Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.3s

Alternatives: 11

Speedup: 1.0×

• 34.8% 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: 46.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-180}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 17000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= x -2.9e-46)
     (fma x z x)
     (if (<= x -6.6e-307)
       t_1
       (if (<= x 6.8e-180) (* y t) (if (<= x 17000000.0) t_1 (fma x z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (x <= -2.9e-46) {
		tmp = fma(x, z, x);
	} else if (x <= -6.6e-307) {
		tmp = t_1;
	} else if (x <= 6.8e-180) {
		tmp = y * t;
	} else if (x <= 17000000.0) {
		tmp = t_1;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (x <= -2.9e-46)
		tmp = fma(x, z, x);
	elseif (x <= -6.6e-307)
		tmp = t_1;
	elseif (x <= 6.8e-180)
		tmp = Float64(y * t);
	elseif (x <= 17000000.0)
		tmp = t_1;
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[x, -2.9e-46], N[(x * z + x), $MachinePrecision], If[LessEqual[x, -6.6e-307], t$95$1, If[LessEqual[x, 6.8e-180], N[(y * t), $MachinePrecision], If[LessEqual[x, 17000000.0], t$95$1, N[(x * z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.90000000000000005e-46 or 1.7e7 < 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 96.6

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

   4. Applied rewrites 96.6%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 84.0

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

   7. Applied rewrites 84.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 53.9%

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

   if -2.90000000000000005e-46 < x < -6.59999999999999999e-307 or 6.79999999999999963e-180 < x < 1.7e7

   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 62.8

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

   5. Applied rewrites 62.8%

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

   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 52.8%

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

   if -6.59999999999999999e-307 < x < 6.79999999999999963e-180

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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 64.2

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

   5. Applied rewrites 64.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 58.1%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-307}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-180}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 17000000:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(y, t - x, x\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+66}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.3e+16)
     t_1
     (if (<= z 1.6e-11)
       (fma y (- t x) x)
       (if (<= z 2.75e+66) (* (- y z) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.3e+16) {
		tmp = t_1;
	} else if (z <= 1.6e-11) {
		tmp = fma(y, (t - x), x);
	} else if (z <= 2.75e+66) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.3e+16)
		tmp = t_1;
	elseif (z <= 1.6e-11)
		tmp = fma(y, Float64(t - x), x);
	elseif (z <= 2.75e+66)
		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[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+16], t$95$1, If[LessEqual[z, 1.6e-11], N[(y * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.75e+66], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e16 or 2.75e66 < 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 83.6

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

   5. Applied rewrites 83.6%

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

   if -1.3e16 < z < 1.59999999999999997e-11

   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 89.8

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

   5. Applied rewrites 89.8%

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

   if 1.59999999999999997e-11 < z < 2.75e66

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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 79.5

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

   5. Applied rewrites 79.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(y, t - x, x\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+66}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq 22000000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+171}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e-44)
   (fma x z x)
   (if (<= x 22000000.0)
     (* (- y z) t)
     (if (<= x 2.6e+171) (* y (- t x)) (fma x z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e-44) {
		tmp = fma(x, z, x);
	} else if (x <= 22000000.0) {
		tmp = (y - z) * t;
	} else if (x <= 2.6e+171) {
		tmp = y * (t - x);
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e-44)
		tmp = fma(x, z, x);
	elseif (x <= 22000000.0)
		tmp = Float64(Float64(y - z) * t);
	elseif (x <= 2.6e+171)
		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, -1.55e-44], N[(x * z + x), $MachinePrecision], If[LessEqual[x, 22000000.0], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, 2.6e+171], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.54999999999999992e-44 or 2.6e171 < 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 97.6

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

   4. Applied rewrites 97.6%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 89.7

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

   7. Applied rewrites 89.7%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 61.0%

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

   if -1.54999999999999992e-44 < x < 2.2e7

   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 78.9

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

   5. Applied rewrites 78.9%

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

   if 2.2e7 < x < 2.6e171

   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 56.5

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

   5. Applied rewrites 56.5%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq 22000000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+171}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, t - x, x\right)\\ \mathbf{if}\;y \leq -6800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(z, x - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma y (- t x) x)))
   (if (<= y -6800000000000.0)
     t_1
     (if (<= y 1.95e-44) (fma z (- x t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(y, (t - x), x);
	double tmp;
	if (y <= -6800000000000.0) {
		tmp = t_1;
	} else if (y <= 1.95e-44) {
		tmp = fma(z, (x - t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(y, Float64(t - x), x)
	tmp = 0.0
	if (y <= -6800000000000.0)
		tmp = t_1;
	elseif (y <= 1.95e-44)
		tmp = fma(z, Float64(x - t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -6800000000000.0], t$95$1, If[LessEqual[y, 1.95e-44], N[(z * N[(x - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e12 or 1.9500000000000001e-44 < 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 80.1

