Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.3s

Alternatives: 10

Speedup: 1.0×

• 35.3% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-245}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+27)
   (* x z)
   (if (<= z -3.8e-245)
     (* y t)
     (if (<= z 2.75e-17) x (if (<= z 2.4e+125) (* y t) (* x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+27) {
		tmp = x * z;
	} else if (z <= -3.8e-245) {
		tmp = y * t;
	} else if (z <= 2.75e-17) {
		tmp = x;
	} else if (z <= 2.4e+125) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.2d+27)) then
        tmp = x * z
    else if (z <= (-3.8d-245)) then
        tmp = y * t
    else if (z <= 2.75d-17) then
        tmp = x
    else if (z <= 2.4d+125) then
        tmp = y * t
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+27) {
		tmp = x * z;
	} else if (z <= -3.8e-245) {
		tmp = y * t;
	} else if (z <= 2.75e-17) {
		tmp = x;
	} else if (z <= 2.4e+125) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+27:
		tmp = x * z
	elif z <= -3.8e-245:
		tmp = y * t
	elif z <= 2.75e-17:
		tmp = x
	elif z <= 2.4e+125:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+27)
		tmp = Float64(x * z);
	elseif (z <= -3.8e-245)
		tmp = Float64(y * t);
	elseif (z <= 2.75e-17)
		tmp = x;
	elseif (z <= 2.4e+125)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+27)
		tmp = x * z;
	elseif (z <= -3.8e-245)
		tmp = y * t;
	elseif (z <= 2.75e-17)
		tmp = x;
	elseif (z <= 2.4e+125)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+27], N[(x * z), $MachinePrecision], If[LessEqual[z, -3.8e-245], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.75e-17], x, If[LessEqual[z, 2.4e+125], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999999e27 or 2.4e125 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 88.7%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 88.7%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 49.2%

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]

   8. Simplified 49.2%

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

   if -1.19999999999999999e27 < z < -3.8000000000000001e-245 or 2.75e-17 < z < 2.4e125

   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

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 64.1%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 64.1%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{t}\right) \]
   7. Step-by-step derivation

   8. Simplified 48.2%

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

   if -3.8000000000000001e-245 < z < 2.75e-17

   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

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 69.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 69.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(x \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{x}\right)\right) \]

      2. *-lowering-*.f64 42.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]

   8. Simplified 42.9%

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

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   10. Step-by-step derivation

   11. Simplified 42.9%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-245}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+125}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - x\right)\\ \mathbf{if}\;y - z \leq -500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{-20}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t x))))
   (if (<= (- y z) -500.0)
     t_1
     (if (<= (- y z) 5e-20) (+ x (* (- y z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - x);
	double tmp;
	if ((y - z) <= -500.0) {
		tmp = t_1;
	} else if ((y - z) <= 5e-20) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - x)
    if ((y - z) <= (-500.0d0)) then
        tmp = t_1
    else if ((y - z) <= 5d-20) then
        tmp = x + ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - x);
	double tmp;
	if ((y - z) <= -500.0) {
		tmp = t_1;
	} else if ((y - z) <= 5e-20) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - x)
	tmp = 0
	if (y - z) <= -500.0:
		tmp = t_1
	elif (y - z) <= 5e-20:
		tmp = x + ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - x))
	tmp = 0.0
	if (Float64(y - z) <= -500.0)
		tmp = t_1;
	elseif (Float64(y - z) <= 5e-20)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - x);
	tmp = 0.0;
	if ((y - z) <= -500.0)
		tmp = t_1;
	elseif ((y - z) <= 5e-20)
		tmp = x + ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -500.0], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 5e-20], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -500 or 4.9999999999999999e-20 < (-.f64 y z)

   1. Initial program 100.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{y \cdot y - z \cdot z}{\color{blue}{y + z}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y + z}{y \cdot y - z \cdot z}\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y + z}}{y \cdot y - z \cdot z}\right)\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{\color{blue}{\frac{y \cdot y - z \cdot z}{y + z}}}\right)\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{y - \color{blue}{z}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]
   5. Step-by-step derivation

      1. div-sub N/A

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

      2. associate-+r- N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{t}{\frac{1}{y - z}}\right), \color{blue}{\left(\frac{x}{\frac{1}{y - z}}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{t}{\frac{1}{y - z}}\right)\right), \left(\frac{\color{blue}{x}}{\frac{1}{y - z}}\right)\right) \]

