Diagrams.Color.HSV:lerp from diagrams-contrib-1.3.0.5

Percentage Accurate: 97.9% → 100.0%

Time: 4.9s

Alternatives: 7

Speedup: 1.3×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * 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 = ((1.0d0 - x) * y) + (x * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((1.0 - x) * y) + (x * 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 = ((1.0d0 - x) * y) + (x * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Step-by-step derivation

   1. *-commutative 98.0%

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

   2. distribute-lft-out-- 98.0%

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

   3. *-rgt-identity 98.0%

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

   4. cancel-sign-sub-inv 98.0%

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

   5. +-commutative 98.0%

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

   6. +-commutative 98.0%

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

   7. associate-+l+ 98.0%

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

   8. +-commutative 98.0%

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

   9. *-commutative 98.0%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-103}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-122}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+30} \lor \neg \left(x \leq 1.2 \cdot 10^{+154}\right) \land x \leq 2.65 \cdot 10^{+272}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e-14)
   (* x z)
   (if (<= x -1.6e-103)
     y
     (if (<= x -1e-122)
       (* x z)
       (if (<= x 2.9e-104)
         y
         (if (or (<= x 1.6e+30) (and (not (<= x 1.2e+154)) (<= x 2.65e+272)))
           (* x z)
           (* x (- y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-14) {
		tmp = x * z;
	} else if (x <= -1.6e-103) {
		tmp = y;
	} else if (x <= -1e-122) {
		tmp = x * z;
	} else if (x <= 2.9e-104) {
		tmp = y;
	} else if ((x <= 1.6e+30) || (!(x <= 1.2e+154) && (x <= 2.65e+272))) {
		tmp = x * z;
	} else {
		tmp = x * -y;
	}
	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 (x <= (-7.5d-14)) then
        tmp = x * z
    else if (x <= (-1.6d-103)) then
        tmp = y
    else if (x <= (-1d-122)) then
        tmp = x * z
    else if (x <= 2.9d-104) then
        tmp = y
    else if ((x <= 1.6d+30) .or. (.not. (x <= 1.2d+154)) .and. (x <= 2.65d+272)) then
        tmp = x * z
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-14) {
		tmp = x * z;
	} else if (x <= -1.6e-103) {
		tmp = y;
	} else if (x <= -1e-122) {
		tmp = x * z;
	} else if (x <= 2.9e-104) {
		tmp = y;
	} else if ((x <= 1.6e+30) || (!(x <= 1.2e+154) && (x <= 2.65e+272))) {
		tmp = x * z;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e-14:
		tmp = x * z
	elif x <= -1.6e-103:
		tmp = y
	elif x <= -1e-122:
		tmp = x * z
	elif x <= 2.9e-104:
		tmp = y
	elif (x <= 1.6e+30) or (not (x <= 1.2e+154) and (x <= 2.65e+272)):
		tmp = x * z
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e-14)
		tmp = Float64(x * z);
	elseif (x <= -1.6e-103)
		tmp = y;
	elseif (x <= -1e-122)
		tmp = Float64(x * z);
	elseif (x <= 2.9e-104)
		tmp = y;
	elseif ((x <= 1.6e+30) || (!(x <= 1.2e+154) && (x <= 2.65e+272)))
		tmp = Float64(x * z);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e-14)
		tmp = x * z;
	elseif (x <= -1.6e-103)
		tmp = y;
	elseif (x <= -1e-122)
		tmp = x * z;
	elseif (x <= 2.9e-104)
		tmp = y;
	elseif ((x <= 1.6e+30) || (~((x <= 1.2e+154)) && (x <= 2.65e+272)))
		tmp = x * z;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e-14], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.6e-103], y, If[LessEqual[x, -1e-122], N[(x * z), $MachinePrecision], If[LessEqual[x, 2.9e-104], y, If[Or[LessEqual[x, 1.6e+30], And[N[Not[LessEqual[x, 1.2e+154]], $MachinePrecision], LessEqual[x, 2.65e+272]]], N[(x * z), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.4999999999999996e-14 or -1.59999999999999988e-103 < x < -1.00000000000000006e-122 or 2.9000000000000001e-104 < x < 1.59999999999999986e30 or 1.20000000000000007e154 < x < 2.65000000000000005e272

   1. Initial program 97.5%

      \[\left(1 - x\right) \cdot y + x \cdot z \]

