Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 95.7% → 99.9%

Time: 7.9s

Alternatives: 9

Speedup: 0.8×

• 21.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-31} \lor \neg \left(z \leq 1.42 \cdot 10^{-11}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y - 1\right) \cdot x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e-31) (not (<= z 1.42e-11)))
   (fma (* (- y 1.0) x) z x)
   (fma (* z y) x x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e-31) || !(z <= 1.42e-11)) {
		tmp = fma(((y - 1.0) * x), z, x);
	} else {
		tmp = fma((z * y), x, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2e-31) || !(z <= 1.42e-11))
		tmp = fma(Float64(Float64(y - 1.0) * x), z, x);
	else
		tmp = fma(Float64(z * y), x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2e-31], N[Not[LessEqual[z, 1.42e-11]], $MachinePrecision]], N[(N[(N[(y - 1.0), $MachinePrecision] * x), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(z * y), $MachinePrecision] * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e-31 or 1.42e-11 < z

   1. Initial program 92.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 99.9%

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

   if -2e-31 < z < 1.42e-11

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 93.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. remove-double-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. sub-neg N/A

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

      10. lift--.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. associate-*r* N/A

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

      13. lift--.f64 N/A

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

      14. neg-mul-1 N/A

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

      15. lower-fma.f64 N/A

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 99.9

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

   9. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-31} \lor \neg \left(z \leq 1.42 \cdot 10^{-11}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y - 1\right) \cdot x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot \left(y - 1\right)\right) \cdot x\\ t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 10000:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z (- y 1.0)) x)) (t_1 (* (- 1.0 y) z)))
   (if (<= t_1 (- INFINITY))
     (* (* z x) y)
     (if (<= t_1 -5e+16)
       t_0
       (if (<= t_1 10000.0)
         (fma (* z y) x x)
         (if (<= t_1 4e+307) t_0 (* (* y x) z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (y - 1.0)) * x;
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (z * x) * y;
	} else if (t_1 <= -5e+16) {
		tmp = t_0;
	} else if (t_1 <= 10000.0) {
		tmp = fma((z * y), x, x);
	} else if (t_1 <= 4e+307) {
		tmp = t_0;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(y - 1.0)) * x)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(z * x) * y);
	elseif (t_1 <= -5e+16)
		tmp = t_0;
	elseif (t_1 <= 10000.0)
		tmp = fma(Float64(z * y), x, x);
	elseif (t_1 <= 4e+307)
		tmp = t_0;
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -5e+16], t$95$0, If[LessEqual[t$95$1, 10000.0], N[(N[(z * y), $MachinePrecision] * x + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+307], t$95$0, N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -inf.0

   1. Initial program 68.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -inf.0 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -5e16 or 1e4 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 3.99999999999999994e307

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 99.3

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

   5. Applied rewrites 99.3%

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

   if -5e16 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1e4

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 98.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. remove-double-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. sub-neg N/A

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

      10. lift--.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. associate-*r* N/A

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

      13. lift--.f64 N/A

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

      14. neg-mul-1 N/A

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

      15. lower-fma.f64 N/A

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

   6. Applied rewrites 100.0%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 98.7

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

   9. Applied rewrites 98.7%

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

   if 3.99999999999999994e307 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 69.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 99.8

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

   5. Applied rewrites 99.8%

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

   7. Applied rewrites 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty:\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+16}:\\ \;\;\;\;\left(z \cdot \left(y - 1\right)\right) \cdot x\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 10000:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x, x\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 4 \cdot 10^{+307}:\\ \;\;\;\;\left(z \cdot \left(y - 1\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -0.05 \lor \neg \left(1 - y \leq 2\right):\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 y) -0.05) (not (<= (- 1.0 y) 2.0)))
   (fma (* z y) x x)
   (* (- 1.0 z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) <= -0.05) || !((1.0 - y) <= 2.0)) {
		tmp = fma((z * y), x, x);
	} else {
		tmp = (1.0 - z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - y) <= -0.05) || !(Float64(1.0 - y) <= 2.0))
		tmp = fma(Float64(z * y), x, x);
	else
		tmp = Float64(Float64(1.0 - z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - y), $MachinePrecision], -0.05], N[Not[LessEqual[N[(1.0 - y), $MachinePrecision], 2.0]], $MachinePrecision]], N[(N[(z * y), $MachinePrecision] * x + x), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -0.050000000000000003 or 2 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 92.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 94.3%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. remove-double-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. sub-neg N/A

