Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.2s

Alternatives: 12

Speedup: 1.0×

• 35.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 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: 49.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-204}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -3.5e+132)
     (* y t)
     (if (<= y -3.9e+49)
       (* y (- x))
       (if (<= y -5.5e-7)
         t_1
         (if (<= y 1.32e-204)
           (fma x z x)
           (if (<= y 2.1e-137)
             t_1
             (if (<= y 1.22e-23) (fma x z x) (* y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -3.5e+132) {
		tmp = y * t;
	} else if (y <= -3.9e+49) {
		tmp = y * -x;
	} else if (y <= -5.5e-7) {
		tmp = t_1;
	} else if (y <= 1.32e-204) {
		tmp = fma(x, z, x);
	} else if (y <= 2.1e-137) {
		tmp = t_1;
	} else if (y <= 1.22e-23) {
		tmp = fma(x, z, x);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -3.5e+132)
		tmp = Float64(y * t);
	elseif (y <= -3.9e+49)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -5.5e-7)
		tmp = t_1;
	elseif (y <= 1.32e-204)
		tmp = fma(x, z, x);
	elseif (y <= 2.1e-137)
		tmp = t_1;
	elseif (y <= 1.22e-23)
		tmp = fma(x, z, x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -3.5e+132], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.9e+49], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -5.5e-7], t$95$1, If[LessEqual[y, 1.32e-204], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 2.1e-137], t$95$1, If[LessEqual[y, 1.22e-23], N[(x * z + x), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.5000000000000002e132 or 1.22000000000000007e-23 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 55.6%

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

   if -3.5000000000000002e132 < y < -3.9000000000000001e49

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 69.4

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

   7. Applied rewrites 69.4%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 49.2%

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

   if -3.9000000000000001e49 < y < -5.5000000000000003e-7 or 1.32e-204 < y < 2.09999999999999992e-137

   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

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 94.8

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

   5. Applied rewrites 94.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 87.3%

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

   if -5.5000000000000003e-7 < y < 1.32e-204 or 2.09999999999999992e-137 < y < 1.22000000000000007e-23

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 91.7

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

   7. Applied rewrites 91.7%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 64.6%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{z}, x\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 48.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+35}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-204}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -4.4e+35)
     (* y t)
     (if (<= y -5.5e-7)
       t_1
       (if (<= y 1.32e-204)
         (fma x z x)
         (if (<= y 2.1e-137) t_1 (if (<= y 1.22e-23) (fma x z x) (* y t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -4.4e+35) {
		tmp = y * t;
	} else if (y <= -5.5e-7) {
		tmp = t_1;
	} else if (y <= 1.32e-204) {
		tmp = fma(x, z, x);
	} else if (y <= 2.1e-137) {
		tmp = t_1;
	} else if (y <= 1.22e-23) {
		tmp = fma(x, z, x);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -4.4e+35)
		tmp = Float64(y * t);
	elseif (y <= -5.5e-7)
		tmp = t_1;
	elseif (y <= 1.32e-204)
		tmp = fma(x, z, x);
	elseif (y <= 2.1e-137)
		tmp = t_1;
	elseif (y <= 1.22e-23)
		tmp = fma(x, z, x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -4.4e+35], N[(y * t), $MachinePrecision], If[LessEqual[y, -5.5e-7], t$95$1, If[LessEqual[y, 1.32e-204], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 2.1e-137], t$95$1, If[LessEqual[y, 1.22e-23], N[(x * z + x), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3999999999999997e35 or 1.22000000000000007e-23 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 76.9

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

   5. Applied rewrites 76.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 50.6%

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

   if -4.3999999999999997e35 < y < -5.5000000000000003e-7 or 1.32e-204 < y < 2.09999999999999992e-137

   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

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 91.9%

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

   if -5.5000000000000003e-7 < y < 1.32e-204 or 2.09999999999999992e-137 < y < 1.22000000000000007e-23

