_1
	elif x <= 7.6e+57:
		tmp = t_2
	elif x <= 1.3e+87:
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (x <= -3.4e+123)
		tmp = t_1;
	elseif (x <= -1e+21)
		tmp = t_2;
	elseif (x <= -1.45e-19)
		tmp = t_1;
	elseif (x <= 5.2e-59)
		tmp = t_2;
	elseif (x <= 3.1e+29)
		tmp = t_1;
	elseif (x <= 7.6e+57)
		tmp = t_2;
	elseif (x <= 1.3e+87)
		tmp = Float64(z * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (x <= -3.4e+123)
		tmp = t_1;
	elseif (x <= -1e+21)
		tmp = t_2;
	elseif (x <= -1.45e-19)
		tmp = t_1;
	elseif (x <= 5.2e-59)
		tmp = t_2;
	elseif (x <= 3.1e+29)
		tmp = t_1;
	elseif (x <= 7.6e+57)
		tmp = t_2;
	elseif (x <= 1.3e+87)
		tmp = z * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[x, -3.4e+123], t$95$1, If[LessEqual[x, -1e+21], t$95$2, If[LessEqual[x, -1.45e-19], t$95$1, If[LessEqual[x, 5.2e-59], t$95$2, If[LessEqual[x, 3.1e+29], t$95$1, If[LessEqual[x, 7.6e+57], t$95$2, If[LessEqual[x, 1.3e+87], N[(z * x), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.40000000000000001e123 or -1e21 < x < -1.45e-19 or 5.19999999999999996e-59 < x < 3.0999999999999999e29 or 1.29999999999999999e87 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 89.2%

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

      1. mul-1-neg 89.2%

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

      2. distribute-rgt-neg-in 89.2%

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

      3. neg-sub0 89.2%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 89.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 89.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 89.2%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 89.2%

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

      8. remove-double-neg 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in z around 0 75.3%

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

      1. *-rgt-identity 75.3%

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

      2. mul-1-neg 75.3%

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

      3. distribute-rgt-neg-out 75.3%

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

      4. distribute-lft-in 75.3%

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

      5. unsub-neg 75.3%

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

   8. Simplified 75.3%

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

   if -3.40000000000000001e123 < x < -1e21 or -1.45e-19 < x < 5.19999999999999996e-59 or 3.0999999999999999e29 < x < 7.5999999999999997e57

   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 84.8%

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

      1. sub-neg 84.8%

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

      2. distribute-rgt-in 80.5%

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

   5. Applied egg-rr 80.5%

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

      1. associate-+r+ 80.5%

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

      2. distribute-lft-neg-out 80.5%

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

      3. unsub-neg 80.5%

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

      4. +-commutative 80.5%

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

      5. *-commutative 80.5%

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

   7. Applied egg-rr 80.5%

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

   8. Taylor expanded in t around inf 77.5%

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

   if 7.5999999999999997e57 < x < 1.29999999999999999e87

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 87.6%

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

      1. mul-1-neg 87.6%

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

      2. distribute-rgt-neg-in 87.6%

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

      3. neg-sub0 87.6%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 87.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 87.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 87.6%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 87.6%

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

      8. remove-double-neg 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in z around inf 75.4%

