Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 14.0s

Alternatives: 12

Speedup: 1.0×

• 34.4% 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, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (x - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]

2. Final simplification 100.0%

   \[\leadsto x - \left(y - z\right) \cdot \left(x - t\right) \]

Alternative 2: 38.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -z \cdot t\\ t_2 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+43}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t))) (t_2 (* y (- x))))
   (if (<= y -1.2e+150)
     t_2
     (if (<= y -2.7e+43)
       (* y t)
       (if (<= y -4.1e+27)
         t_2
         (if (<= y -2.5e-44)
           t_1
           (if (<= y -4.2e-248)
             x
             (if (<= y 5.5e-204)
               t_1
               (if (<= y 4.2e-14) x (if (<= y 6.6e+57) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -(z * t);
	double t_2 = y * -x;
	double tmp;
	if (y <= -1.2e+150) {
		tmp = t_2;
	} else if (y <= -2.7e+43) {
		tmp = y * t;
	} else if (y <= -4.1e+27) {
		tmp = t_2;
	} else if (y <= -2.5e-44) {
		tmp = t_1;
	} else if (y <= -4.2e-248) {
		tmp = x;
	} else if (y <= 5.5e-204) {
		tmp = t_1;
	} else if (y <= 4.2e-14) {
		tmp = x;
	} else if (y <= 6.6e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -(z * t)
    t_2 = y * -x
    if (y <= (-1.2d+150)) then
        tmp = t_2
    else if (y <= (-2.7d+43)) then
        tmp = y * t
    else if (y <= (-4.1d+27)) then
        tmp = t_2
    else if (y <= (-2.5d-44)) then
        tmp = t_1
    else if (y <= (-4.2d-248)) then
        tmp = x
    else if (y <= 5.5d-204) then
        tmp = t_1
    else if (y <= 4.2d-14) then
        tmp = x
    else if (y <= 6.6d+57) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -(z * t);
	double t_2 = y * -x;
	double tmp;
	if (y <= -1.2e+150) {
		tmp = t_2;
	} else if (y <= -2.7e+43) {
		tmp = y * t;
	} else if (y <= -4.1e+27) {
		tmp = t_2;
	} else if (y <= -2.5e-44) {
		tmp = t_1;
	} else if (y <= -4.2e-248) {
		tmp = x;
	} else if (y <= 5.5e-204) {
		tmp = t_1;
	} else if (y <= 4.2e-14) {
		tmp = x;
	} else if (y <= 6.6e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -(z * t)
	t_2 = y * -x
	tmp = 0
	if y <= -1.2e+150:
		tmp = t_2
	elif y <= -2.7e+43:
		tmp = y * t
	elif y <= -4.1e+27:
		tmp = t_2
	elif y <= -2.5e-44:
		tmp = t_1
	elif y <= -4.2e-248:
		tmp = x
	elif y <= 5.5e-204:
		tmp = t_1
	elif y <= 4.2e-14:
		tmp = x
	elif y <= 6.6e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(z * t))
	t_2 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.2e+150)
		tmp = t_2;
	elseif (y <= -2.7e+43)
		tmp = Float64(y * t);
	elseif (y <= -4.1e+27)
		tmp = t_2;
	elseif (y <= -2.5e-44)
		tmp = t_1;
	elseif (y <= -4.2e-248)
		tmp = x;
	elseif (y <= 5.5e-204)
		tmp = t_1;
	elseif (y <= 4.2e-14)
		tmp = x;
	elseif (y <= 6.6e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -(z * t);
	t_2 = y * -x;
	tmp = 0.0;
	if (y <= -1.2e+150)
		tmp = t_2;
	elseif (y <= -2.7e+43)
		tmp = y * t;
	elseif (y <= -4.1e+27)
		tmp = t_2;
	elseif (y <= -2.5e-44)
		tmp = t_1;
	elseif (y <= -4.2e-248)
		tmp = x;
	elseif (y <= 5.5e-204)
		tmp = t_1;
	elseif (y <= 4.2e-14)
		tmp = x;
	elseif (y <= 6.6e+57)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(z * t), $MachinePrecision])}, Block[{t$95$2 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.2e+150], t$95$2, If[LessEqual[y, -2.7e+43], N[(y * t), $MachinePrecision], If[LessEqual[y, -4.1e+27], t$95$2, If[LessEqual[y, -2.5e-44], t$95$1, If[LessEqual[y, -4.2e-248], x, If[LessEqual[y, 5.5e-204], t$95$1, If[LessEqual[y, 4.2e-14], x, If[LessEqual[y, 6.6e+57], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.20000000000000001e150 or -2.7000000000000002e43 < y < -4.1000000000000002e27 or 6.6000000000000002e57 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

