Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.0s

Alternatives: 9

Speedup: 1.0×

• 34.7% 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: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1600000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+43}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1600000000.0) t_1 (if (<= y 2.6e+43) (+ x (* z (- x t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1600000000.0) {
		tmp = t_1;
	} else if (y <= 2.6e+43) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-1600000000.0d0)) then
        tmp = t_1
    else if (y <= 2.6d+43) then
        tmp = x + (z * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1600000000.0) {
		tmp = t_1;
	} else if (y <= 2.6e+43) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -1600000000.0:
		tmp = t_1
	elif y <= 2.6e+43:
		tmp = x + (z * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -1600000000.0)
		tmp = t_1;
	elseif (y <= 2.6e+43)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -1600000000.0)
		tmp = t_1;
	elseif (y <= 2.6e+43)
		tmp = x + (z * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1600000000.0], t$95$1, If[LessEqual[y, 2.6e+43], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e9 or 2.60000000000000021e43 < 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 82.8%

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

   5. Simplified 82.8%

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

   if -1.6e9 < y < 2.60000000000000021e43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. --lowering--.f64 88.2%

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

   5. Simplified 88.2%

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

Alternative 3: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -5.3 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(1 + \left(z - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -5.3e+39) t_1 (if (<= t 5.2e+96) (* x (+ 1.0 (- 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 <= -5.3e+39) {
		tmp = t_1;
	} else if (t <= 5.2e+96) {
		tmp = x * (1.0 + (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 <= (-5.3d+39)) then
        tmp = t_1
    else if (t <= 5.2d+96) then
        tmp = x * (1.0d0 + (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 <= -5.3e+39) {
		tmp = t_1;
	} else if (t <= 5.2e+96) {
		tmp = x * (1.0 + (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -5.3e+39:
		tmp = t_1
	elif t <= 5.2e+96:
		tmp = x * (1.0 + (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 <= -5.3e+39)
		tmp = t_1;
	elseif (t <= 5.2e+96)
		tmp = Float64(x * Float64(1.0 + 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 <= -5.3e+39)
		tmp = t_1;
	elseif (t <= 5.2e+96)
		tmp = x * (1.0 + (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, -5.3e+39], t$95$1, If[LessEqual[t, 5.2e+96], N[(x * N[(1.0 + N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.29999999999999979e39 or 5.2e96 < 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 88.3%

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

   5. Simplified 88.3%

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

   if -5.29999999999999979e39 < t < 5.2e96

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

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

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

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

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. unsub-neg N/A

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

      8. remove-double-neg N/A

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

      9. --lowering--.f64 78.1%

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

   5. Simplified 78.1%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+39}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(1 + \left(z - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -3.9e-17) t_1 (if (<= z 5.2e+28) (* y (- t x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -3.9e-17) {
		tmp = t_1;
	} else if (z <= 5.2e+28) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-3.9d-17)) then
        tmp = t_1
    else if (z <= 5.2d+28) then
        tmp = y * (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -3.9e-17) {
		tmp = t_1;
	} else if (z <= 5.2e+28) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -3.9e-17:
		tmp = t_1
	elif z <= 5.2e+28:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -3.9e-17)
		tmp = t_1;
	elseif (z <= 5.2e+28)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -3.9e-17)
		tmp = t_1;
	elseif (z <= 5.2e+28)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e-17], t$95$1, If[LessEqual[z, 5.2e+28], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999989e-17 or 5.2000000000000004e28 < 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 81.5%

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

   5. Simplified 81.5%

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

   if -3.89999999999999989e-17 < z < 5.2000000000000004e28

   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 71.2%

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

   5. Simplified 71.2%

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

Alternative 5: 62.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -3.25 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 530000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -3.25e+39) t_1 (if (<= t 530000000.0) (* x (- 1.0 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -3.25e+39) {
		tmp = t_1;
	} else if (t <= 530000000.0) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-3.25d+39)) then
        tmp = t_1
    else if (t <= 530000000.0d0) then
        tmp = x * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -3.25e+39) {
		tmp = t_1;
	} else if (t <= 530000000.0) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -3.25e+39:
		tmp = t_1
	elif t <= 530000000.0:
		tmp = x * (1.0 - 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 <= -3.25e+39)
		tmp = t_1;
	elseif (t <= 530000000.0)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -3.25e+39)
		tmp = t_1;
	elseif (t <= 530000000.0)
		tmp = x * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -3.25e+39], t$95$1, If[LessEqual[t, 530000000.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2500000000000001e39 or 5.3e8 < 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 83.4%