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

      1. *-commutative 75.4%

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

   8. Simplified 75.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+21}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-59}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+57}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+87}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+60}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-267}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+46}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -6.2e+125)
     t_1
     (if (<= z -2.1e+60)
       (* z x)
       (if (<= z -2.8e-76)
         t_1
         (if (<= z -3.5e-155)
           x
           (if (<= z -1.65e-267)
             (* y t)
             (if (<= z 1.95e-174) x (if (<= z 4.7e+46) (* y t) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -6.2e+125) {
		tmp = t_1;
	} else if (z <= -2.1e+60) {
		tmp = z * x;
	} else if (z <= -2.8e-76) {
		tmp = t_1;
	} else if (z <= -3.5e-155) {
		tmp = x;
	} else if (z <= -1.65e-267) {
		tmp = y * t;
	} else if (z <= 1.95e-174) {
		tmp = x;
	} else if (z <= 4.7e+46) {
		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) :: tmp
    t_1 = z * -t
    if (z <= (-6.2d+125)) then
        tmp = t_1
    else if (z <= (-2.1d+60)) then
        tmp = z * x
    else if (z <= (-2.8d-76)) then
        tmp = t_1
    else if (z <= (-3.5d-155)) then
        tmp = x
    else if (z <= (-1.65d-267)) then
        tmp = y * t
    else if (z <= 1.95d-174) then
        tmp = x
    else if (z <= 4.7d+46) 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 = z * -t;
	double tmp;
	if (z <= -6.2e+125) {
		tmp = t_1;
	} else if (z <= -2.1e+60) {
		tmp = z * x;
	} else if (z <= -2.8e-76) {
		tmp = t_1;
	} else if (z <= -3.5e-155) {
		tmp = x;
	} else if (z <= -1.65e-267) {
		tmp = y * t;
	} else if (z <= 1.95e-174) {
		tmp = x;
	} else if (z <= 4.7e+46) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -6.2e+125:
		tmp = t_1
	elif z <= -2.1e+60:
		tmp = z * x
	elif z <= -2.8e-76:
		tmp = t_1
	elif z <= -3.5e-155:
		tmp = x
	elif z <= -1.65e-267:
		tmp = y * t
	elif z <= 1.95e-174:
		tmp = x
	elif z <= 4.7e+46:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -6.2e+125)
		tmp = t_1;
	elseif (z <= -2.1e+60)
		tmp = Float64(z * x);
	elseif (z <= -2.8e-76)
		tmp = t_1;
	elseif (z <= -3.5e-155)
		tmp = x;
	elseif (z <= -1.65e-267)
		tmp = Float64(y * t);
	elseif (z <= 1.95e-174)
		tmp = x;
	elseif (z <= 4.7e+46)
		tmp = Float64(y * t);
	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 <= -6.2e+125)
		tmp = t_1;
	elseif (z <= -2.1e+60)
		tmp = z * x;
	elseif (z <= -2.8e-76)
		tmp = t_1;
	elseif (z <= -3.5e-155)
		tmp = x;
	elseif (z <= -1.65e-267)
		tmp = y * t;
	elseif (z <= 1.95e-174)
		tmp = x;
	elseif (z <= 4.7e+46)
		tmp = y * t;
	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, -6.2e+125], t$95$1, If[LessEqual[z, -2.1e+60], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.8e-76], t$95$1, If[LessEqual[z, -3.5e-155], x, If[LessEqual[z, -1.65e-267], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.95e-174], x, If[LessEqual[z, 4.7e+46], N[(y * t), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2e125 or -2.1000000000000001e60 < z < -2.8000000000000001e-76 or 4.6999999999999996e46 < z

   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 62.4%

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

      1. sub-neg 62.4%

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

      2. distribute-rgt-in 56.5%

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

   5. Applied egg-rr 56.5%

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

      1. associate-+r+ 56.5%

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

      2. distribute-lft-neg-out 56.5%

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

      3. unsub-neg 56.5%

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

      4. +-commutative 56.5%

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

      5. *-commutative 56.5%

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

   7. Applied egg-rr 56.5%

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

   8. Taylor expanded in z around inf 51.0%

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

      1. neg-mul-1 51.0%

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

      2. distribute-rgt-neg-in 51.0%

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

   10. Simplified 51.0%

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

   if -6.2e125 < z < -2.1000000000000001e60

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 88.7%

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

      1. mul-1-neg 88.7%

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

      2. distribute-rgt-neg-in 88.7%

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

      3. neg-sub0 88.7%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 88.7%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 88.7%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 88.7%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 88.7%

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

      8. remove-double-neg 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in z around inf 52.9%

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

      1. *-commutative 52.9%

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

   8. Simplified 52.9%

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

   if -2.8000000000000001e-76 < z < -3.50000000000000015e-155 or -1.65000000000000002e-267 < z < 1.9499999999999999e-174

   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 80.7%

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

   4. Taylor expanded in x around inf 55.2%

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

   if -3.50000000000000015e-155 < z < -1.65000000000000002e-267 or 1.9499999999999999e-174 < z < 4.6999999999999996e46