   4. Simplified 88.1%

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

   5. Taylor expanded in x around inf 60.2%

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

      1. +-commutative 60.2%

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

      2. distribute-rgt1-in 60.2%

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

      3. associate-*r* 60.2%

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

      4. mul-1-neg 60.2%

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

      5. unsub-neg 60.2%

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

      6. *-commutative 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in y around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. distribute-rgt-neg-out 60.2%

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

   10. Simplified 60.2%

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

   if -1.20000000000000001e150 < y < -2.7000000000000002e43

   1. Initial program 99.8%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 62.4%

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

   3. Taylor expanded in y around inf 55.6%

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

   if -4.1000000000000002e27 < y < -2.50000000000000019e-44 or -4.2e-248 < y < 5.4999999999999999e-204 or 4.1999999999999998e-14 < y < 6.6000000000000002e57

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 74.1%

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

   3. Taylor expanded in z around inf 49.1%

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

      1. associate-*r* 49.1%

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

      2. mul-1-neg 49.1%

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

   5. Simplified 49.1%

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

   if -2.50000000000000019e-44 < y < -4.2e-248 or 5.4999999999999999e-204 < y < 4.1999999999999998e-14

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 73.8%

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

   3. Taylor expanded in x around inf 43.6%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+43}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-44}:\\ \;\;\;\;-z \cdot t\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-204}:\\ \;\;\;\;-z \cdot t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+57}:\\ \;\;\;\;-z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot y\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-303}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* x y))) (t_2 (* z (- x t))) (t_3 (* y (- t x))))
   (if (<= z -8.2e+40)
     t_2
     (if (<= z -8.8e-51)
       t_3
       (if (<= z -1e-188)
         t_1
         (if (<= z -1.1e-228)
           t_3
           (if (<= z 5e-303)
             (+ x (* y t))
             (if (<= z 3.6e-262) t_3 (if (<= z 3.9e-56) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (x * y);
	double t_2 = z * (x - t);
	double t_3 = y * (t - x);
	double tmp;
	if (z <= -8.2e+40) {
		tmp = t_2;
	} else if (z <= -8.8e-51) {
		tmp = t_3;
	} else if (z <= -1e-188) {
		tmp = t_1;
	} else if (z <= -1.1e-228) {
		tmp = t_3;
	} else if (z <= 5e-303) {
		tmp = x + (y * t);
	} else if (z <= 3.6e-262) {
		tmp = t_3;
	} else if (z <= 3.9e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x - (x * y)
    t_2 = z * (x - t)
    t_3 = y * (t - x)
    if (z <= (-8.2d+40)) then
        tmp = t_2
    else if (z <= (-8.8d-51)) then
        tmp = t_3
    else if (z <= (-1d-188)) then
        tmp = t_1
    else if (z <= (-1.1d-228)) then
        tmp = t_3
    else if (z <= 5d-303) then
        tmp = x + (y * t)
    else if (z <= 3.6d-262) then
        tmp = t_3
    else if (z <= 3.9d-56) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (x * y);
	double t_2 = z * (x - t);
	double t_3 = y * (t - x);
	double tmp;
	if (z <= -8.2e+40) {
		tmp = t_2;
	} else if (z <= -8.8e-51) {
		tmp = t_3;
	} else if (z <= -1e-188) {
		tmp = t_1;
	} else if (z <= -1.1e-228) {
		tmp = t_3;
	} else if (z <= 5e-303) {
		tmp = x + (y * t);
	} else if (z <= 3.6e-262) {
		tmp = t_3;
	} else if (z <= 3.9e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (x * y)
	t_2 = z * (x - t)
	t_3 = y * (t - x)
	tmp = 0
	if z <= -8.2e+40:
		tmp = t_2
	elif z <= -8.8e-51:
		tmp = t_3
	elif z <= -1e-188:
		tmp = t_1
	elif z <= -1.1e-228:
		tmp = t_3
	elif z <= 5e-303:
		tmp = x + (y * t)
	elif z <= 3.6e-262:
		tmp = t_3
	elif z <= 3.9e-56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(x * y))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (z <= -8.2e+40)
		tmp = t_2;
	elseif (z <= -8.8e-51)
		tmp = t_3;
	elseif (z <= -1e-188)
		tmp = t_1;
	elseif (z <= -1.1e-228)
		tmp = t_3;
	elseif (z <= 5e-303)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 3.6e-262)
		tmp = t_3;
	elseif (z <= 3.9e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (x * y);
	t_2 = z * (x - t);
	t_3 = y * (t - x);
	tmp = 0.0;
	if (z <= -8.2e+40)
		tmp = t_2;
	elseif (z <= -8.8e-51)
		tmp = t_3;
	elseif (z <= -1e-188)
		tmp = t_1;
	elseif (z <= -1.1e-228)
		tmp = t_3;
	elseif (z <= 5e-303)
		tmp = x + (y * t);
	elseif (z <= 3.6e-262)
		tmp = t_3;
	elseif (z <= 3.9e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(x * 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, -8.2e+40], t$95$2, If[LessEqual[z, -8.8e-51], t$95$3, If[LessEqual[z, -1e-188], t$95$1, If[LessEqual[z, -1.1e-228], t$95$3, If[LessEqual[z, 5e-303], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-262], t$95$3, If[LessEqual[z, 3.9e-56], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2000000000000003e40 or 3.9e-56 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 96.7%

