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

Percentage Accurate: 98.1% → 100.0%

Time: 4.0s

Alternatives: 9

Speedup: 1.3×

• 21.0% 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: 98.1% 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 97.6%

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

   1. sub-neg 97.6%

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

   2. +-commutative 97.6%

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

   3. distribute-lft1-in 97.6%

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

   4. associate-+r+ 97.6%

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

   5. +-commutative 97.6%

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

   6. *-commutative 97.6%

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

   7. neg-mul-1 97.6%

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

   8. associate-*r* 97.6%

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

   9. *-commutative 97.6%

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

   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: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - x\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{-54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-142} \lor \neg \left(z \leq 4.3 \cdot 10^{-109}\right) \land \left(z \leq 0.28 \lor \neg \left(z \leq 4.5 \cdot 10^{+15}\right)\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 x))))
   (if (<= z -2.15e-54)
     t_0
     (if (<= z -5.1e-82)
       (* x (+ y z))
       (if (or (<= z -1.65e-142)
               (and (not (<= z 4.3e-109))
                    (or (<= z 0.28) (not (<= z 4.5e+15)))))
         t_0
         (* x y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - x);
	double tmp;
	if (z <= -2.15e-54) {
		tmp = t_0;
	} else if (z <= -5.1e-82) {
		tmp = x * (y + z);
	} else if ((z <= -1.65e-142) || (!(z <= 4.3e-109) && ((z <= 0.28) || !(z <= 4.5e+15)))) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - x)
    if (z <= (-2.15d-54)) then
        tmp = t_0
    else if (z <= (-5.1d-82)) then
        tmp = x * (y + z)
    else if ((z <= (-1.65d-142)) .or. (.not. (z <= 4.3d-109)) .and. (z <= 0.28d0) .or. (.not. (z <= 4.5d+15))) then
        tmp = t_0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - x);
	double tmp;
	if (z <= -2.15e-54) {
		tmp = t_0;
	} else if (z <= -5.1e-82) {
		tmp = x * (y + z);
	} else if ((z <= -1.65e-142) || (!(z <= 4.3e-109) && ((z <= 0.28) || !(z <= 4.5e+15)))) {
		tmp = t_0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - x)
	tmp = 0
	if z <= -2.15e-54:
		tmp = t_0
	elif z <= -5.1e-82:
		tmp = x * (y + z)
	elif (z <= -1.65e-142) or (not (z <= 4.3e-109) and ((z <= 0.28) or not (z <= 4.5e+15))):
		tmp = t_0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - x))
	tmp = 0.0
	if (z <= -2.15e-54)
		tmp = t_0;
	elseif (z <= -5.1e-82)
		tmp = Float64(x * Float64(y + z));
	elseif ((z <= -1.65e-142) || (!(z <= 4.3e-109) && ((z <= 0.28) || !(z <= 4.5e+15))))
		tmp = t_0;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - x);
	tmp = 0.0;
	if (z <= -2.15e-54)
		tmp = t_0;
	elseif (z <= -5.1e-82)
		tmp = x * (y + z);
	elseif ((z <= -1.65e-142) || (~((z <= 4.3e-109)) && ((z <= 0.28) || ~((z <= 4.5e+15)))))
		tmp = t_0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e-54], t$95$0, If[LessEqual[z, -5.1e-82], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.65e-142], And[N[Not[LessEqual[z, 4.3e-109]], $MachinePrecision], Or[LessEqual[z, 0.28], N[Not[LessEqual[z, 4.5e+15]], $MachinePrecision]]]], t$95$0, N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.15e-54 or -5.09999999999999992e-82 < z < -1.6499999999999998e-142 or 4.2999999999999997e-109 < z < 0.28000000000000003 or 4.5e15 < z

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 90.6%

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

   if -2.15e-54 < z < -5.09999999999999992e-82

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 69.3%

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

      1. neg-mul-1 69.3%

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

      2. +-commutative 69.3%

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

      3. unsub-neg 69.3%

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

   4. Simplified 69.3%

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

      1. sub-neg 69.3%

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

      2. mul-1-neg 69.3%

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

      3. +-commutative 69.3%

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

      4. add-log-exp 26.2%

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

      5. *-un-lft-identity 26.2%

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

      6. log-prod 26.2%

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

      7. metadata-eval 26.2%

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

      8. add-log-exp 69.3%

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

      9. *-commutative 69.3%

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

      10. add-sqr-sqrt 69.3%

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

      11. sqrt-unprod 69.3%

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

      12. mul-1-neg 69.3%

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

      13. mul-1-neg 69.3%

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

      14. sqr-neg 69.3%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 69.6%

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

   6. Applied egg-rr 69.6%

      \[\leadsto \color{blue}{0 + x \cdot \left(z + y\right)} \]
   7. Step-by-step derivation