   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 71.9%

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

      1. sub-neg 71.9%

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

      2. distribute-rgt-in 71.9%

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

   5. Applied egg-rr 71.9%

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

      1. associate-+r+ 71.9%

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

      2. distribute-lft-neg-out 71.9%

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

      3. unsub-neg 71.9%

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

      4. +-commutative 71.9%

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

      5. *-commutative 71.9%

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

   7. Applied egg-rr 71.9%

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

   8. Taylor expanded in y around inf 43.0%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+125}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+60}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-76}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-267}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-174}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+46}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-269}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* z (- x t))) (t_3 (* y (- t x))))
   (if (<= z -1.2e+25)
     t_2
     (if (<= z -4.5e-74)
       (* (- y z) t)
       (if (<= z -1.75e-178)
         t_1
         (if (<= z -7.2e-269)
           t_3
           (if (<= z 1.6e-169) t_1 (if (<= z 3.3e+86) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * (x - t);
	double t_3 = y * (t - x);
	double tmp;
	if (z <= -1.2e+25) {
		tmp = t_2;
	} else if (z <= -4.5e-74) {
		tmp = (y - z) * t;
	} else if (z <= -1.75e-178) {
		tmp = t_1;
	} else if (z <= -7.2e-269) {
		tmp = t_3;
	} else if (z <= 1.6e-169) {
		tmp = t_1;
	} else if (z <= 3.3e+86) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = z * (x - t)
    t_3 = y * (t - x)
    if (z <= (-1.2d+25)) then
        tmp = t_2
    else if (z <= (-4.5d-74)) then
        tmp = (y - z) * t
    else if (z <= (-1.75d-178)) then
        tmp = t_1
    else if (z <= (-7.2d-269)) then
        tmp = t_3
    else if (z <= 1.6d-169) then
        tmp = t_1
    else if (z <= 3.3d+86) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * (x - t);
	double t_3 = y * (t - x);
	double tmp;
	if (z <= -1.2e+25) {
		tmp = t_2;
	} else if (z <= -4.5e-74) {
		tmp = (y - z) * t;
	} else if (z <= -1.75e-178) {
		tmp = t_1;
	} else if (z <= -7.2e-269) {
		tmp = t_3;
	} else if (z <= 1.6e-169) {
		tmp = t_1;
	} else if (z <= 3.3e+86) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = z * (x - t)
	t_3 = y * (t - x)
	tmp = 0
	if z <= -1.2e+25:
		tmp = t_2
	elif z <= -4.5e-74:
		tmp = (y - z) * t
	elif z <= -1.75e-178:
		tmp = t_1
	elif z <= -7.2e-269:
		tmp = t_3
	elif z <= 1.6e-169:
		tmp = t_1
	elif z <= 3.3e+86:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (z <= -1.2e+25)
		tmp = t_2;
	elseif (z <= -4.5e-74)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= -1.75e-178)
		tmp = t_1;
	elseif (z <= -7.2e-269)
		tmp = t_3;
	elseif (z <= 1.6e-169)
		tmp = t_1;
	elseif (z <= 3.3e+86)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = z * (x - t);
	t_3 = y * (t - x);
	tmp = 0.0;
	if (z <= -1.2e+25)
		tmp = t_2;
	elseif (z <= -4.5e-74)
		tmp = (y - z) * t;
	elseif (z <= -1.75e-178)
		tmp = t_1;
	elseif (z <= -7.2e-269)
		tmp = t_3;
	elseif (z <= 1.6e-169)
		tmp = t_1;
	elseif (z <= 3.3e+86)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+25], t$95$2, If[LessEqual[z, -4.5e-74], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, -1.75e-178], t$95$1, If[LessEqual[z, -7.2e-269], t$95$3, If[LessEqual[z, 1.6e-169], t$95$1, If[LessEqual[z, 3.3e+86], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.19999999999999998e25 or 3.2999999999999999e86 < 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 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in z around inf 81.4%

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

   if -1.19999999999999998e25 < z < -4.4999999999999999e-74

   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 85.1%

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

      1. sub-neg 85.1%

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

      2. distribute-rgt-in 85.2%

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

   5. Applied egg-rr 85.2%

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

      1. associate-+r+ 85.2%

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

      2. distribute-lft-neg-out 85.2%

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

      3. unsub-neg 85.2%

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

      4. +-commutative 85.2%

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

      5. *-commutative 85.2%

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

   7. Applied egg-rr 85.2%

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

   8. Taylor expanded in t around inf 74.1%

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

   if -4.4999999999999999e-74 < z < -1.74999999999999992e-178 or -7.19999999999999996e-269 < z < 1.59999999999999997e-169

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-rgt-neg-in 78.1%

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

      3. neg-sub0 78.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 78.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 78.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 78.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 78.1%

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

      8. remove-double-neg 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around 0 78.1%

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

      1. *-rgt-identity 78.1%

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

      2. mul-1-neg 78.1%

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

      3. distribute-rgt-neg-out 78.1%

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

      4. distribute-lft-in 78.1%

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

      5. unsub-neg 78.1%

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

   8. Simplified 78.1%

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

   if -1.74999999999999992e-178 < z < -7.19999999999999996e-269 or 1.59999999999999997e-169 < z < 3.2999999999999999e86