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

      3. fma-def 97.5%

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

   3. Applied egg-rr 97.5%

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

   4. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-*r* 83.9%

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

      4. distribute-rgt-in 86.4%

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

      5. mul-1-neg 86.4%

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

      6. sub-neg 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in z around inf 84.9%

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

   if -8.2000000000000003e40 < z < -8.8000000000000001e-51 or -9.9999999999999995e-189 < z < -1.1e-228 or 4.9999999999999998e-303 < z < 3.5999999999999998e-262

   1. Initial program 100.0%

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

      1. flip-- 84.1%

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

      2. associate-*l/ 73.2%

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

   3. Applied egg-rr 73.2%

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

   4. Taylor expanded in y around inf 59.4%

      \[\leadsto x + \frac{\color{blue}{{y}^{2} \cdot \left(t - x\right)}}{y + z} \]
   5. Step-by-step derivation

      1. unpow2 59.4%

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

      2. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in y around -inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. *-commutative 77.0%

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

      3. distribute-rgt-neg-in 77.0%

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

      4. neg-mul-1 77.0%

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

      5. cancel-sign-sub-inv 77.0%

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

      6. metadata-eval 77.0%

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

      7. *-lft-identity 77.0%

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

      8. +-commutative 77.0%

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

      9. sub-neg 77.0%

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

   9. Simplified 77.0%

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

   if -8.8000000000000001e-51 < z < -9.9999999999999995e-189 or 3.5999999999999998e-262 < z < 3.9e-56