      1. +-lft-identity 69.6%

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

   8. Simplified 69.6%

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

   if -1.6499999999999998e-142 < z < 4.2999999999999997e-109 or 0.28000000000000003 < z < 4.5e15

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-142} \lor \neg \left(z \leq 4.3 \cdot 10^{-109}\right) \land \left(z \leq 0.28 \lor \neg \left(z \leq 4.5 \cdot 10^{+15}\right)\right):\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-29}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= x -1.2e+24)
     t_0
     (if (<= x -3.2e-15)
       (* x y)
       (if (<= x 1.6e-29) z (if (<= x 2.25e+29) (* x (+ y z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -1.2e+24) {
		tmp = t_0;
	} else if (x <= -3.2e-15) {
		tmp = x * y;
	} else if (x <= 1.6e-29) {
		tmp = z;
	} else if (x <= 2.25e+29) {
		tmp = x * (y + z);
	} 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
    if (x <= (-1.2d+24)) then
        tmp = t_0
    else if (x <= (-3.2d-15)) then
        tmp = x * y
    else if (x <= 1.6d-29) then
        tmp = z
    else if (x <= 2.25d+29) then
        tmp = x * (y + z)
    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;
	double tmp;
	if (x <= -1.2e+24) {
		tmp = t_0;
	} else if (x <= -3.2e-15) {
		tmp = x * y;
	} else if (x <= 1.6e-29) {
		tmp = z;
	} else if (x <= 2.25e+29) {
		tmp = x * (y + z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if x <= -1.2e+24:
		tmp = t_0
	elif x <= -3.2e-15:
		tmp = x * y
	elif x <= 1.6e-29:
		tmp = z
	elif x <= 2.25e+29:
		tmp = x * (y + z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (x <= -1.2e+24)
		tmp = t_0;
	elseif (x <= -3.2e-15)
		tmp = Float64(x * y);
	elseif (x <= 1.6e-29)
		tmp = z;
	elseif (x <= 2.25e+29)
		tmp = Float64(x * Float64(y + z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (x <= -1.2e+24)
		tmp = t_0;
	elseif (x <= -3.2e-15)
		tmp = x * y;
	elseif (x <= 1.6e-29)
		tmp = z;
	elseif (x <= 2.25e+29)
		tmp = x * (y + z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[x, -1.2e+24], t$95$0, If[LessEqual[x, -3.2e-15], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.6e-29], z, If[LessEqual[x, 2.25e+29], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e24 or 2.2500000000000001e29 < x

   1. Initial program 94.5%

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

   2. Taylor expanded in y around 0 63.5%

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

   3. Taylor expanded in x around inf 63.5%

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

      1. associate-*r* 63.5%

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

      2. mul-1-neg 63.5%

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

   5. Simplified 63.5%

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

   if -1.2e24 < x < -3.1999999999999999e-15

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 67.8%

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

   if -3.1999999999999999e-15 < x < 1.6e-29

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.2%

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

   if 1.6e-29 < x < 2.2500000000000001e29

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.7%

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

      1. neg-mul-1 81.7%

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

      2. +-commutative 81.7%

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

      3. unsub-neg 81.7%

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

   4. Simplified 81.7%

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

      1. sub-neg 81.7%

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

      2. mul-1-neg 81.7%

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

      3. +-commutative 81.7%

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

      4. add-log-exp 12.1%

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

      5. *-un-lft-identity 12.1%

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

      6. log-prod 12.1%

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

      7. metadata-eval 12.1%

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

      8. add-log-exp 81.7%

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

      9. *-commutative 81.7%

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

      10. add-sqr-sqrt 17.8%

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

      11. sqrt-unprod 74.8%

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

      12. mul-1-neg 74.8%

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

      13. mul-1-neg 74.8%

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

      14. sqr-neg 74.8%

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

      15. sqrt-unprod 56.9%

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

      16. add-sqr-sqrt 72.5%

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

   6. Applied egg-rr 72.5%

      \[\leadsto \color{blue}{0 + x \cdot \left(z + y\right)} \]
   7. Step-by-step derivation