   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 82.7%

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

      1. *-commutative 82.7%

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

   5. Simplified 82.7%

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

      1. *-commutative 82.7%

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

      2. sub-neg 82.7%

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

      3. distribute-lft-in 81.3%

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

   7. Applied egg-rr 81.3%

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

      1. associate-+r+ 81.3%

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

      2. distribute-rgt-neg-out 81.3%

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

      3. unsub-neg 81.3%

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

      4. +-commutative 81.3%

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

   9. Applied egg-rr 81.3%

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

   10. Taylor expanded in y around inf 68.6%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := t \cdot \left(y - z\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-140}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-62}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 255000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* t (- y z))))
   (if (<= y -3.1e+41)
     t_1
     (if (<= y -3.2e-88)
       t_2
       (if (<= y 8.5e-140)
         (- x (* z t))
         (if (<= y 2.7e-62)
           (+ x (* z x))
           (if (<= y 255000000000.0) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = t * (y - z);
	double tmp;
	if (y <= -3.1e+41) {
		tmp = t_1;
	} else if (y <= -3.2e-88) {
		tmp = t_2;
	} else if (y <= 8.5e-140) {
		tmp = x - (z * t);
	} else if (y <= 2.7e-62) {
		tmp = x + (z * x);
	} else if (y <= 255000000000.0) {
		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 = t * (y - z)
    if (y <= (-3.1d+41)) then
        tmp = t_1
    else if (y <= (-3.2d-88)) then
        tmp = t_2
    else if (y <= 8.5d-140) then
        tmp = x - (z * t)
    else if (y <= 2.7d-62) then
        tmp = x + (z * x)
    else if (y <= 255000000000.0d0) 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 = t * (y - z);
	double tmp;
	if (y <= -3.1e+41) {
		tmp = t_1;
	} else if (y <= -3.2e-88) {
		tmp = t_2;
	} else if (y <= 8.5e-140) {
		tmp = x - (z * t);
	} else if (y <= 2.7e-62) {
		tmp = x + (z * x);
	} else if (y <= 255000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = t * (y - z)
	tmp = 0
	if y <= -3.1e+41:
		tmp = t_1
	elif y <= -3.2e-88:
		tmp = t_2
	elif y <= 8.5e-140:
		tmp = x - (z * t)
	elif y <= 2.7e-62:
		tmp = x + (z * x)
	elif y <= 255000000000.0:
		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(t * Float64(y - z))
	tmp = 0.0
	if (y <= -3.1e+41)
		tmp = t_1;
	elseif (y <= -3.2e-88)
		tmp = t_2;
	elseif (y <= 8.5e-140)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 2.7e-62)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 255000000000.0)
		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 = t * (y - z);
	tmp = 0.0;
	if (y <= -3.1e+41)
		tmp = t_1;
	elseif (y <= -3.2e-88)
		tmp = t_2;
	elseif (y <= 8.5e-140)
		tmp = x - (z * t);
	elseif (y <= 2.7e-62)
		tmp = x + (z * x);
	elseif (y <= 255000000000.0)
		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[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+41], t$95$1, If[LessEqual[y, -3.2e-88], t$95$2, If[LessEqual[y, 8.5e-140], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-62], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 255000000000.0], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.1e41 or 2.55e11 < 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 81.3%

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

      1. *-commutative 81.3%

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

   5. Simplified 81.3%

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

      1. *-commutative 81.3%

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

      2. sub-neg 81.3%

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

      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%

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

   9. Applied egg-rr 77.2%

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

   10. Taylor expanded in y around inf 81.2%

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

   if -3.1e41 < y < -3.20000000000000012e-88 or 2.70000000000000019e-62 < y < 2.55e11

   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%

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

      1. sub-neg 83.6%

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

      2. distribute-rgt-in 83.6%

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

   5. Applied egg-rr 83.6%

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

      1. associate-+r+ 83.6%

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

      2. distribute-lft-neg-out 83.6%

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

      3. unsub-neg 83.6%

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

      4. +-commutative 83.6%

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

      5. *-commutative 83.6%

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

   7. Applied egg-rr 83.6%

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

   8. Taylor expanded in t around inf 69.9%

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

   if -3.20000000000000012e-88 < y < 8.49999999999999997e-140

   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 87.7%

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

   4. Taylor expanded in y around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   6. Simplified 86.0%

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

   if 8.49999999999999997e-140 < y < 2.70000000000000019e-62

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-rgt-neg-in 81.7%

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

      3. neg-sub0 81.7%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 81.7%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 81.7%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 81.7%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 81.7%

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

      8. remove-double-neg 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in y around 0 81.7%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-140}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-62}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 255000000000:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + t \cdot \left(y - z\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-70}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 145000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* t (- y z)))))
   (if (<= y -3.1e+41)
     t_1
     (if (<= y 3.5e-140)
       t_2
       (if (<= y 1.42e-70)
         (+ x (* z x))
         (if (<= y 145000000000.0) 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 + (t * (y - z));
	double tmp;
	if (y <= -3.1e+41) {
		tmp = t_1;
	} else if (y <= 3.5e-140) {
		tmp = t_2;
	} else if (y <= 1.42e-70) {
		tmp = x + (z * x);
	} else if (y <= 145000000000.0) {
		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 + (t * (y - z))
    if (y <= (-3.1d+41)) then
        tmp = t_1
    else if (y <= 3.5d-140) then
        tmp = t_2
    else if (y <= 1.42d-70) then
        tmp = x + (z * x)
    else if (y <= 145000000000.0d0) 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 + (t * (y - z));
	double tmp;
	if (y <= -3.1e+41) {
		tmp = t_1;
	} else if (y <= 3.5e-140) {
		tmp = t_2;
	} else if (y <= 1.42e-70) {
		tmp = x + (z * x);
	} else if (y <= 145000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + (t * (y - z))
	tmp = 0
	if y <= -3.1e+41:
		tmp = t_1
	elif y <= 3.5e-140:
		tmp = t_2
	elif y <= 1.42e-70:
		tmp = x + (z * x)
	elif y <= 145000000000.0:
		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(t * Float64(y - z)))
	tmp = 0.0
	if (y <= -3.1e+41)
		tmp = t_1;
	elseif (y <= 3.5e-140)
		tmp = t_2;
	elseif (y <= 1.42e-70)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 145000000000.0)
		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 + (t * (y - z));
	tmp = 0.0;
	if (y <= -3.1e+41)
		tmp = t_1;
	elseif (y <= 3.5e-140)
		tmp = t_2;
	elseif (y <= 1.42e-70)
		tmp = x + (z * x);
	elseif (y <= 145000000000.0)
		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[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+41], t$95$1, If[LessEqual[y, 3.5e-140], t$95$2, If[LessEqual[y, 1.42e-70], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 145000000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1e41 or 1.45e11 < 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 81.3%