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

      10. lift--.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. associate-*r* N/A

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

      13. lift--.f64 N/A

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

      14. neg-mul-1 N/A

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

      15. lower-fma.f64 N/A

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

   6. Applied rewrites 92.1%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 91.5

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

   9. Applied rewrites 91.5%

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

   if -0.050000000000000003 < (-.f64 #s(literal 1 binary64) y) < 2

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 98.7

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

   5. Applied rewrites 98.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -0.05 \lor \neg \left(1 - y \leq 2\right):\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+37} \lor \neg \left(1 - y \leq 5 \cdot 10^{+38}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 y) -2e+37) (not (<= (- 1.0 y) 5e+38)))
   (* (* y x) z)
   (* (- 1.0 z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) <= -2e+37) || !((1.0 - y) <= 5e+38)) {
		tmp = (y * x) * z;
	} else {
		tmp = (1.0 - z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) <= (-2d+37)) .or. (.not. ((1.0d0 - y) <= 5d+38))) then
        tmp = (y * x) * z
    else
        tmp = (1.0d0 - z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) <= -2e+37) || !((1.0 - y) <= 5e+38)) {
		tmp = (y * x) * z;
	} else {
		tmp = (1.0 - z) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) <= -2e+37) or not ((1.0 - y) <= 5e+38):
		tmp = (y * x) * z
	else:
		tmp = (1.0 - z) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - y) <= -2e+37) || !(Float64(1.0 - y) <= 5e+38))
		tmp = Float64(Float64(y * x) * z);
	else
		tmp = Float64(Float64(1.0 - z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) <= -2e+37) || ~(((1.0 - y) <= 5e+38)))
		tmp = (y * x) * z;
	else
		tmp = (1.0 - z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - y), $MachinePrecision], -2e+37], N[Not[LessEqual[N[(1.0 - y), $MachinePrecision], 5e+38]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -1.99999999999999991e37 or 4.9999999999999997e38 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 90.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 77.6

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

   5. Applied rewrites 77.6%

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

   7. Applied rewrites 79.1%

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

   if -1.99999999999999991e37 < (-.f64 #s(literal 1 binary64) y) < 4.9999999999999997e38

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 95.8

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

   5. Applied rewrites 95.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+37} \lor \neg \left(1 - y \leq 5 \cdot 10^{+38}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+37} \lor \neg \left(1 - y \leq 5 \cdot 10^{+38}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 y) -2e+37) (not (<= (- 1.0 y) 5e+38)))
   (* (* z x) y)
   (* (- 1.0 z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) <= -2e+37) || !((1.0 - y) <= 5e+38)) {
		tmp = (z * x) * y;
	} else {
		tmp = (1.0 - z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) <= (-2d+37)) .or. (.not. ((1.0d0 - y) <= 5d+38))) then
        tmp = (z * x) * y
    else
        tmp = (1.0d0 - z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) <= -2e+37) || !((1.0 - y) <= 5e+38)) {
		tmp = (z * x) * y;
	} else {
		tmp = (1.0 - z) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) <= -2e+37) or not ((1.0 - y) <= 5e+38):
		tmp = (z * x) * y
	else:
		tmp = (1.0 - z) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - y) <= -2e+37) || !(Float64(1.0 - y) <= 5e+38))
		tmp = Float64(Float64(z * x) * y);
	else
		tmp = Float64(Float64(1.0 - z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) <= -2e+37) || ~(((1.0 - y) <= 5e+38)))
		tmp = (z * x) * y;
	else
		tmp = (1.0 - z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - y), $MachinePrecision], -2e+37], N[Not[LessEqual[N[(1.0 - y), $MachinePrecision], 5e+38]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -1.99999999999999991e37 or 4.9999999999999997e38 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 90.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 77.6