   2. Taylor expanded in y around 0 69.4%

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

   if -7.4999999999999996e-14 < x < -1.59999999999999988e-103 or -1.00000000000000006e-122 < x < 2.9000000000000001e-104

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]

   2. Taylor expanded in x around 0 75.7%

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

   if 1.59999999999999986e30 < x < 1.20000000000000007e154 or 2.65000000000000005e272 < x

   1. Initial program 95.1%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Step-by-step derivation

      1. *-commutative 95.1%

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

      2. distribute-lft-out-- 95.1%

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

      3. *-rgt-identity 95.1%

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

      4. cancel-sign-sub-inv 95.1%

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

      5. +-commutative 95.1%

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

      6. +-commutative 95.1%

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

      7. associate-+l+ 95.1%

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

      8. +-commutative 95.1%

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

      9. *-commutative 95.1%

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

      10. distribute-rgt-out 100.0%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

   5. Taylor expanded in z around 0 77.9%

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

      1. associate-*r* 77.9%

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

      2. neg-mul-1 77.9%

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

   7. Simplified 77.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-103}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-122}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+30} \lor \neg \left(x \leq 1.2 \cdot 10^{+154}\right) \land x \leq 2.65 \cdot 10^{+272}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-99}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z y))))
   (if (<= x -7e-14)
     t_0
     (if (<= x -9.5e-99)
       y
       (if (<= x -1.8e-122) (* x z) (if (<= x 2.55e-104) y t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -7e-14) {
		tmp = t_0;
	} else if (x <= -9.5e-99) {
		tmp = y;
	} else if (x <= -1.8e-122) {
		tmp = x * z;
	} else if (x <= 2.55e-104) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	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) :: tmp
    t_0 = x * (z - y)
    if (x <= (-7d-14)) then
        tmp = t_0
    else if (x <= (-9.5d-99)) then
        tmp = y
    else if (x <= (-1.8d-122)) then
        tmp = x * z
    else if (x <= 2.55d-104) then
        tmp = y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z - y);
	double tmp;
	if (x <= -7e-14) {
		tmp = t_0;
	} else if (x <= -9.5e-99) {
		tmp = y;
	} else if (x <= -1.8e-122) {
		tmp = x * z;
	} else if (x <= 2.55e-104) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z - y)
	tmp = 0
	if x <= -7e-14:
		tmp = t_0
	elif x <= -9.5e-99:
		tmp = y
	elif x <= -1.8e-122:
		tmp = x * z
	elif x <= 2.55e-104:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -7e-14)
		tmp = t_0;
	elseif (x <= -9.5e-99)
		tmp = y;
	elseif (x <= -1.8e-122)
		tmp = Float64(x * z);
	elseif (x <= 2.55e-104)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z - y);
	tmp = 0.0;
	if (x <= -7e-14)
		tmp = t_0;
	elseif (x <= -9.5e-99)
		tmp = y;
	elseif (x <= -1.8e-122)
		tmp = x * z;
	elseif (x <= 2.55e-104)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-14], t$95$0, If[LessEqual[x, -9.5e-99], y, If[LessEqual[x, -1.8e-122], N[(x * z), $MachinePrecision], If[LessEqual[x, 2.55e-104], y, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.0000000000000005e-14 or 2.54999999999999996e-104 < x

   1. Initial program 96.8%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Step-by-step derivation

      1. *-commutative 96.8%

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

      2. distribute-lft-out-- 96.8%

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

      3. *-rgt-identity 96.8%

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

      4. cancel-sign-sub-inv 96.8%

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

      5. +-commutative 96.8%

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

      6. +-commutative 96.8%

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

      7. associate-+l+ 96.8%

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

      8. +-commutative 96.8%

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

      9. *-commutative 96.8%

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

      10. distribute-rgt-out 99.9%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 92.2%

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

   if -7.0000000000000005e-14 < x < -9.5000000000000008e-99 or -1.79999999999999997e-122 < x < 2.54999999999999996e-104

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]

   2. Taylor expanded in x around 0 75.7%

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

   if -9.5000000000000008e-99 < x < -1.79999999999999997e-122

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]