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

      1. *-commutative 81.3%

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

   5. Simplified 81.3%

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

      1. *-commutative 81.3%

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

      2. sub-neg 81.3%

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

      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%

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

   9. Applied egg-rr 77.2%

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

   10. Taylor expanded in y around inf 81.2%

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

   if -3.1e41 < y < 3.4999999999999998e-140 or 1.42000000000000002e-70 < y < 1.45e11

   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 86.7%

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

   if 3.4999999999999998e-140 < y < 1.42000000000000002e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. distribute-rgt-neg-in 85.1%

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

      3. neg-sub0 85.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 85.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 85.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 85.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 85.1%

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

      8. remove-double-neg 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in y around 0 85.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-140}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-70}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 145000000000:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-93}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -3.6e+26)
     t_1
     (if (<= z -3e-72)
       (* t (- y z))
       (if (<= z 3.1e-93)
         (+ x (* y t))
         (if (<= z 3.3e+86) (* y (- t x)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -3.6e+26) {
		tmp = t_1;
	} else if (z <= -3e-72) {
		tmp = t * (y - z);
	} else if (z <= 3.1e-93) {
		tmp = x + (y * t);
	} else if (z <= 3.3e+86) {
		tmp = y * (t - 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 * (x - t)
    if (z <= (-3.6d+26)) then
        tmp = t_1
    else if (z <= (-3d-72)) then
        tmp = t * (y - z)
    else if (z <= 3.1d-93) then
        tmp = x + (y * t)
    else if (z <= 3.3d+86) then
        tmp = y * (t - 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 * (x - t);
	double tmp;
	if (z <= -3.6e+26) {
		tmp = t_1;
	} else if (z <= -3e-72) {
		tmp = t * (y - z);
	} else if (z <= 3.1e-93) {
		tmp = x + (y * t);
	} else if (z <= 3.3e+86) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -3.6e+26:
		tmp = t_1
	elif z <= -3e-72:
		tmp = t * (y - z)
	elif z <= 3.1e-93:
		tmp = x + (y * t)
	elif z <= 3.3e+86:
		tmp = y * (t - x)
	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 <= -3.6e+26)
		tmp = t_1;
	elseif (z <= -3e-72)
		tmp = Float64(t * Float64(y - z));
	elseif (z <= 3.1e-93)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 3.3e+86)
		tmp = Float64(y * Float64(t - x));
	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 <= -3.6e+26)
		tmp = t_1;
	elseif (z <= -3e-72)
		tmp = t * (y - z);
	elseif (z <= 3.1e-93)
		tmp = x + (y * t);
	elseif (z <= 3.3e+86)
		tmp = y * (t - x);
	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, -3.6e+26], t$95$1, If[LessEqual[z, -3e-72], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-93], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+86], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.60000000000000024e26 or 3.2999999999999999e86 < 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 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in z around inf 81.4%