      5. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{t}{1} \cdot \left(y - z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      6. /-rgt-identity N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(t \cdot \left(y - z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \left(y - z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      9. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \left(x \cdot \color{blue}{\frac{1}{\frac{1}{y - z}}}\right)\right) \]

      10. remove-double-div N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \left(x \cdot \left(y - \color{blue}{z}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \mathsf{*.f64}\left(x, \color{blue}{\left(y - z\right)}\right)\right) \]

      12. --lowering--.f64 95.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(t \cdot \left(y - z\right)\right)}, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \mathsf{*.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(y, z\right)\right)\right) \]

      2. --lowering--.f64 95.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right)\right) \]

   9. Simplified 95.5%

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

       1. distribute-rgt-out-- N/A

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

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(t - x\right)}\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{t} - x\right)\right) \]

       4. --lowering--.f64 99.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   11. Applied egg-rr 99.6%

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

   if -500 < (-.f64 y z) < 4.9999999999999999e-20

   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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 99.4%

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

Alternative 4: 94.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - x\right)\\ \mathbf{if}\;y - z \leq -500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y - z \leq 5 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t x))))
   (if (<= (- y z) -500.0) t_1 (if (<= (- y z) 5e-20) (+ x (* y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - x);
	double tmp;
	if ((y - z) <= -500.0) {
		tmp = t_1;
	} else if ((y - z) <= 5e-20) {
		tmp = x + (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 - z) * (t - x)
    if ((y - z) <= (-500.0d0)) then
        tmp = t_1
    else if ((y - z) <= 5d-20) then
        tmp = x + (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 - z) * (t - x);
	double tmp;
	if ((y - z) <= -500.0) {
		tmp = t_1;
	} else if ((y - z) <= 5e-20) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - x)
	tmp = 0
	if (y - z) <= -500.0:
		tmp = t_1
	elif (y - z) <= 5e-20:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - x))
	tmp = 0.0
	if (Float64(y - z) <= -500.0)
		tmp = t_1;
	elseif (Float64(y - z) <= 5e-20)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - x);
	tmp = 0.0;
	if ((y - z) <= -500.0)
		tmp = t_1;
	elseif ((y - z) <= 5e-20)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -500.0], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 5e-20], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -500 or 4.9999999999999999e-20 < (-.f64 y z)

   1. Initial program 100.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{y \cdot y - z \cdot z}{\color{blue}{y + z}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y + z}{y \cdot y - z \cdot z}\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y + z}}{y \cdot y - z \cdot z}\right)\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{\color{blue}{\frac{y \cdot y - z \cdot z}{y + z}}}\right)\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{y - \color{blue}{z}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]
   5. Step-by-step derivation

      1. div-sub N/A

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

      2. associate-+r- N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{t}{\frac{1}{y - z}}\right), \color{blue}{\left(\frac{x}{\frac{1}{y - z}}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{t}{\frac{1}{y - z}}\right)\right), \left(\frac{\color{blue}{x}}{\frac{1}{y - z}}\right)\right) \]

      5. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{t}{1} \cdot \left(y - z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      6. /-rgt-identity N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(t \cdot \left(y - z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \left(y - z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      9. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \left(x \cdot \color{blue}{\frac{1}{\frac{1}{y - z}}}\right)\right) \]

      10. remove-double-div N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \left(x \cdot \left(y - \color{blue}{z}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \mathsf{*.f64}\left(x, \color{blue}{\left(y - z\right)}\right)\right) \]

      12. --lowering--.f64 95.9%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(t \cdot \left(y - z\right)\right)}, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \mathsf{*.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(y, z\right)\right)\right) \]

      2. --lowering--.f64 95.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right)\right) \]

   9. Simplified 95.5%

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

       1. distribute-rgt-out-- N/A

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

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(t - x\right)}\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{t} - x\right)\right) \]

       4. --lowering--.f64 99.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   11. Applied egg-rr 99.6%

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

   if -500 < (-.f64 y z) < 4.9999999999999999e-20

   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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 99.4%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, t\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 89.7%