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 92.3%

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

      1. *-commutative 92.3%

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

   4. Simplified 92.3%

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

   5. Taylor expanded in x around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. distribute-rgt1-in 76.3%

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

      3. associate-*r* 76.3%

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

      4. mul-1-neg 76.3%

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

      5. unsub-neg 76.3%

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

      6. *-commutative 76.3%

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

   7. Simplified 76.3%

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

   if -1.1e-228 < z < 4.9999999999999998e-303

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 82.9%

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

   3. Taylor expanded in z around 0 82.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-188}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-303}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-262}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 4: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-198}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-59}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* (- y z) t))))
   (if (<= y -8.2e+27)
     t_1
     (if (<= y 2.55e-307)
       t_2
       (if (<= y 5.6e-198)
         (* z (- x t))
         (if (<= y 1.9e-119)
           t_2
           (if (<= y 3.7e-59) (+ x (* x z)) (if (<= y 4.3e+57) 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 + ((y - z) * t);
	double tmp;
	if (y <= -8.2e+27) {
		tmp = t_1;
	} else if (y <= 2.55e-307) {
		tmp = t_2;
	} else if (y <= 5.6e-198) {
		tmp = z * (x - t);
	} else if (y <= 1.9e-119) {
		tmp = t_2;
	} else if (y <= 3.7e-59) {
		tmp = x + (x * z);
	} else if (y <= 4.3e+57) {
		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 + ((y - z) * t)
    if (y <= (-8.2d+27)) then
        tmp = t_1
    else if (y <= 2.55d-307) then
        tmp = t_2
    else if (y <= 5.6d-198) then
        tmp = z * (x - t)
    else if (y <= 1.9d-119) then
        tmp = t_2
    else if (y <= 3.7d-59) then
        tmp = x + (x * z)
    else if (y <= 4.3d+57) 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 + ((y - z) * t);
	double tmp;
	if (y <= -8.2e+27) {
		tmp = t_1;
	} else if (y <= 2.55e-307) {
		tmp = t_2;
	} else if (y <= 5.6e-198) {
		tmp = z * (x - t);
	} else if (y <= 1.9e-119) {
		tmp = t_2;
	} else if (y <= 3.7e-59) {
		tmp = x + (x * z);
	} else if (y <= 4.3e+57) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if y <= -8.2e+27:
		tmp = t_1
	elif y <= 2.55e-307:
		tmp = t_2
	elif y <= 5.6e-198:
		tmp = z * (x - t)
	elif y <= 1.9e-119:
		tmp = t_2
	elif y <= 3.7e-59:
		tmp = x + (x * z)
	elif y <= 4.3e+57:
		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(Float64(y - z) * t))
	tmp = 0.0
	if (y <= -8.2e+27)
		tmp = t_1;
	elseif (y <= 2.55e-307)
		tmp = t_2;
	elseif (y <= 5.6e-198)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= 1.9e-119)
		tmp = t_2;
	elseif (y <= 3.7e-59)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 4.3e+57)
		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 + ((y - z) * t);
	tmp = 0.0;
	if (y <= -8.2e+27)
		tmp = t_1;
	elseif (y <= 2.55e-307)
		tmp = t_2;
	elseif (y <= 5.6e-198)
		tmp = z * (x - t);
	elseif (y <= 1.9e-119)
		tmp = t_2;
	elseif (y <= 3.7e-59)
		tmp = x + (x * z);
	elseif (y <= 4.3e+57)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+27], t$95$1, If[LessEqual[y, 2.55e-307], t$95$2, If[LessEqual[y, 5.6e-198], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-119], t$95$2, If[LessEqual[y, 3.7e-59], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+57], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.2000000000000005e27 or 4.30000000000000033e57 < y

   1. Initial program 99.9%

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

      1. flip-- 63.5%

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

      2. associate-*l/ 55.7%

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

   3. Applied egg-rr 55.7%

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

   4. Taylor expanded in y around inf 53.8%

      \[\leadsto x + \frac{\color{blue}{{y}^{2} \cdot \left(t - x\right)}}{y + z} \]
   5. Step-by-step derivation

      1. unpow2 53.8%

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

      2. *-commutative 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in y around -inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. *-commutative 87.1%