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

   if -3.60000000000000024e26 < z < -3e-72

   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 85.1%

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

      1. sub-neg 85.1%

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

      2. distribute-rgt-in 85.2%

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

   5. Applied egg-rr 85.2%

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

      1. associate-+r+ 85.2%

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

      2. distribute-lft-neg-out 85.2%

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

      3. unsub-neg 85.2%

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

      4. +-commutative 85.2%

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

      5. *-commutative 85.2%

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

   7. Applied egg-rr 85.2%

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

   8. Taylor expanded in t around inf 74.1%

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

   if -3e-72 < z < 3.1e-93

   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 81.6%

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

   4. Taylor expanded in y around inf 74.6%

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

   if 3.1e-93 < z < 3.2999999999999999e86

   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 74.8%

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

      1. *-commutative 74.8%

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

   5. Simplified 74.8%

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

      1. *-commutative 74.8%

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

      2. sub-neg 74.8%

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

      3. distribute-lft-in 72.2%

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

   7. Applied egg-rr 72.2%

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

      1. associate-+r+ 72.2%

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

      2. distribute-rgt-neg-out 72.2%

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

      3. unsub-neg 72.2%

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

      4. +-commutative 72.2%

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

   9. Applied egg-rr 72.2%

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

   10. Taylor expanded in y around inf 66.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-93}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 270000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))) (t_2 (* z (- t))))
   (if (<= y -1.1e+41)
     t_1
     (if (<= y -6.5e-52)
       t_2
       (if (<= y -9e-205) x (if (<= y 270000000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double t_2 = z * -t;
	double tmp;
	if (y <= -1.1e+41) {
		tmp = t_1;
	} else if (y <= -6.5e-52) {
		tmp = t_2;
	} else if (y <= -9e-205) {
		tmp = x;
	} else if (y <= 270000000000.0) {
		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 = x * -y
    t_2 = z * -t
    if (y <= (-1.1d+41)) then
        tmp = t_1
    else if (y <= (-6.5d-52)) then
        tmp = t_2
    else if (y <= (-9d-205)) then
        tmp = x
    else if (y <= 270000000000.0d0) 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 = x * -y;
	double t_2 = z * -t;
	double tmp;
	if (y <= -1.1e+41) {
		tmp = t_1;
	} else if (y <= -6.5e-52) {
		tmp = t_2;
	} else if (y <= -9e-205) {
		tmp = x;
	} else if (y <= 270000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	t_2 = z * -t
	tmp = 0
	if y <= -1.1e+41:
		tmp = t_1
	elif y <= -6.5e-52:
		tmp = t_2
	elif y <= -9e-205:
		tmp = x
	elif y <= 270000000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -1.1e+41)
		tmp = t_1;
	elseif (y <= -6.5e-52)
		tmp = t_2;
	elseif (y <= -9e-205)
		tmp = x;
	elseif (y <= 270000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	t_2 = z * -t;
	tmp = 0.0;
	if (y <= -1.1e+41)
		tmp = t_1;
	elseif (y <= -6.5e-52)
		tmp = t_2;
	elseif (y <= -9e-205)
		tmp = x;
	elseif (y <= 270000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -1.1e+41], t$95$1, If[LessEqual[y, -6.5e-52], t$95$2, If[LessEqual[y, -9e-205], x, If[LessEqual[y, 270000000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.09999999999999995e41 or 2.7e11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. distribute-rgt-neg-in 58.2%

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

      3. neg-sub0 58.2%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 58.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 58.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 58.2%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 58.2%

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

      8. remove-double-neg 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in y around inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. distribute-lft-neg-out 50.8%

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

      3. *-commutative 50.8%

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

   8. Simplified 50.8%

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

   if -1.09999999999999995e41 < y < -6.5e-52 or -8.99999999999999912e-205 < y < 2.7e11

   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 80.5%

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

      1. sub-neg 80.5%

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

      2. distribute-rgt-in 80.5%

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

   5. Applied egg-rr 80.5%

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

      1. associate-+r+ 80.5%

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

      2. distribute-lft-neg-out 80.5%

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

      3. unsub-neg 80.5%

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

      4. +-commutative 80.5%

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

      5. *-commutative 80.5%

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

   7. Applied egg-rr 80.5%

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

   8. Taylor expanded in z around inf 46.0%

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

      1. neg-mul-1 46.0%

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

      2. distribute-rgt-neg-in 46.0%

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

   10. Simplified 46.0%

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

   if -6.5e-52 < y < -8.99999999999999912e-205

   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 87.7%

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

   4. Taylor expanded in x around inf 48.9%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 270000000000:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-70}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e-90)
   (* y t)
   (if (<= y 1.95e-140)
     x
     (if (<= y 7e-70) (* z x) (if (<= y 6e-55) x (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-90) {
		tmp = y * t;
	} else if (y <= 1.95e-140) {
		tmp = x;
	} else if (y <= 7e-70) {
		tmp = z * x;
	} else if (y <= 6e-55) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.5d-90)) then
        tmp = y * t
    else if (y <= 1.95d-140) then
        tmp = x
    else if (y <= 7d-70) then
        tmp = z * x
    else if (y <= 6d-55) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-90) {
		tmp = y * t;
	} else if (y <= 1.95e-140) {
		tmp = x;
	} else if (y <= 7e-70) {
		tmp = z * x;
	} else if (y <= 6e-55) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e-90:
		tmp = y * t
	elif y <= 1.95e-140:
		tmp = x
	elif y <= 7e-70:
		tmp = z * x
	elif y <= 6e-55:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e-90)
		tmp = Float64(y * t);
	elseif (y <= 1.95e-140)
		tmp = x;
	elseif (y <= 7e-70)
		tmp = Float64(z * x);
	elseif (y <= 6e-55)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e-90)
		tmp = y * t;
	elseif (y <= 1.95e-140)
		tmp = x;
	elseif (y <= 7e-70)
		tmp = z * x;
	elseif (y <= 6e-55)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e-90], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.95e-140], x, If[LessEqual[y, 7e-70], N[(z * x), $MachinePrecision], If[LessEqual[y, 6e-55], x, N[(y * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999999e-90 or 6.00000000000000033e-55 < y

   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 57.0%

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

      1. sub-neg 57.0%

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

      2. distribute-rgt-in 52.6%

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

   5. Applied egg-rr 52.6%

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

      1. associate-+r+ 52.6%

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

      2. distribute-lft-neg-out 52.6%

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

      3. unsub-neg 52.6%

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

      4. +-commutative 52.6%

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

      5. *-commutative 52.6%

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

   7. Applied egg-rr 52.6%

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

   8. Taylor expanded in y around inf 37.0%

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

   if -7.4999999999999999e-90 < y < 1.9500000000000001e-140 or 6.99999999999999949e-70 < y < 6.00000000000000033e-55