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

   5. Applied rewrites 80.1%

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

   if -6.8e12 < y < 1.9500000000000001e-44

   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. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 93.0

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

   5. Applied rewrites 93.0%

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

Alternative 6: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, z - y, x\right)\\ \mathbf{if}\;x \leq -4.38 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 35000000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (- z y) x)))
   (if (<= x -4.38e-59) t_1 (if (<= x 35000000.0) (* (- y z) 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 <= -4.38e-59) {
		tmp = t_1;
	} else if (x <= 35000000.0) {
		tmp = (y - z) * 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 <= -4.38e-59)
		tmp = t_1;
	elseif (x <= 35000000.0)
		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[(x * N[(z - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -4.38e-59], t$95$1, If[LessEqual[x, 35000000.0], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.38000000000000004e-59 or 3.5e7 < 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 83.6

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

   5. Applied rewrites 83.6%

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

   if -4.38000000000000004e-59 < x < 3.5e7

   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 80.5

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

   5. Applied rewrites 80.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.38 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(x, z - y, x\right)\\ \mathbf{elif}\;x \leq 35000000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z - y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -6800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -6800000000000.0) t_1 (if (<= y 1.95e-44) (* 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 <= -6800000000000.0) {
		tmp = t_1;
	} else if (y <= 1.95e-44) {
		tmp = 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 <= (-6800000000000.0d0)) then
        tmp = t_1
    else if (y <= 1.95d-44) then
        tmp = 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 <= -6800000000000.0) {
		tmp = t_1;
	} else if (y <= 1.95e-44) {
		tmp = 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 <= -6800000000000.0:
		tmp = t_1
	elif y <= 1.95e-44:
		tmp = 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 <= -6800000000000.0)
		tmp = t_1;
	elseif (y <= 1.95e-44)
		tmp = 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 <= -6800000000000.0)
		tmp = t_1;
	elseif (y <= 1.95e-44)
		tmp = 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, -6800000000000.0], t$95$1, If[LessEqual[y, 1.95e-44], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e12 or 1.9500000000000001e-44 < 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 78.1

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

   5. Applied rewrites 78.1%

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

   if -6.8e12 < y < 1.9500000000000001e-44

   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 70.0

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

   5. Applied rewrites 70.0%

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

Alternative 8: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq 45000000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e-44)
   (fma x z x)
   (if (<= x 45000000.0) (* (- y z) t) (fma x z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e-44) {
		tmp = fma(x, z, x);
	} else if (x <= 45000000.0) {
		tmp = (y - z) * t;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e-44)
		tmp = fma(x, z, x);
	elseif (x <= 45000000.0)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.55e-44], N[(x * z + x), $MachinePrecision], If[LessEqual[x, 45000000.0], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.54999999999999992e-44 or 4.5e7 < 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 96.6

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

   4. Applied rewrites 96.6%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 84.6

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

   7. Applied rewrites 84.6%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 54.4%

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

   if -1.54999999999999992e-44 < x < 4.5e7

   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 79.1

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

   5. Applied rewrites 79.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq 45000000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+71}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+71) (* y t) (if (<= y 9.2e-28) (fma x z x) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+71) {
		tmp = y * t;
	} else if (y <= 9.2e-28) {
		tmp = fma(x, z, x);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+71)
		tmp = Float64(y * t);
	elseif (y <= 9.2e-28)
		tmp = fma(x, z, x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+71], N[(y * t), $MachinePrecision], If[LessEqual[y, 9.2e-28], N[(x * z + x), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999995e71 or 9.19999999999999942e-28 < 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 80.8

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 44.7%

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

   if -1.04999999999999995e71 < y < 9.19999999999999942e-28

   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 99.3

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 53.2

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

   7. Applied rewrites 53.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 48.8%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+71}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+103}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+66}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3e+103) (* x z) (if (<= z 2.75e+66) (* y t) (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3e+103) {
		tmp = x * z;
	} else if (z <= 2.75e+66) {
		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 <= (-3d+103)) then
        tmp = x * z
    else if (z <= 2.75d+66) 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 <= -3e+103) {
		tmp = x * z;
	} else if (z <= 2.75e+66) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3e+103:
		tmp = x * z
	elif z <= 2.75e+66:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3e+103)
		tmp = Float64(x * z);
	elseif (z <= 2.75e+66)
		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 <= -3e+103)
		tmp = x * z;
	elseif (z <= 2.75e+66)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3e+103], N[(x * z), $MachinePrecision], If[LessEqual[z, 2.75e+66], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3e103 or 2.75e66 < 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 87.6

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

   5. Applied rewrites 87.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 45.0%

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

   if -3e103 < z < 2.75e66

   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 79.6

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

   5. Applied rewrites 79.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 35.5%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+103}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+66}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 22.7% 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 47.6

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

5. Applied rewrites 47.6%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 21.0%

   \[\leadsto x \cdot \color{blue}{z} \]
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 2024226 
(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))))