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

Alternative 5: 55.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -2 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y - z \leq 10^{-92}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= (- y z) -2e-33) t_1 (if (<= (- y z) 1e-92) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -2e-33) {
		tmp = t_1;
	} else if ((y - z) <= 1e-92) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if ((y - z) <= (-2d-33)) then
        tmp = t_1
    else if ((y - z) <= 1d-92) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -2e-33) {
		tmp = t_1;
	} else if ((y - z) <= 1e-92) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if (y - z) <= -2e-33:
		tmp = t_1
	elif (y - z) <= 1e-92:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (Float64(y - z) <= -2e-33)
		tmp = t_1;
	elseif (Float64(y - z) <= 1e-92)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if ((y - z) <= -2e-33)
		tmp = t_1;
	elseif ((y - z) <= 1e-92)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -2e-33], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 1e-92], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -2.0000000000000001e-33 or 9.99999999999999988e-93 < (-.f64 y z)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 59.2%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 59.2%

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

   if -2.0000000000000001e-33 < (-.f64 y z) < 9.99999999999999988e-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 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 86.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 86.3%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(x \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{x}\right)\right) \]

      2. *-lowering-*.f64 86.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]

   8. Simplified 86.3%

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

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   10. Step-by-step derivation

   11. Simplified 86.3%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -2 \cdot 10^{-33}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 10^{-92}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+65}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -2.3e-14) t_1 (if (<= z 8e+65) (+ x (* y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -2.3e-14) {
		tmp = t_1;
	} else if (z <= 8e+65) {
		tmp = x + (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 * (x - t)
    if (z <= (-2.3d-14)) then
        tmp = t_1
    else if (z <= 8d+65) then
        tmp = x + (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 * (x - t);
	double tmp;
	if (z <= -2.3e-14) {
		tmp = t_1;
	} else if (z <= 8e+65) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -2.3e-14:
		tmp = t_1
	elif z <= 8e+65:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -2.3e-14)
		tmp = t_1;
	elseif (z <= 8e+65)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -2.3e-14)
		tmp = t_1;
	elseif (z <= 8e+65)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e-14], t$95$1, If[LessEqual[z, 8e+65], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999998e-14 or 7.9999999999999999e65 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 87.3%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 87.3%

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

   if -2.29999999999999998e-14 < z < 7.9999999999999999e65

   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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 75.1%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, t\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 69.8%

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

Alternative 7: 67.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -2.3e-14) t_1 (if (<= z 1.6e+66) (* 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 <= -2.3e-14) {
		tmp = t_1;
	} else if (z <= 1.6e+66) {
		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 <= (-2.3d-14)) then
        tmp = t_1
    else if (z <= 1.6d+66) 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 <= -2.3e-14) {
		tmp = t_1;
	} else if (z <= 1.6e+66) {
		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 <= -2.3e-14:
		tmp = t_1
	elif z <= 1.6e+66:
		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 <= -2.3e-14)
		tmp = t_1;
	elseif (z <= 1.6e+66)
		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 <= -2.3e-14)
		tmp = t_1;
	elseif (z <= 1.6e+66)
		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, -2.3e-14], t$95$1, If[LessEqual[z, 1.6e+66], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999998e-14 or 1.6e66 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \left(t - x\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 87.3%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 87.3%

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

   if -2.29999999999999998e-14 < z < 1.6e66

   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

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 62.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 62.8%

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

Alternative 8: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -8 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -8e-60) t_1 (if (<= t 8.8e-76) (* x (- z y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -8e-60) {
		tmp = t_1;
	} else if (t <= 8.8e-76) {
		tmp = x * (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-8d-60)) then
        tmp = t_1
    else if (t <= 8.8d-76) then
        tmp = x * (z - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -8e-60) {
		tmp = t_1;
	} else if (t <= 8.8e-76) {
		tmp = x * (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -8e-60:
		tmp = t_1
	elif t <= 8.8e-76:
		tmp = x * (z - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -8e-60)
		tmp = t_1;
	elseif (t <= 8.8e-76)
		tmp = Float64(x * Float64(z - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -8e-60)
		tmp = t_1;
	elseif (t <= 8.8e-76)
		tmp = x * (z - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -8e-60], t$95$1, If[LessEqual[t, 8.8e-76], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.9999999999999998e-60 or 8.79999999999999997e-76 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 75.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 75.5%