   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 88.3%

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

   4. Taylor expanded in x around inf 43.0%

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

   if 1.9500000000000001e-140 < y < 6.99999999999999949e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. distribute-rgt-neg-in 79.1%

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

      3. neg-sub0 79.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 79.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 79.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 79.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 79.1%

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

      8. remove-double-neg 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in z around inf 58.7%

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

      1. *-commutative 58.7%

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

   8. Simplified 58.7%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-70}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-166}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.15e+26)
     t_1
     (if (<= z -2.8e-166)
       (+ x (* t (- y z)))
       (if (<= z 3.3e+86) (+ x (* y (- t x))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.15e+26) {
		tmp = t_1;
	} else if (z <= -2.8e-166) {
		tmp = x + (t * (y - z));
	} else if (z <= 3.3e+86) {
		tmp = x + (y * (t - 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 * (x - t)
    if (z <= (-1.15d+26)) then
        tmp = t_1
    else if (z <= (-2.8d-166)) then
        tmp = x + (t * (y - z))
    else if (z <= 3.3d+86) then
        tmp = x + (y * (t - 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 * (x - t);
	double tmp;
	if (z <= -1.15e+26) {
		tmp = t_1;
	} else if (z <= -2.8e-166) {
		tmp = x + (t * (y - z));
	} else if (z <= 3.3e+86) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.15e+26:
		tmp = t_1
	elif z <= -2.8e-166:
		tmp = x + (t * (y - z))
	elif z <= 3.3e+86:
		tmp = x + (y * (t - x))
	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 <= -1.15e+26)
		tmp = t_1;
	elseif (z <= -2.8e-166)
		tmp = Float64(x + Float64(t * Float64(y - z)));
	elseif (z <= 3.3e+86)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	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 <= -1.15e+26)
		tmp = t_1;
	elseif (z <= -2.8e-166)
		tmp = x + (t * (y - z));
	elseif (z <= 3.3e+86)
		tmp = x + (y * (t - x));
	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, -1.15e+26], t$95$1, If[LessEqual[z, -2.8e-166], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+86], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e26 or 3.2999999999999999e86 < 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 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in z around inf 81.4%

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

   if -1.15e26 < z < -2.7999999999999999e-166

   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 88.8%

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

   if -2.7999999999999999e-166 < z < 3.2999999999999999e86

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.7%

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

      1. *-commutative 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-166}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-126}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq 155000000000:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -3.3e+45)
     t_1
     (if (<= y -1.2e-126)
       (+ x (* t (- y z)))
       (if (<= y 155000000000.0) (- x (* z (- t x))) (+ x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -3.3e+45) {
		tmp = t_1;
	} else if (y <= -1.2e-126) {
		tmp = x + (t * (y - z));
	} else if (y <= 155000000000.0) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + 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 <= (-3.3d+45)) then
        tmp = t_1
    else if (y <= (-1.2d-126)) then
        tmp = x + (t * (y - z))
    else if (y <= 155000000000.0d0) then
        tmp = x - (z * (t - x))
    else
        tmp = x + 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 <= -3.3e+45) {
		tmp = t_1;
	} else if (y <= -1.2e-126) {
		tmp = x + (t * (y - z));
	} else if (y <= 155000000000.0) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -3.3e+45:
		tmp = t_1
	elif y <= -1.2e-126:
		tmp = x + (t * (y - z))
	elif y <= 155000000000.0:
		tmp = x - (z * (t - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -3.3e+45)
		tmp = t_1;
	elseif (y <= -1.2e-126)
		tmp = Float64(x + Float64(t * Float64(y - z)));
	elseif (y <= 155000000000.0)
		tmp = Float64(x - Float64(z * Float64(t - x)));
	else
		tmp = Float64(x + 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 <= -3.3e+45)
		tmp = t_1;
	elseif (y <= -1.2e-126)
		tmp = x + (t * (y - z));
	elseif (y <= 155000000000.0)
		tmp = x - (z * (t - x));
	else
		tmp = x + 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, -3.3e+45], t$95$1, If[LessEqual[y, -1.2e-126], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 155000000000.0], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.3000000000000001e45