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

      3. distribute-rgt-neg-in 87.1%

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

      4. neg-mul-1 87.1%

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

      5. cancel-sign-sub-inv 87.1%

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

      6. metadata-eval 87.1%

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

      7. *-lft-identity 87.1%

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

      8. +-commutative 87.1%

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

      9. sub-neg 87.1%

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

   9. Simplified 87.1%

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

   if -8.2000000000000005e27 < y < 2.55e-307 or 5.5999999999999998e-198 < y < 1.89999999999999987e-119 or 3.6999999999999999e-59 < y < 4.30000000000000033e57

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 81.9%

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

   if 2.55e-307 < y < 5.5999999999999998e-198

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 99.8%

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

      3. fma-def 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around 0 93.7%

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

      1. +-commutative 93.7%

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

      2. *-commutative 93.7%

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

      3. associate-*r* 93.7%

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

      4. distribute-rgt-in 93.9%

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

      5. mul-1-neg 93.9%

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

      6. sub-neg 93.9%

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

   6. Simplified 93.9%

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

   7. Taylor expanded in z around inf 77.8%

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

   if 1.89999999999999987e-119 < y < 3.6999999999999999e-59

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 95.4%

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

      1. mul-1-neg 95.4%

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

      2. distribute-lft-neg-out 95.4%

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

      3. *-commutative 95.4%

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

   4. Simplified 95.4%

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

   5. Taylor expanded in t around 0 82.0%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-307}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-198}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-59}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+57}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 5: 38.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+43}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -340000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+56}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -1.25e+150)
     t_1
     (if (<= y -3.4e+43)
       (* y t)
       (if (<= y -340000000.0)
         t_1
         (if (<= y 2.3e-14) x (if (<= y 1.5e+56) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -1.25e+150) {
		tmp = t_1;
	} else if (y <= -3.4e+43) {
		tmp = y * t;
	} else if (y <= -340000000.0) {
		tmp = t_1;
	} else if (y <= 2.3e-14) {
		tmp = x;
	} else if (y <= 1.5e+56) {
		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 = y * -x
    if (y <= (-1.25d+150)) then
        tmp = t_1
    else if (y <= (-3.4d+43)) then
        tmp = y * t
    else if (y <= (-340000000.0d0)) then
        tmp = t_1
    else if (y <= 2.3d-14) then
        tmp = x
    else if (y <= 1.5d+56) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -1.25e+150) {
		tmp = t_1;
	} else if (y <= -3.4e+43) {
		tmp = y * t;
	} else if (y <= -340000000.0) {
		tmp = t_1;
	} else if (y <= 2.3e-14) {
		tmp = x;
	} else if (y <= 1.5e+56) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -1.25e+150:
		tmp = t_1
	elif y <= -3.4e+43:
		tmp = y * t
	elif y <= -340000000.0:
		tmp = t_1
	elif y <= 2.3e-14:
		tmp = x
	elif y <= 1.5e+56:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.25e+150)
		tmp = t_1;
	elseif (y <= -3.4e+43)
		tmp = Float64(y * t);
	elseif (y <= -340000000.0)
		tmp = t_1;
	elseif (y <= 2.3e-14)
		tmp = x;
	elseif (y <= 1.5e+56)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -1.25e+150)
		tmp = t_1;
	elseif (y <= -3.4e+43)
		tmp = y * t;
	elseif (y <= -340000000.0)
		tmp = t_1;
	elseif (y <= 2.3e-14)
		tmp = x;
	elseif (y <= 1.5e+56)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.25e+150], t$95$1, If[LessEqual[y, -3.4e+43], N[(y * t), $MachinePrecision], If[LessEqual[y, -340000000.0], t$95$1, If[LessEqual[y, 2.3e-14], x, If[LessEqual[y, 1.5e+56], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000002e150 or -3.40000000000000012e43 < y < -3.4e8 or 1.50000000000000003e56 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 85.4%

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

      1. *-commutative 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in x around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. distribute-rgt1-in 58.4%

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

      3. associate-*r* 58.4%

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

      4. mul-1-neg 58.4%

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

      5. unsub-neg 58.4%

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

      6. *-commutative 58.4%

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

   7. Simplified 58.4%

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

   8. Taylor expanded in y around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. distribute-rgt-neg-out 58.4%

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

   10. Simplified 58.4%

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

   if -1.25000000000000002e150 < y < -3.40000000000000012e43 or 2.29999999999999998e-14 < y < 1.50000000000000003e56