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 91.7

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

   7. Applied rewrites 91.7%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 64.6%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{z}, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, z - y, x\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-164}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(z, -t, x\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (- z y) x)))
   (if (<= x -4.2e+48)
     t_1
     (if (<= x 2.8e-164)
       (* (- y z) t)
       (if (<= x 1.2e-91)
         (fma z (- t) x)
         (if (<= x 1.6e+107) (* z (- x t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, (z - y), x);
	double tmp;
	if (x <= -4.2e+48) {
		tmp = t_1;
	} else if (x <= 2.8e-164) {
		tmp = (y - z) * t;
	} else if (x <= 1.2e-91) {
		tmp = fma(z, -t, x);
	} else if (x <= 1.6e+107) {
		tmp = z * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, Float64(z - y), x)
	tmp = 0.0
	if (x <= -4.2e+48)
		tmp = t_1;
	elseif (x <= 2.8e-164)
		tmp = Float64(Float64(y - z) * t);
	elseif (x <= 1.2e-91)
		tmp = fma(z, Float64(-t), x);
	elseif (x <= 1.6e+107)
		tmp = Float64(z * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -4.2e+48], t$95$1, If[LessEqual[x, 2.8e-164], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, 1.2e-91], N[(z * (-t) + x), $MachinePrecision], If[LessEqual[x, 1.6e+107], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.1999999999999997e48 or 1.60000000000000015e107 < x

   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. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 88.2

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

   5. Applied rewrites 88.2%

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

   if -4.1999999999999997e48 < x < 2.8000000000000001e-164

   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. lower-*.f64 N/A

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

      2. lower--.f64 81.6

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

   5. Applied rewrites 81.6%

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

   if 2.8000000000000001e-164 < x < 1.20000000000000005e-91

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 79.6

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

   7. Applied rewrites 79.6%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 74.4%

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

   if 1.20000000000000005e-91 < x < 1.60000000000000015e107

   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

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 67.3

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

   5. Applied rewrites 67.3%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(x, z - y, x\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-164}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(z, -t, x\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z - y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.36 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(z, -t, x\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+57}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.36e+35)
     t_1
     (if (<= y 3.1e-24)
       (fma z (- t) x)
       (if (<= y 1.9e+57) (* (- y z) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1.36e+35) {
		tmp = t_1;
	} else if (y <= 3.1e-24) {
		tmp = fma(z, -t, x);
	} else if (y <= 1.9e+57) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -1.36e+35)
		tmp = t_1;
	elseif (y <= 3.1e-24)
		tmp = fma(z, Float64(-t), x);
	elseif (y <= 1.9e+57)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.36e+35], t$95$1, If[LessEqual[y, 3.1e-24], N[(z * (-t) + x), $MachinePrecision], If[LessEqual[y, 1.9e+57], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.36e35 or 1.8999999999999999e57 < 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. lower-*.f64 N/A

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

      2. lower--.f64 80.1

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

   5. Applied rewrites 80.1%

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

   if -1.36e35 < y < 3.1e-24

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 98.4

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

   4. Applied rewrites 98.4%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 92.9

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

   7. Applied rewrites 92.9%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 71.6%

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

   if 3.1e-24 < y < 1.8999999999999999e57

   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. lower-*.f64 N/A

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

      2. lower--.f64 79.3

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

   5. Applied rewrites 79.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(z, -t, x\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+57}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+107}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.45e+49)
   (fma x z x)
   (if (<= x 2.3e+107)
     (* (- y z) t)
     (if (<= x 6.2e+157) (* y (- t x)) (fma x z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e+49) {
		tmp = fma(x, z, x);
	} else if (x <= 2.3e+107) {
		tmp = (y - z) * t;
	} else if (x <= 6.2e+157) {
		tmp = y * (t - x);
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.45e+49)
		tmp = fma(x, z, x);
	elseif (x <= 2.3e+107)
		tmp = Float64(Float64(y - z) * t);
	elseif (x <= 6.2e+157)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.45e+49], N[(x * z + x), $MachinePrecision], If[LessEqual[x, 2.3e+107], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, 6.2e+157], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e49 or 6.1999999999999994e157 < x

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 93.8

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

   4. Applied rewrites 93.8%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 73.5

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

   7. Applied rewrites 73.5%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 69.8%

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

   if -1.45e49 < x < 2.3e107

   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. lower-*.f64 N/A

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

      2. lower--.f64 71.2

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

   5. Applied rewrites 71.2%

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

   if 2.3e107 < x < 6.1999999999999994e157

   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. lower-*.f64 N/A

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

      2. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+107}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(y, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.32e+20) t_1 (if (<= z 2.2e+51) (fma y (- t x) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.32e+20) {
		tmp = t_1;
	} else if (z <= 2.2e+51) {
		tmp = fma(y, (t - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.32e+20)
		tmp = t_1;
	elseif (z <= 2.2e+51)
		tmp = fma(y, Float64(t - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.32e+20], t$95$1, If[LessEqual[z, 2.2e+51], N[(y * N[(t - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32e20 or 2.19999999999999992e51 < 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