   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 81.0%

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

      1. *-commutative 81.0%

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

   5. Simplified 81.0%

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

      1. *-commutative 81.0%

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

      2. sub-neg 81.0%

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

      3. distribute-lft-in 72.5%

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

   7. Applied egg-rr 72.5%

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

      1. associate-+r+ 72.5%

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

      2. distribute-rgt-neg-out 72.5%

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

      3. unsub-neg 72.5%

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

      4. +-commutative 72.5%

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

   9. Applied egg-rr 72.5%

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

   10. Taylor expanded in y around inf 81.0%

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

   if -3.3000000000000001e45 < y < -1.20000000000000003e-126

   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 87.2%

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

   if -1.20000000000000003e-126 < y < 1.55e11

   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 95.9%

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

      1. mul-1-neg 95.9%

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

      2. unsub-neg 95.9%

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

   5. Simplified 95.9%

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

   if 1.55e11 < 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 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%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-126}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq 155000000000:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{-93} \lor \neg \left(t \leq 2.5 \cdot 10^{-107}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.35e-93) (not (<= t 2.5e-107)))
   (+ x (* t (- y z)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.35e-93) || !(t <= 2.5e-107)) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.35d-93)) .or. (.not. (t <= 2.5d-107))) then
        tmp = x + (t * (y - z))
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.35e-93) || !(t <= 2.5e-107)) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.35e-93) or not (t <= 2.5e-107):
		tmp = x + (t * (y - z))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.35e-93) || !(t <= 2.5e-107))
		tmp = Float64(x + Float64(t * Float64(y - z)));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.35e-93) || ~((t <= 2.5e-107)))
		tmp = x + (t * (y - z));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.35e-93], N[Not[LessEqual[t, 2.5e-107]], $MachinePrecision]], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.34999999999999987e-93 or 2.49999999999999985e-107 < 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 83.1%

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

   if -3.34999999999999987e-93 < t < 2.49999999999999985e-107

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 83.1%

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

      1. mul-1-neg 83.1%

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

      2. distribute-rgt-neg-in 83.1%

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

      3. neg-sub0 83.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 83.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 83.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 83.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 83.1%

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

      8. remove-double-neg 83.1%

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

   5. Simplified 83.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{-93} \lor \neg \left(t \leq 2.5 \cdot 10^{-107}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{-90} \lor \neg \left(t \leq 3.5 \cdot 10^{-106}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.35e-90) (not (<= t 3.5e-106))) (* t (- y z)) (* x (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.35e-90) || !(t <= 3.5e-106)) {
		tmp = t * (y - z);
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.35d-90)) .or. (.not. (t <= 3.5d-106))) then
        tmp = t * (y - z)
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.35e-90) || !(t <= 3.5e-106)) {
		tmp = t * (y - z);
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.35e-90) or not (t <= 3.5e-106):
		tmp = t * (y - z)
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.35e-90) || !(t <= 3.5e-106))
		tmp = Float64(t * Float64(y - z));
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.35e-90) || ~((t <= 3.5e-106)))
		tmp = t * (y - z);
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.35e-90], N[Not[LessEqual[t, 3.5e-106]], $MachinePrecision]], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3500000000000002e-90 or 3.5e-106 < 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 83.1%

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

      1. sub-neg 83.1%

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

      2. distribute-rgt-in 78.8%

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

   5. Applied egg-rr 78.8%

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

      1. associate-+r+ 78.8%

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

      2. distribute-lft-neg-out 78.8%

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

      3. unsub-neg 78.8%

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

      4. +-commutative 78.8%

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

      5. *-commutative 78.8%

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

   7. Applied egg-rr 78.8%

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

   8. Taylor expanded in t around inf 68.3%

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

   if -3.3500000000000002e-90 < t < 3.5e-106

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 83.1%

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

      1. mul-1-neg 83.1%

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

      2. distribute-rgt-neg-in 83.1%

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

      3. neg-sub0 83.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 83.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 83.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 83.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 83.1%

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

      8. remove-double-neg 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in y around inf 41.5%

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

      1. mul-1-neg 41.5%

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

      2. distribute-lft-neg-out 41.5%

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

      3. *-commutative 41.5%

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

   8. Simplified 41.5%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{-90} \lor \neg \left(t \leq 3.5 \cdot 10^{-106}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-88} \lor \neg \left(y \leq 1.22 \cdot 10^{-54}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e-88) (not (<= y 1.22e-54))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e-88) || !(y <= 1.22e-54)) {
		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 <= (-2.6d-88)) .or. (.not. (y <= 1.22d-54))) 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 <= -2.6e-88) || !(y <= 1.22e-54)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.6e-88) or not (y <= 1.22e-54):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e-88) || !(y <= 1.22e-54))
		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 <= -2.6e-88) || ~((y <= 1.22e-54)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.6e-88], N[Not[LessEqual[y, 1.22e-54]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000014e-88 or 1.22e-54 < y

   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 57.0%

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

      1. sub-neg 57.0%

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

      2. distribute-rgt-in 52.6%

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

   5. Applied egg-rr 52.6%

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

      1. associate-+r+ 52.6%

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

      2. distribute-lft-neg-out 52.6%

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

      3. unsub-neg 52.6%

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

      4. +-commutative 52.6%

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

      5. *-commutative 52.6%

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

   7. Applied egg-rr 52.6%

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

   8. Taylor expanded in y around inf 37.0%

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

   if -2.60000000000000014e-88 < y < 1.22e-54

   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 82.0%

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

   4. Taylor expanded in x around inf 40.2%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-88} \lor \neg \left(y \leq 1.22 \cdot 10^{-54}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 16: 17.6% 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 66.7%

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

4. Taylor expanded in x around inf 18.8%

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

5. Final simplification 18.8%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.4% 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 2024073 
(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))))