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 68.2%

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

   3. Taylor expanded in y around inf 45.3%

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

   if -3.4e8 < y < 2.29999999999999998e-14

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 73.4%

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

   3. Taylor expanded in x around inf 33.9%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+43}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -340000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+56}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 6: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -5 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y t))))
   (if (<= z -5e+40)
     t_1
     (if (<= z 7e-237)
       t_2
       (if (<= z 5.9e-187) (* y (- x)) (if (<= z 2.75e-45) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -5e+40) {
		tmp = t_1;
	} else if (z <= 7e-237) {
		tmp = t_2;
	} else if (z <= 5.9e-187) {
		tmp = y * -x;
	} else if (z <= 2.75e-45) {
		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 = z * (x - t)
    t_2 = x + (y * t)
    if (z <= (-5d+40)) then
        tmp = t_1
    else if (z <= 7d-237) then
        tmp = t_2
    else if (z <= 5.9d-187) then
        tmp = y * -x
    else if (z <= 2.75d-45) 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 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -5e+40) {
		tmp = t_1;
	} else if (z <= 7e-237) {
		tmp = t_2;
	} else if (z <= 5.9e-187) {
		tmp = y * -x;
	} else if (z <= 2.75e-45) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -5e+40:
		tmp = t_1
	elif z <= 7e-237:
		tmp = t_2
	elif z <= 5.9e-187:
		tmp = y * -x
	elif z <= 2.75e-45:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -5e+40)
		tmp = t_1;
	elseif (z <= 7e-237)
		tmp = t_2;
	elseif (z <= 5.9e-187)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 2.75e-45)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -5e+40)
		tmp = t_1;
	elseif (z <= 7e-237)
		tmp = t_2;
	elseif (z <= 5.9e-187)
		tmp = y * -x;
	elseif (z <= 2.75e-45)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+40], t$95$1, If[LessEqual[z, 7e-237], t$95$2, If[LessEqual[z, 5.9e-187], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 2.75e-45], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000003e40 or 2.75000000000000015e-45 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 96.6%

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

      3. fma-def 97.5%

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

   3. Applied egg-rr 97.5%

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

   4. Taylor expanded in y around 0 85.2%

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

      1. +-commutative 85.2%

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

      2. *-commutative 85.2%

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

      3. associate-*r* 85.2%

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

      4. distribute-rgt-in 87.7%

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

      5. mul-1-neg 87.7%

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

      6. sub-neg 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in z around inf 86.1%

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

   if -5.00000000000000003e40 < z < 6.99999999999999966e-237 or 5.8999999999999999e-187 < z < 2.75000000000000015e-45

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 71.6%

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

   3. Taylor expanded in z around 0 64.6%

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

   if 6.99999999999999966e-237 < z < 5.8999999999999999e-187

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 93.3%

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

      1. *-commutative 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in x around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. distribute-rgt1-in 86.0%

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

      3. associate-*r* 86.0%

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

      4. mul-1-neg 86.0%

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

      5. unsub-neg 86.0%

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

      6. *-commutative 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in y around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. distribute-rgt-neg-out 63.5%

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

   10. Simplified 63.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-237}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 7: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+27} \lor \neg \left(y \leq 4.3 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.6e+27) (not (<= y 4.3e+57)))
   (* y (- t x))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e+27) || !(y <= 4.3e+57)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.6d+27)) .or. (.not. (y <= 4.3d+57))) then
        tmp = y * (t - x)
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e+27) || !(y <= 4.3e+57)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.6e+27) or not (y <= 4.3e+57):
		tmp = y * (t - x)
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.6e+27) || !(y <= 4.3e+57))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.6e+27) || ~((y <= 4.3e+57)))
		tmp = y * (t - x);
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.6e+27], N[Not[LessEqual[y, 4.3e+57]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6000000000000001e27 or 4.30000000000000033e57 < y

