Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Percentage Accurate: 97.7% → 100.0%

Time: 5.6s

Alternatives: 8

Speedup: 1.3×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. *-commutative 97.2%

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

   2. distribute-lft-out-- 97.2%

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

   3. *-rgt-identity 97.2%

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

   4. cancel-sign-sub-inv 97.2%

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

   5. +-commutative 97.2%

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

   6. associate-+r+ 97.2%

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

   7. +-commutative 97.2%

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

   8. *-commutative 97.2%

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

   9. distribute-rgt-out 100.0%

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

   10. fma-define 100.0%

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

   11. +-commutative 100.0%

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

   12. unsub-neg 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+291}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-39} \lor \neg \left(x \leq 5 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.7e+291)
   (* x (- z))
   (if (or (<= x -2e-39) (not (<= x 5e-23))) (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.7e+291) {
		tmp = x * -z;
	} else if ((x <= -2e-39) || !(x <= 5e-23)) {
		tmp = x * y;
	} else {
		tmp = 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 <= (-4.7d+291)) then
        tmp = x * -z
    else if ((x <= (-2d-39)) .or. (.not. (x <= 5d-23))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.7e+291) {
		tmp = x * -z;
	} else if ((x <= -2e-39) || !(x <= 5e-23)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.7e+291:
		tmp = x * -z
	elif (x <= -2e-39) or not (x <= 5e-23):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.7e+291)
		tmp = Float64(x * Float64(-z));
	elseif ((x <= -2e-39) || !(x <= 5e-23))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.7e+291)
		tmp = x * -z;
	elseif ((x <= -2e-39) || ~((x <= 5e-23)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.7e+291], N[(x * (-z)), $MachinePrecision], If[Or[LessEqual[x, -2e-39], N[Not[LessEqual[x, 5e-23]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]]

Derivation

1. Split input into 3 regimes

2. if x < -4.7e291

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. sub-neg 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 94.7%

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

      1. associate-*r* 94.7%

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

      2. mul-1-neg 94.7%

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

   8. Simplified 94.7%

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

   if -4.7e291 < x < -1.99999999999999986e-39 or 5.0000000000000002e-23 < x

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf 64.4%

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

   if -1.99999999999999986e-39 < x < 5.0000000000000002e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+291}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-39} \lor \neg \left(x \leq 5 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-51} \lor \neg \left(x \leq 4.8 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e-51) (not (<= x 4.8e-23))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-51) || !(x <= 4.8e-23)) {
		tmp = x * (y - z);
	} else {
		tmp = 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 <= (-1.15d-51)) .or. (.not. (x <= 4.8d-23))) then
        tmp = x * (y - z)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-51) || !(x <= 4.8e-23)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.15e-51) or not (x <= 4.8e-23):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e-51) || !(x <= 4.8e-23))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.15e-51) || ~((x <= 4.8e-23)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e-51], N[Not[LessEqual[x, 4.8e-23]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.15000000000000001e-51 or 4.79999999999999993e-23 < x

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 93.5%

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

      1. mul-1-neg 93.5%

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

      2. sub-neg 93.5%

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

   5. Simplified 93.5%

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

   if -1.15000000000000001e-51 < x < 4.79999999999999993e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.5%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-51} \lor \neg \left(x \leq 4.8 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0036 \lor \neg \left(x \leq 2.8 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0036) (not (<= x 2.8e-9))) (* x (- y z)) (* z (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0036) || !(x <= 2.8e-9)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (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 ((x <= (-0.0036d0)) .or. (.not. (x <= 2.8d-9))) then
        tmp = x * (y - z)
    else
        tmp = z * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0036) || !(x <= 2.8e-9)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0036) or not (x <= 2.8e-9):
		tmp = x * (y - z)
	else:
		tmp = z * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0036) || !(x <= 2.8e-9))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.0036) || ~((x <= 2.8e-9)))
		tmp = x * (y - z);
	else
		tmp = z * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0036], N[Not[LessEqual[x, 2.8e-9]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0035999999999999999 or 2.79999999999999984e-9 < x

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. sub-neg 98.5%

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

   5. Simplified 98.5%

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

   if -0.0035999999999999999 < x < 2.79999999999999984e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0036 \lor \neg \left(x \leq 2.8 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -26000 \lor \neg \left(x \leq 0.00046\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -26000.0) (not (<= x 0.00046))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -26000.0) || !(x <= 0.00046)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (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 <= (-26000.0d0)) .or. (.not. (x <= 0.00046d0))) then
        tmp = x * (y - z)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -26000.0) || !(x <= 0.00046)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -26000.0) or not (x <= 0.00046):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -26000.0) || !(x <= 0.00046))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -26000.0) || ~((x <= 0.00046)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -26000.0], N[Not[LessEqual[x, 0.00046]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -26000 or 4.6000000000000001e-4 < x

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. sub-neg 98.5%

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

   5. Simplified 98.5%

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

   if -26000 < x < 4.6000000000000001e-4

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-z\right)\right)} + x \cdot y \]

      5. neg-sub0 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. distribute-rgt-out-- 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-+l- 100.0%

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

      12. distribute-lft-out-- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-out 98.9%

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

   7. Simplified 98.9%

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

      1. *-commutative 98.9%

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

      2. cancel-sign-sub 98.9%

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

      3. *-commutative 98.9%

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

      4. +-commutative 98.9%

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

   9. Applied egg-rr 98.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -26000 \lor \neg \left(x \leq 0.00046\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-38} \lor \neg \left(x \leq 4.9 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.02e-38) (not (<= x 4.9e-23))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.02e-38) || !(x <= 4.9e-23)) {
		tmp = x * y;
	} else {
		tmp = 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 <= (-1.02d-38)) .or. (.not. (x <= 4.9d-23))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.02e-38) || !(x <= 4.9e-23)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.02e-38) or not (x <= 4.9e-23):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.02e-38) || !(x <= 4.9e-23))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.02e-38) || ~((x <= 4.9e-23)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.02e-38], N[Not[LessEqual[x, 4.9e-23]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999998e-38 or 4.8999999999999998e-23 < x

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 62.7%

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

   if -1.01999999999999998e-38 < x < 4.8999999999999998e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.7%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-38} \lor \neg \left(x \leq 4.9 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. +-commutative 97.2%

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

   2. remove-double-neg 97.2%

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

   3. distribute-rgt-neg-out 97.2%

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

   4. neg-sub0 97.2%

      \[\leadsto \color{blue}{\left(0 - \left(1 - x\right) \cdot \left(-z\right)\right)} + x \cdot y \]

   5. neg-sub0 97.2%

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

   6. *-commutative 97.2%

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

   7. distribute-lft-neg-in 97.2%

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

   8. remove-double-neg 97.2%

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

   9. distribute-rgt-out-- 97.2%

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

   10. *-lft-identity 97.2%

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

   11. associate-+l- 97.2%

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

   12. distribute-lft-out-- 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 8: 36.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in x around 0 37.5%

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

4. Final simplification 37.5%

   \[\leadsto z \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))