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

   5. Simplified 83.4%

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

   if -3.2500000000000001e39 < t < 5.3e8

   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. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 65.9%

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

   7. Simplified 65.9%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{1}{y}}} \]

   8. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto x \cdot \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right) \]

      2. sub-neg N/A

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

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

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

      4. --lowering--.f64 55.2%

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

   10. Simplified 55.2%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.25 \cdot 10^{+39}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 530000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-158}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1e-15) t_1 (if (<= t 9.2e-158) (* x z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1e-15) {
		tmp = t_1;
	} else if (t <= 9.2e-158) {
		tmp = x * z;
	} 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 <= (-1d-15)) then
        tmp = t_1
    else if (t <= 9.2d-158) then
        tmp = x * z
    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 <= -1e-15) {
		tmp = t_1;
	} else if (t <= 9.2e-158) {
		tmp = x * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1e-15:
		tmp = t_1
	elif t <= 9.2e-158:
		tmp = x * z
	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 <= -1e-15)
		tmp = t_1;
	elseif (t <= 9.2e-158)
		tmp = Float64(x * z);
	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 <= -1e-15)
		tmp = t_1;
	elseif (t <= 9.2e-158)
		tmp = x * z;
	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, -1e-15], t$95$1, If[LessEqual[t, 9.2e-158], N[(x * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0000000000000001e-15 or 9.1999999999999995e-158 < 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 69.4%

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

   5. Simplified 69.4%

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

   if -1.0000000000000001e-15 < t < 9.1999999999999995e-158

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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 43.2%

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

   5. Simplified 43.2%

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

   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 36.3%

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

   8. Simplified 36.3%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-158}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 62000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.2e-13) (* x z) (if (<= z 62000000000.0) (* y t) (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e-13) {
		tmp = x * z;
	} else if (z <= 62000000000.0) {
		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 <= (-6.2d-13)) then
        tmp = x * z
    else if (z <= 62000000000.0d0) 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 <= -6.2e-13) {
		tmp = x * z;
	} else if (z <= 62000000000.0) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.2e-13:
		tmp = x * z
	elif z <= 62000000000.0:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.2e-13)
		tmp = Float64(x * z);
	elseif (z <= 62000000000.0)
		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 <= -6.2e-13)
		tmp = x * z;
	elseif (z <= 62000000000.0)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.2e-13], N[(x * z), $MachinePrecision], If[LessEqual[z, 62000000000.0], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999998e-13 or 6.2e10 < 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 79.9%

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

   5. Simplified 79.9%

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

   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 42.2%

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

   8. Simplified 42.2%

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

   if -6.1999999999999998e-13 < z < 6.2e10

   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 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 39.3%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 62000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-68}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e-68) (* y t) (if (<= y 2.8e-64) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-68) {
		tmp = y * t;
	} else if (y <= 2.8e-64) {
		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 <= (-3d-68)) then
        tmp = y * t
    else if (y <= 2.8d-64) 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 <= -3e-68) {
		tmp = y * t;
	} else if (y <= 2.8e-64) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e-68:
		tmp = y * t
	elif y <= 2.8e-64:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e-68)
		tmp = Float64(y * t);
	elseif (y <= 2.8e-64)
		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 <= -3e-68)
		tmp = y * t;
	elseif (y <= 2.8e-64)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e-68], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.8e-64], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3e-68 or 2.80000000000000004e-64 < y

   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 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 37.1%

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

   if -3e-68 < y < 2.80000000000000004e-64

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. --lowering--.f64 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 33.4%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-68}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 18.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0

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

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

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

   2. mul-1-neg N/A

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

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

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

   4. mul-1-neg N/A

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

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

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

   6. mul-1-neg N/A

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

   7. sub-neg N/A

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

   8. +-commutative N/A

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

   9. distribute-neg-in N/A

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

   10. unsub-neg N/A

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

   11. remove-double-neg N/A

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

   12. --lowering--.f64 54.9%

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

5. Simplified 54.9%

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

6. Taylor expanded in z around 0

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

8. Simplified 13.5%

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

Developer Target 1: 96.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024158 
(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))))