   1. Initial program 99.9%

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

      1. flip-- 63.5%

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

      2. associate-*l/ 55.7%

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

   3. Applied egg-rr 55.7%

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

   4. Taylor expanded in y around inf 53.8%

      \[\leadsto x + \frac{\color{blue}{{y}^{2} \cdot \left(t - x\right)}}{y + z} \]
   5. Step-by-step derivation

      1. unpow2 53.8%

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

      2. *-commutative 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in y around -inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. *-commutative 87.1%

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

      3. distribute-rgt-neg-in 87.1%

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

      4. neg-mul-1 87.1%

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

      5. cancel-sign-sub-inv 87.1%

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

      6. metadata-eval 87.1%

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

      7. *-lft-identity 87.1%

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

      8. +-commutative 87.1%

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

      9. sub-neg 87.1%

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

   9. Simplified 87.1%

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

   if -4.6000000000000001e27 < y < 4.30000000000000033e57

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 99.3%

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

      3. fma-def 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in y around 0 87.7%

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

      1. +-commutative 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*r* 87.7%

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

      4. distribute-rgt-in 88.4%

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

      5. mul-1-neg 88.4%

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

      6. sub-neg 88.4%

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

   6. Simplified 88.4%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+27} \lor \neg \left(y \leq 4.3 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 8: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -7.8e+40) t_1 (if (<= z 3.7e-45) (+ x (* y (- t x))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.8e+40) {
		tmp = t_1;
	} else if (z <= 3.7e-45) {
		tmp = x + (y * (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 = z * (x - t)
    if (z <= (-7.8d+40)) then
        tmp = t_1
    else if (z <= 3.7d-45) then
        tmp = x + (y * (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 = z * (x - t);
	double tmp;
	if (z <= -7.8e+40) {
		tmp = t_1;
	} else if (z <= 3.7e-45) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -7.8e+40:
		tmp = t_1
	elif z <= 3.7e-45:
		tmp = x + (y * (t - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -7.8e+40)
		tmp = t_1;
	elseif (z <= 3.7e-45)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -7.8e+40)
		tmp = t_1;
	elseif (z <= 3.7e-45)
		tmp = x + (y * (t - x));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+40], t$95$1, If[LessEqual[z, 3.7e-45], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8000000000000002e40

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 96.2%

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

      3. fma-def 98.1%

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

   3. Applied egg-rr 98.1%

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

   4. Taylor expanded in y around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. *-commutative 81.6%

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

      3. associate-*r* 81.6%

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

      4. distribute-rgt-in 85.4%

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

      5. mul-1-neg 85.4%

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

      6. sub-neg 85.4%

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

   6. Simplified 85.4%

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

   7. Taylor expanded in z around inf 85.4%

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

   if -7.8000000000000002e40 < z < 3.7e-45

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 91.0%

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

      1. *-commutative 91.0%

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

   4. Simplified 91.0%

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

   if 3.7e-45 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 96.9%

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

      3. fma-def 96.9%

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

   3. Applied egg-rr 96.9%

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

   4. Taylor expanded in y around 0 89.3%

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

      1. +-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*r* 89.3%

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

      4. distribute-rgt-in 90.8%

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

      5. mul-1-neg 90.8%

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

      6. sub-neg 90.8%

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

   6. Simplified 90.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-45}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+84} \lor \neg \left(y \leq 2.45 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.2e+84) (not (<= y 2.45e+58))) (* y (- x)) (* z (- x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e+84) || !(y <= 2.45e+58)) {
		tmp = y * -x;
	} else {
		tmp = z * (x - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7.2d+84)) .or. (.not. (y <= 2.45d+58))) then
        tmp = y * -x
    else
        tmp = z * (x - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e+84) || !(y <= 2.45e+58)) {
		tmp = y * -x;
	} else {
		tmp = z * (x - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.2e+84) or not (y <= 2.45e+58):
		tmp = y * -x
	else:
		tmp = z * (x - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.2e+84) || !(y <= 2.45e+58))
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(z * Float64(x - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.2e+84) || ~((y <= 2.45e+58)))
		tmp = y * -x;
	else
		tmp = z * (x - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.2e+84], N[Not[LessEqual[y, 2.45e+58]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.1999999999999999e84 or 2.45000000000000009e58 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 89.6%