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

   if -7.9999999999999998e-60 < t < 8.79999999999999997e-76

   1. Initial program 100.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{y \cdot y - z \cdot z}{\color{blue}{y + z}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y + z}{y \cdot y - z \cdot z}\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y + z}}{y \cdot y - z \cdot z}\right)\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{\color{blue}{\frac{y \cdot y - z \cdot z}{y + z}}}\right)\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{y - \color{blue}{z}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]
   5. Step-by-step derivation

      1. div-sub N/A

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

      2. associate-+r- N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{t}{\frac{1}{y - z}}\right), \color{blue}{\left(\frac{x}{\frac{1}{y - z}}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{t}{\frac{1}{y - z}}\right)\right), \left(\frac{\color{blue}{x}}{\frac{1}{y - z}}\right)\right) \]

      5. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{t}{1} \cdot \left(y - z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      6. /-rgt-identity N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(t \cdot \left(y - z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \left(y - z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \left(\frac{x}{\frac{1}{y - z}}\right)\right) \]

      9. div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \left(x \cdot \color{blue}{\frac{1}{\frac{1}{y - z}}}\right)\right) \]

      10. remove-double-div N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \left(x \cdot \left(y - \color{blue}{z}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \mathsf{*.f64}\left(x, \color{blue}{\left(y - z\right)}\right)\right) \]

      12. --lowering--.f64 100.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right)\right), \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(t \cdot \left(y - z\right)\right)}, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(y - z\right)\right), \mathsf{*.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(y, z\right)\right)\right) \]

      2. --lowering--.f64 73.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right)\right) \]

   9. Simplified 73.9%

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

   10. Taylor expanded in t around 0

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

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(x \cdot \left(y - z\right)\right) \]

       2. distribute-rgt-neg-in N/A

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

       3. mul-1-neg N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

       6. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\left(y - z\right)}\right)\right) \]

       7. associate-+l- N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - y\right) + \color{blue}{z}\right)\right) \]

       8. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(y\right)\right) + z\right)\right) \]

       9. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

       10. sub-neg N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(z - \color{blue}{y}\right)\right) \]

       11. --lowering--.f64 59.0%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right) \]

   12. Simplified 59.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-60}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-37}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e-37) (* y t) (if (<= y 5.5e-91) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e-37) {
		tmp = y * t;
	} else if (y <= 5.5e-91) {
		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 <= (-6.8d-37)) then
        tmp = y * t
    else if (y <= 5.5d-91) 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 <= -6.8e-37) {
		tmp = y * t;
	} else if (y <= 5.5e-91) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e-37:
		tmp = y * t
	elif y <= 5.5e-91:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e-37)
		tmp = Float64(y * t);
	elseif (y <= 5.5e-91)
		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 <= -6.8e-37)
		tmp = y * t;
	elseif (y <= 5.5e-91)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e-37], N[(y * t), $MachinePrecision], If[LessEqual[y, 5.5e-91], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.80000000000000037e-37 or 5.49999999999999965e-91 < 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

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 67.2%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 67.2%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{t}\right) \]
   7. Step-by-step derivation

   8. Simplified 42.2%

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

   if -6.80000000000000037e-37 < y < 5.49999999999999965e-91

   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

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

      11. --lowering--.f64 68.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 68.3%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(x \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{x}\right)\right) \]

      2. *-lowering-*.f64 68.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]

   8. Simplified 68.3%

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

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   10. Step-by-step derivation

   11. Simplified 40.2%

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

Alternative 10: 17.7% 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 0

   \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(x \cdot \left(y - z\right)\right)\right)}\right) \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(x \cdot \left(y - z\right)\right)\right)\right) \]

   2. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

   3. mul-1-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(x \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

   5. mul-1-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

   8. distribute-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

   9. unsub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

   10. remove-double-neg N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \left(z - y\right)\right)\right) \]

   11. --lowering--.f64 53.8%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

5. Simplified 53.8%

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

6. Taylor expanded in z around inf

   \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(x \cdot z\right)}\right) \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{x}\right)\right) \]

   2. *-lowering-*.f64 38.4%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]

8. Simplified 38.4%

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

9. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
10. Step-by-step derivation

11. Simplified 19.1%

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

Developer Target 1: 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 2024160 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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