Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 10

Speedup: 1.2×

• 33.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 49.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-x\right) \cdot y\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -19000000000:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x) y)))
   (if (<= y -8.2e+68)
     t_1
     (if (<= y -19000000000.0) (* t y) (if (<= y 1.8e+70) (fma x z x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x * y;
	double tmp;
	if (y <= -8.2e+68) {
		tmp = t_1;
	} else if (y <= -19000000000.0) {
		tmp = t * y;
	} else if (y <= 1.8e+70) {
		tmp = fma(x, z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) * y)
	tmp = 0.0
	if (y <= -8.2e+68)
		tmp = t_1;
	elseif (y <= -19000000000.0)
		tmp = Float64(t * y);
	elseif (y <= 1.8e+70)
		tmp = fma(x, z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) * y), $MachinePrecision]}, If[LessEqual[y, -8.2e+68], t$95$1, If[LessEqual[y, -19000000000.0], N[(t * y), $MachinePrecision], If[LessEqual[y, 1.8e+70], N[(x * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.1999999999999998e68 or 1.8e70 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(-1 \cdot x\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 55.8%

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

   if -8.1999999999999998e68 < y < -1.9e10

   1. Initial program 99.8%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.9

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 53.8%

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

   if -1.9e10 < y < 1.8e70

   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

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. lower-fma.f64 N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sign-sub-inv N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. mul-1-neg N/A

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

      13. distribute-lft-out-- N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. distribute-lft-neg-in N/A

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

      17. *-commutative N/A

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

      18. mul-1-neg N/A

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

      19. remove-double-neg N/A

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

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

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

      21. mul-1-neg N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 61.5

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

   5. Applied rewrites 61.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 55.3%

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

Alternative 3: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00385 \lor \neg \left(z \leq 4.3 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(x - t, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00385) (not (<= z 4.3e-5)))
   (fma (- x t) z x)
   (fma (- t x) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00385) || !(z <= 4.3e-5)) {
		tmp = fma((x - t), z, x);
	} else {
		tmp = fma((t - x), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00385) || !(z <= 4.3e-5))
		tmp = fma(Float64(x - t), z, x);
	else
		tmp = fma(Float64(t - x), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00385], N[Not[LessEqual[z, 4.3e-5]], $MachinePrecision]], N[(N[(x - t), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0038500000000000001 or 4.3000000000000002e-5 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. *-lft-identity N/A

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

      7. metadata-eval N/A

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

      8. fp-cancel-sign-sub-inv N/A

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

      9. +-commutative N/A

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

      10. *-lft-identity N/A

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

      11. fp-cancel-sign-sub-inv N/A

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

      12. metadata-eval N/A

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

      13. distribute-lft-out-- N/A

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

      14. distribute-lft-neg-in N/A

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

      15. metadata-eval N/A

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

      16. distribute-lft-out-- N/A

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

      17. *-lft-identity N/A

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

      18. *-lft-identity N/A

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

      19. lower--.f64 76.6

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

   5. Applied rewrites 76.6%

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

   if -0.0038500000000000001 < z < 4.3000000000000002e-5

   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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 95.0

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

   5. Applied rewrites 95.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00385 \lor \neg \left(z \leq 4.3 \cdot 10^{-5}\right):\\ \;\;\;\;\mathsf{fma}\left(x - t, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{+46} \lor \neg \left(z \leq 540000000\right):\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.9e+46) (not (<= z 540000000.0)))
   (* (- x t) z)
   (fma (- t x) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.9e+46) || !(z <= 540000000.0)) {
		tmp = (x - t) * z;
	} else {
		tmp = fma((t - x), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.9e+46) || !(z <= 540000000.0))
		tmp = Float64(Float64(x - t) * z);
	else
		tmp = fma(Float64(t - x), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.9e+46], N[Not[LessEqual[z, 540000000.0]], $MachinePrecision]], N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.90000000000000018e46 or 5.4e8 < z

   1. Initial program 100.0%

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

      1. 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. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. distribute-lft-out-- N/A

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

      6. mul-1-neg N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. fp-cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. lower--.f64 79.1

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

   7. Applied rewrites 79.1%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 79.1%

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

   if -6.90000000000000018e46 < z < 5.4e8

   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. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 90.7

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

   5. Applied rewrites 90.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.9 \cdot 10^{+46} \lor \neg \left(z \leq 540000000\right):\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -150000 \lor \neg \left(y \leq 750000\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -150000.0) (not (<= y 750000.0)))
   (* (- t x) y)
   (fma (- t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -150000.0) || !(y <= 750000.0)) {
		tmp = (t - x) * y;
	} else {
		tmp = fma(-t, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -150000.0) || !(y <= 750000.0))
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = fma(Float64(-t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -150000.0], N[Not[LessEqual[y, 750000.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], N[((-t) * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e5 or 7.5e5 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 78.5

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

   5. Applied rewrites 78.5%

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

   if -1.5e5 < y < 7.5e5

   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. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. distribute-lft-out-- N/A

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

      6. mul-1-neg N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. fp-cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. lower--.f64 84.0

