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

Percentage Accurate: 98.0% → 100.0%

Time: 3.9s

Alternatives: 7

Speedup: 1.3×

• 20.2% 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: 98.0% 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 96.8%

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

   1. sub-neg 96.8%

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

   2. +-commutative 96.8%

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

   3. distribute-lft1-in 96.8%

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

   4. associate-+r+ 96.8%

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

   5. +-commutative 96.8%

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

   6. *-commutative 96.8%

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

   7. neg-mul-1 96.8%

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

   8. associate-*r* 96.8%

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

   9. *-commutative 96.8%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. 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. Final simplification 100.0%

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

Alternative 2: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-69} \lor \neg \left(z \leq 9.8 \cdot 10^{-107}\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e-69) (not (<= z 9.8e-107))) (* z (- 1.0 x)) (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-69) || !(z <= 9.8e-107)) {
		tmp = z * (1.0 - x);
	} 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 ((z <= (-2.5d-69)) .or. (.not. (z <= 9.8d-107))) then
        tmp = z * (1.0d0 - x)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e-69) || !(z <= 9.8e-107)) {
		tmp = z * (1.0 - x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e-69) or not (z <= 9.8e-107):
		tmp = z * (1.0 - x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e-69) || !(z <= 9.8e-107))
		tmp = Float64(z * Float64(1.0 - x));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.5e-69) || ~((z <= 9.8e-107)))
		tmp = z * (1.0 - x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e-69], N[Not[LessEqual[z, 9.8e-107]], $MachinePrecision]], N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000017e-69 or 9.79999999999999959e-107 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 83.3%

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

   if -2.50000000000000017e-69 < z < 9.79999999999999959e-107

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 68.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-69} \lor \neg \left(z \leq 9.8 \cdot 10^{-107}\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-108} \lor \neg \left(x \leq 2.8 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.2e-108) (not (<= x 2.8e-32))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.2e-108) || !(x <= 2.8e-32)) {
		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 <= (-5.2d-108)) .or. (.not. (x <= 2.8d-32))) 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 <= -5.2e-108) || !(x <= 2.8e-32)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.2e-108) or not (x <= 2.8e-32):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.2e-108) || !(x <= 2.8e-32))
		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 <= -5.2e-108) || ~((x <= 2.8e-32)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.2e-108], N[Not[LessEqual[x, 2.8e-32]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -5.19999999999999968e-108 or 2.7999999999999999e-32 < x

   1. Initial program 94.3%

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

   2. Taylor expanded in x around inf 92.3%

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

      1. neg-mul-1 92.3%

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

      2. +-commutative 92.3%

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

      3. unsub-neg 92.3%

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

   4. Simplified 92.3%

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

   if -5.19999999999999968e-108 < x < 2.7999999999999999e-32

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.3%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-108} \lor \neg \left(x \leq 2.8 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 61.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-81}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e-81) (* x y) (if (<= x 3.5e-33) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-81) {
		tmp = x * y;
	} else if (x <= 3.5e-33) {
		tmp = 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 <= (-2.6d-81)) then
        tmp = x * y
    else if (x <= 3.5d-33) then
        tmp = 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 <= -2.6e-81) {
		tmp = x * y;
	} else if (x <= 3.5e-33) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e-81:
		tmp = x * y
	elif x <= 3.5e-33:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e-81)
		tmp = Float64(x * y);
	elseif (x <= 3.5e-33)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.6e-81)
		tmp = x * y;
	elseif (x <= 3.5e-33)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e-81], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.5e-33], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e-81 or 3.4999999999999999e-33 < x

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf 48.9%

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

   if -2.5999999999999999e-81 < x < 3.4999999999999999e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 73.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-81}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 61.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0) (* x (- z)) (if (<= x 6.1e-33) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x * -z;
	} else if (x <= 6.1e-33) {
		tmp = 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 <= (-1.0d0)) then
        tmp = x * -z
    else if (x <= 6.1d-33) then
        tmp = 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 <= -1.0) {
		tmp = x * -z;
	} else if (x <= 6.1e-33) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = x * -z
	elif x <= 6.1e-33:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x * Float64(-z));
	elseif (x <= 6.1e-33)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x * -z;
	elseif (x <= 6.1e-33)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], N[(x * (-z)), $MachinePrecision], If[LessEqual[x, 6.1e-33], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 89.7%

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

   2. Taylor expanded in y around 0 65.1%

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

   3. Taylor expanded in x around inf 63.4%

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

      1. associate-*r* 63.4%

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

      2. mul-1-neg 63.4%

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

   5. Simplified 63.4%

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

   if -1 < x < 6.1000000000000001e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 69.1%

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

   if 6.1000000000000001e-33 < x

   1. Initial program 96.7%

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

   2. Taylor expanded in y around inf 60.6%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 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 96.8%

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

2. Taylor expanded in x around 0 100.0%

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

3. Taylor expanded in z around 0 96.8%

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

   1. *-commutative 96.8%

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

   2. neg-mul-1 96.8%

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

   3. distribute-lft-in 96.8%

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

   4. *-rgt-identity 96.8%

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

   5. associate-+l+ 96.8%

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

   6. +-commutative 96.8%

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

   7. distribute-rgt-neg-out 96.8%

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

   8. unsub-neg 96.8%

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

   9. distribute-rgt-out-- 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 7: 37.5% 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 96.8%

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

2. Taylor expanded in x around 0 38.5%

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

3. Final simplification 38.5%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023185 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))