   2. Taylor expanded in y around 0 100.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-99}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 4: 59.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-102}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-125}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-107}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.8e-14)
   (* x z)
   (if (<= x -1.1e-102)
     y
     (if (<= x -4e-125) (* x z) (if (<= x 9.5e-107) y (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.8e-14) {
		tmp = x * z;
	} else if (x <= -1.1e-102) {
		tmp = y;
	} else if (x <= -4e-125) {
		tmp = x * z;
	} else if (x <= 9.5e-107) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	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 (x <= (-7.8d-14)) then
        tmp = x * z
    else if (x <= (-1.1d-102)) then
        tmp = y
    else if (x <= (-4d-125)) then
        tmp = x * z
    else if (x <= 9.5d-107) then
        tmp = y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.8e-14) {
		tmp = x * z;
	} else if (x <= -1.1e-102) {
		tmp = y;
	} else if (x <= -4e-125) {
		tmp = x * z;
	} else if (x <= 9.5e-107) {
		tmp = y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.8e-14:
		tmp = x * z
	elif x <= -1.1e-102:
		tmp = y
	elif x <= -4e-125:
		tmp = x * z
	elif x <= 9.5e-107:
		tmp = y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.8e-14)
		tmp = Float64(x * z);
	elseif (x <= -1.1e-102)
		tmp = y;
	elseif (x <= -4e-125)
		tmp = Float64(x * z);
	elseif (x <= 9.5e-107)
		tmp = y;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.8e-14)
		tmp = x * z;
	elseif (x <= -1.1e-102)
		tmp = y;
	elseif (x <= -4e-125)
		tmp = x * z;
	elseif (x <= 9.5e-107)
		tmp = y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.8e-14], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.1e-102], y, If[LessEqual[x, -4e-125], N[(x * z), $MachinePrecision], If[LessEqual[x, 9.5e-107], y, N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.7999999999999996e-14 or -1.10000000000000006e-102 < x < -4.00000000000000005e-125 or 9.4999999999999999e-107 < x

   1. Initial program 96.9%

      \[\left(1 - x\right) \cdot y + x \cdot z \]

   2. Taylor expanded in y around 0 58.5%

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

   if -7.7999999999999996e-14 < x < -1.10000000000000006e-102 or -4.00000000000000005e-125 < x < 9.4999999999999999e-107

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]

   2. Taylor expanded in x around 0 75.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-102}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-125}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-107}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -70 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -70.0) (not (<= x 1.0))) (* x (- z y)) (+ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -70.0) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	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 ((x <= (-70.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (z - y)
    else
        tmp = y + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -70.0) || !(x <= 1.0)) {
		tmp = x * (z - y);
	} else {
		tmp = y + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -70.0) or not (x <= 1.0):
		tmp = x * (z - y)
	else:
		tmp = y + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -70.0) || !(x <= 1.0))
		tmp = Float64(x * Float64(z - y));
	else
		tmp = Float64(y + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -70.0) || ~((x <= 1.0)))
		tmp = x * (z - y);
	else
		tmp = y + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -70.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -70 or 1 < x

   1. Initial program 96.1%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Step-by-step derivation

      1. *-commutative 96.1%

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

      2. distribute-lft-out-- 96.1%

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

      3. *-rgt-identity 96.1%

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

      4. cancel-sign-sub-inv 96.1%

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

      5. +-commutative 96.1%

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

      6. +-commutative 96.1%

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

      7. associate-+l+ 96.1%

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

      8. +-commutative 96.1%

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

      9. *-commutative 96.1%

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

      10. distribute-rgt-out 99.9%

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

      11. fma-def 99.9%

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

      12. +-commutative 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 99.7%

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

   if -70 < x < 1

   1. Initial program 100.0%

      \[\left(1 - x\right) \cdot y + x \cdot z \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. distribute-lft-out-- 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. *-commutative 100.0%

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

      10. distribute-rgt-out 100.0%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

   5. Taylor expanded in z around inf 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -70 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot z\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]
2. Step-by-step derivation

   1. *-commutative 98.0%

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

   2. distribute-lft-out-- 98.0%

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

   3. *-rgt-identity 98.0%

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

   4. cancel-sign-sub-inv 98.0%

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

   5. +-commutative 98.0%

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

   6. +-commutative 98.0%

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

   7. associate-+l+ 98.0%

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

   8. +-commutative 98.0%

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

   9. *-commutative 98.0%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 7: 36.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 98.0%

   \[\left(1 - x\right) \cdot y + x \cdot z \]

2. Taylor expanded in x around 0 32.9%

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

3. Final simplification 32.9%

   \[\leadsto y \]

Developer target: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (- y (* x (- y z)))

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