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

   5. Applied rewrites 77.6%

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

   if -1.99999999999999991e37 < (-.f64 #s(literal 1 binary64) y) < 4.9999999999999997e38

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower--.f64 95.8

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

   5. Applied rewrites 95.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -2 \cdot 10^{+37} \lor \neg \left(1 - y \leq 5 \cdot 10^{+38}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{-97}:\\ \;\;\;\;\mathsf{fma}\left(\left(y - 1\right) \cdot x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(y - 1\right), x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1e-97) (fma (* (- y 1.0) x) z x) (fma (* z (- y 1.0)) x x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e-97) {
		tmp = fma(((y - 1.0) * x), z, x);
	} else {
		tmp = fma((z * (y - 1.0)), x, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1e-97)
		tmp = fma(Float64(Float64(y - 1.0) * x), z, x);
	else
		tmp = fma(Float64(z * Float64(y - 1.0)), x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1e-97], N[(N[(N[(y - 1.0), $MachinePrecision] * x), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000004e-97

   1. Initial program 94.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 97.7%

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

   if 1.00000000000000004e-97 < x

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   4. Applied rewrites 99.9%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*r* N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. remove-double-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. sub-neg N/A

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

      10. lift--.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. associate-*r* N/A

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

      13. lift--.f64 N/A

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

      14. neg-mul-1 N/A

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

      15. lower-fma.f64 N/A

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

   6. Applied rewrites 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{-97}:\\ \;\;\;\;\mathsf{fma}\left(\left(y - 1\right) \cdot x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(y - 1\right), x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-8} \lor \neg \left(z \leq 0.0122\right):\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e-8) (not (<= z 0.0122))) (* (- z) x) (* 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-8) || !(z <= 0.0122)) {
		tmp = -z * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.5d-8)) .or. (.not. (z <= 0.0122d0))) then
        tmp = -z * x
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-8) || !(z <= 0.0122)) {
		tmp = -z * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e-8) or not (z <= 0.0122):
		tmp = -z * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e-8) || !(z <= 0.0122))
		tmp = Float64(Float64(-z) * x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e-8) || ~((z <= 0.0122)))
		tmp = -z * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e-8], N[Not[LessEqual[z, 0.0122]], $MachinePrecision]], N[((-z) * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999999e-8 or 0.0122000000000000008 < z

   1. Initial program 92.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 90.9

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

   5. Applied rewrites 90.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.1%

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

   if -2.4999999999999999e-8 < z < 0.0122000000000000008

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 72.2%

      \[\leadsto x \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-8} \lor \neg \left(z \leq 0.0122\right):\\ \;\;\;\;\left(-z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \left(1 - z\right) \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (- 1.0 z) x))

C

double code(double x, double y, double z) {
	return (1.0 - z) * x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (1.0d0 - z) * x
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 - z) * x;
}

Python

def code(x, y, z):
	return (1.0 - z) * x

Julia

function code(x, y, z)
	return Float64(Float64(1.0 - z) * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 - z) * x;
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 95.8%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. lower--.f64 64.6

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

5. Applied rewrites 64.6%

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

6. Final simplification 64.6%

   \[\leadsto \left(1 - z\right) \cdot x \]
7. Add Preprocessing

Alternative 9: 38.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z) {
	return 1.0 * x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 * x;
}

Python

def code(x, y, z):
	return 1.0 * x

Julia

function code(x, y, z)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 95.8%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto x \cdot \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 36.8%

   \[\leadsto x \cdot \color{blue}{1} \]

6. Final simplification 36.8%

   \[\leadsto 1 \cdot x \]
7. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t\_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024271 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- 1 (* (- 1 y) z))) -161819597360704900000000000000000000000000000000000) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 389223764966390300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x))))))

  (* x (- 1.0 (* (- 1.0 y) z))))