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

   7. Applied rewrites 84.0%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 62.4%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -150000 \lor \neg \left(y \leq 750000\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8500000 \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8500000.0) (not (<= z 0.00018)))
   (* (- x t) z)
   (fma (- y) x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8500000.0) || !(z <= 0.00018)) {
		tmp = (x - t) * z;
	} else {
		tmp = fma(-y, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8500000.0) || !(z <= 0.00018))
		tmp = Float64(Float64(x - t) * z);
	else
		tmp = fma(Float64(-y), x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8500000.0], N[Not[LessEqual[z, 0.00018]], $MachinePrecision]], N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision], N[((-y) * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e6 or 1.80000000000000011e-4 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. lower-fma.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. distribute-lft-out-- N/A

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

      6. mul-1-neg N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. metadata-eval N/A

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

      9. *-lft-identity N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. fp-cancel-sign-sub-inv N/A

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

      13. metadata-eval N/A

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

      14. *-lft-identity N/A

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

      15. lower--.f64 76.6

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

   7. Applied rewrites 76.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 76.2%

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

   if -8.5e6 < z < 1.80000000000000011e-4

   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

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. lower-fma.f64 N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sign-sub-inv N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. mul-1-neg N/A

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

      13. distribute-lft-out-- N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. distribute-lft-neg-in N/A

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

      17. *-commutative N/A

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

      18. mul-1-neg N/A

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

      19. remove-double-neg N/A

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

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

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

      21. mul-1-neg N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 63.7

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

   5. Applied rewrites 63.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot y, x, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 62.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8500000 \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -145000 \lor \neg \left(y \leq 4.5 \cdot 10^{+22}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -145000.0) (not (<= y 4.5e+22))) (* (- t x) y) (fma x z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -145000.0) || !(y <= 4.5e+22)) {
		tmp = (t - x) * y;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -145000.0) || !(y <= 4.5e+22))
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -145000.0], N[Not[LessEqual[y, 4.5e+22]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], N[(x * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -145000 or 4.4999999999999998e22 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.6

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

   5. Applied rewrites 79.6%

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

   if -145000 < y < 4.4999999999999998e22

   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

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. lower-fma.f64 N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sign-sub-inv N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. mul-1-neg N/A

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

      13. distribute-lft-out-- N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. distribute-lft-neg-in N/A

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

      17. *-commutative N/A

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

      18. mul-1-neg N/A

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

      19. remove-double-neg N/A

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

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

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

      21. mul-1-neg N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 60.8

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 57.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -145000 \lor \neg \left(y \leq 4.5 \cdot 10^{+22}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -19000000000 \lor \neg \left(y \leq 3.6 \cdot 10^{+175}\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -19000000000.0) (not (<= y 3.6e+175))) (* t y) (fma x z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -19000000000.0) || !(y <= 3.6e+175)) {
		tmp = t * y;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -19000000000.0) || !(y <= 3.6e+175))
		tmp = Float64(t * y);
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -19000000000.0], N[Not[LessEqual[y, 3.6e+175]], $MachinePrecision]], N[(t * y), $MachinePrecision], N[(x * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e10 or 3.60000000000000034e175 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 84.7

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

   5. Applied rewrites 84.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 40.5%

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

   if -1.9e10 < y < 3.60000000000000034e175

   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

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. lower-fma.f64 N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sign-sub-inv N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. mul-1-neg N/A

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

      13. distribute-lft-out-- N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. distribute-lft-neg-in N/A

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

      17. *-commutative N/A

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

      18. mul-1-neg N/A

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

      19. remove-double-neg N/A

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

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

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

      21. mul-1-neg N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 63.0

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

   5. Applied rewrites 63.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 52.3%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -19000000000 \lor \neg \left(y \leq 3.6 \cdot 10^{+175}\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+64} \lor \neg \left(z \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e+64) (not (<= z 5e+19))) (* x z) (* t y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+64) || !(z <= 5e+19)) {
		tmp = x * z;
	} else {
		tmp = t * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.2d+64)) .or. (.not. (z <= 5d+19))) then
        tmp = x * z
    else
        tmp = t * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+64) || !(z <= 5e+19)) {
		tmp = x * z;
	} else {
		tmp = t * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e+64) or not (z <= 5e+19):
		tmp = x * z
	else:
		tmp = t * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e+64) || !(z <= 5e+19))
		tmp = Float64(x * z);
	else
		tmp = Float64(t * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e+64) || ~((z <= 5e+19)))
		tmp = x * z;
	else
		tmp = t * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e+64], N[Not[LessEqual[z, 5e+19]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(t * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000019e64 or 5e19 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. lower-fma.f64 N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sign-sub-inv N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. mul-1-neg N/A

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

      13. distribute-lft-out-- N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. distribute-lft-neg-in N/A

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

      17. *-commutative N/A

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

      18. mul-1-neg N/A

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

      19. remove-double-neg N/A

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

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

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

      21. mul-1-neg N/A

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

      22. remove-double-neg N/A

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

      23. lower--.f64 61.8

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.8%

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

   if -3.20000000000000019e64 < z < 5e19

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 59.3

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

   5. Applied rewrites 59.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 33.3%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+64} \lor \neg \left(z \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 26.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ t \cdot y \end{array} \]

FPCore

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

C

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

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 = t * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 46.8

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

5. Applied rewrites 46.8%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 24.7%

   \[\leadsto t \cdot \color{blue}{y} \]
9. Add Preprocessing

Developer Target 1: 96.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024342 
(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))))