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

      1. *-commutative 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in x around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. distribute-rgt1-in 58.4%

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

      3. associate-*r* 58.4%

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

      4. mul-1-neg 58.4%

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

      5. unsub-neg 58.4%

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

      6. *-commutative 58.4%

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

   7. Simplified 58.4%

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

   8. Taylor expanded in y around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. distribute-rgt-neg-out 58.4%

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

   10. Simplified 58.4%

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

   if -7.1999999999999999e84 < y < 2.45000000000000009e58

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 98.7%

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

      3. fma-def 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-*r* 83.9%

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

      4. distribute-rgt-in 85.2%

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

      5. mul-1-neg 85.2%

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

      6. sub-neg 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in z around inf 60.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+84} \lor \neg \left(y \leq 2.45 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 10: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+19} \lor \neg \left(z \leq 3.9 \cdot 10^{-56}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+19) (not (<= z 3.9e-56))) (* z (- x t)) (- x (* x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+19) || !(z <= 3.9e-56)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (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 ((z <= (-8d+19)) .or. (.not. (z <= 3.9d-56))) then
        tmp = z * (x - t)
    else
        tmp = x - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+19) || !(z <= 3.9e-56)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+19) or not (z <= 3.9e-56):
		tmp = z * (x - t)
	else:
		tmp = x - (x * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+19) || !(z <= 3.9e-56))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8e+19) || ~((z <= 3.9e-56)))
		tmp = z * (x - t);
	else
		tmp = x - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e+19], N[Not[LessEqual[z, 3.9e-56]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e19 or 3.9e-56 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 96.8%

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

      3. fma-def 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in y around 0 81.7%

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

      1. +-commutative 81.7%

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

      2. *-commutative 81.7%

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

      3. associate-*r* 81.7%

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

      4. distribute-rgt-in 84.1%

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

      5. mul-1-neg 84.1%

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

      6. sub-neg 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in z around inf 82.7%

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

   if -8e19 < z < 3.9e-56

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 93.2%

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

      1. *-commutative 93.2%

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

   4. Simplified 93.2%

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

   5. Taylor expanded in x around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. distribute-rgt1-in 65.0%

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

      3. associate-*r* 65.0%

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

      4. mul-1-neg 65.0%

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

      5. unsub-neg 65.0%

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

      6. *-commutative 65.0%

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

   7. Simplified 65.0%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+19} \lor \neg \left(z \leq 3.9 \cdot 10^{-56}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 11: 37.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-44}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.5e-44) (* y t) (if (<= y 1.7e-13) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-44) {
		tmp = y * t;
	} else if (y <= 1.7e-13) {
		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 <= (-3.5d-44)) then
        tmp = y * t
    else if (y <= 1.7d-13) 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 <= -3.5e-44) {
		tmp = y * t;
	} else if (y <= 1.7e-13) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.5e-44:
		tmp = y * t
	elif y <= 1.7e-13:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.5e-44)
		tmp = Float64(y * t);
	elseif (y <= 1.7e-13)
		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 <= -3.5e-44)
		tmp = y * t;
	elseif (y <= 1.7e-13)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.5e-44], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.7e-13], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999998e-44 or 1.70000000000000008e-13 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 51.0%

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

   3. Taylor expanded in y around inf 34.6%

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

   if -3.4999999999999998e-44 < y < 1.70000000000000008e-13

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 72.6%

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

   3. Taylor expanded in x around inf 36.1%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-44}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 12: 17.9% 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. Taylor expanded in t around inf 61.2%

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

3. Taylor expanded in x around inf 19.1%

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

4. Final simplification 19.1%

   \[\leadsto x \]

Developer target: 96.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023278 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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