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if -1.32e20 < z < 2.19999999999999992e51

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 88.8

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

   5. Applied rewrites 88.8%

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

Alternative 8: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.32e+20) t_1 (if (<= z 2.2e+51) (* y (- t x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.32e+20) {
		tmp = t_1;
	} else if (z <= 2.2e+51) {
		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 <= (-1.32d+20)) then
        tmp = t_1
    else if (z <= 2.2d+51) 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 <= -1.32e+20) {
		tmp = t_1;
	} else if (z <= 2.2e+51) {
		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 <= -1.32e+20:
		tmp = t_1
	elif z <= 2.2e+51:
		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 <= -1.32e+20)
		tmp = t_1;
	elseif (z <= 2.2e+51)
		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 <= -1.32e+20)
		tmp = t_1;
	elseif (z <= 2.2e+51)
		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, -1.32e+20], t$95$1, If[LessEqual[z, 2.2e+51], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32e20 or 2.19999999999999992e51 < 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

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if -1.32e20 < z < 2.19999999999999992e51

   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. lower-*.f64 N/A

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

      2. lower--.f64 60.0

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

   5. Applied rewrites 60.0%

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

Alternative 9: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-110}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -9.5e-58) t_1 (if (<= t 1.12e-110) (fma x z x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -9.5e-58) {
		tmp = t_1;
	} else if (t <= 1.12e-110) {
		tmp = fma(x, z, 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 (t <= -9.5e-58)
		tmp = t_1;
	elseif (t <= 1.12e-110)
		tmp = fma(x, z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -9.5e-58], t$95$1, If[LessEqual[t, 1.12e-110], N[(x * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4999999999999994e-58 or 1.11999999999999998e-110 < 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. lower-*.f64 N/A

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

      2. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   if -9.4999999999999994e-58 < t < 1.11999999999999998e-110

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 66.0

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

   7. Applied rewrites 66.0%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 61.6%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{z}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-58}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-110}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+118}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e+118) (* y t) (if (<= y 1.22e-23) (fma x z x) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+118) {
		tmp = y * t;
	} else if (y <= 1.22e-23) {
		tmp = fma(x, z, x);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e+118)
		tmp = Float64(y * t);
	elseif (y <= 1.22e-23)
		tmp = fma(x, z, x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e+118], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.22e-23], N[(x * z + x), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000016e118 or 1.22000000000000007e-23 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 78.0

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

   5. Applied rewrites 78.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 54.6%

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

   if -2.60000000000000016e118 < y < 1.22000000000000007e-23

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 98.6

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 87.2

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

   7. Applied rewrites 87.2%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 53.3%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{z}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 38.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -750000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+51}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -750000000000.0) (* x z) (if (<= z 2.45e+51) (* y t) (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -750000000000.0) {
		tmp = x * z;
	} else if (z <= 2.45e+51) {
		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 <= (-750000000000.0d0)) then
        tmp = x * z
    else if (z <= 2.45d+51) 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 <= -750000000000.0) {
		tmp = x * z;
	} else if (z <= 2.45e+51) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -750000000000.0:
		tmp = x * z
	elif z <= 2.45e+51:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -750000000000.0)
		tmp = Float64(x * z);
	elseif (z <= 2.45e+51)
		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 <= -750000000000.0)
		tmp = x * z;
	elseif (z <= 2.45e+51)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -750000000000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 2.45e+51], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e11 or 2.44999999999999992e51 < 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

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 84.3

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

   5. Applied rewrites 84.3%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 44.9%

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

   if -7.5e11 < z < 2.44999999999999992e51

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 88.6

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

   5. Applied rewrites 88.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 42.5%

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

Alternative 12: 22.2% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

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

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

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

   3. mul-1-neg N/A

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

   4. lower-*.f64 N/A

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

   5. mul-1-neg N/A

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

   6. sub-neg N/A

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

   7. +-commutative N/A

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

   8. distribute-neg-in N/A

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

   9. unsub-neg N/A

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

   10. remove-double-neg N/A

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

   11. lower--.f64 48.1

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

5. Applied rewrites 48.1%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 23.7%

   \[\leadsto x \cdot \color{blue}{z} \]
9. 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 2024223 
(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))))