      1. +-lft-identity 72.5%

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

   8. Simplified 72.5%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-29}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-12}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-30}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= x -1.05e+24)
     t_0
     (if (<= x -6.5e-12)
       (* x y)
       (if (<= x 2.7e-30) z (if (<= x 2e+36) (* x y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -1.05e+24) {
		tmp = t_0;
	} else if (x <= -6.5e-12) {
		tmp = x * y;
	} else if (x <= 2.7e-30) {
		tmp = z;
	} else if (x <= 2e+36) {
		tmp = x * 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
    if (x <= (-1.05d+24)) then
        tmp = t_0
    else if (x <= (-6.5d-12)) then
        tmp = x * y
    else if (x <= 2.7d-30) then
        tmp = z
    else if (x <= 2d+36) then
        tmp = x * 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;
	double tmp;
	if (x <= -1.05e+24) {
		tmp = t_0;
	} else if (x <= -6.5e-12) {
		tmp = x * y;
	} else if (x <= 2.7e-30) {
		tmp = z;
	} else if (x <= 2e+36) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if x <= -1.05e+24:
		tmp = t_0
	elif x <= -6.5e-12:
		tmp = x * y
	elif x <= 2.7e-30:
		tmp = z
	elif x <= 2e+36:
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (x <= -1.05e+24)
		tmp = t_0;
	elseif (x <= -6.5e-12)
		tmp = Float64(x * y);
	elseif (x <= 2.7e-30)
		tmp = z;
	elseif (x <= 2e+36)
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (x <= -1.05e+24)
		tmp = t_0;
	elseif (x <= -6.5e-12)
		tmp = x * y;
	elseif (x <= 2.7e-30)
		tmp = z;
	elseif (x <= 2e+36)
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[x, -1.05e+24], t$95$0, If[LessEqual[x, -6.5e-12], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.7e-30], z, If[LessEqual[x, 2e+36], N[(x * y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0500000000000001e24 or 2.00000000000000008e36 < x

   1. Initial program 94.5%

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

   2. Taylor expanded in y around 0 63.5%

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

   3. Taylor expanded in x around inf 63.5%

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

      1. associate-*r* 63.5%

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

      2. mul-1-neg 63.5%

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

   5. Simplified 63.5%

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

   if -1.0500000000000001e24 < x < -6.5000000000000002e-12 or 2.69999999999999987e-30 < x < 2.00000000000000008e36

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 69.9%

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

   if -6.5000000000000002e-12 < x < 2.69999999999999987e-30

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-12}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-30}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+36}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -16500000000 \lor \neg \left(x \leq 1.2 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -16500000000.0) (not (<= x 1.2e-29)))
   (* x (- y z))
   (* z (- 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -16500000000.0) || !(x <= 1.2e-29)) {
		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 <= (-16500000000.0d0)) .or. (.not. (x <= 1.2d-29))) 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 <= -16500000000.0) || !(x <= 1.2e-29)) {
		tmp = x * (y - z);
	} else {
		tmp = z * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -16500000000.0) or not (x <= 1.2e-29):
		tmp = x * (y - z)
	else:
		tmp = z * (1.0 - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -16500000000.0) || !(x <= 1.2e-29))
		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 <= -16500000000.0) || ~((x <= 1.2e-29)))
		tmp = x * (y - z);
	else
		tmp = z * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -16500000000.0], N[Not[LessEqual[x, 1.2e-29]], $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 < -1.65e10 or 1.19999999999999996e-29 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. +-commutative 98.2%

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

      3. unsub-neg 98.2%

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

   4. Simplified 98.2%

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

   if -1.65e10 < x < 1.19999999999999996e-29

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.3%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16500000000 \lor \neg \left(x \leq 1.2 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 6: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -16500000000 \lor \neg \left(x \leq 3.4 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -16500000000.0) (not (<= x 3.4e-31)))
   (* x (- y z))
   (- z (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -16500000000.0) || !(x <= 3.4e-31)) {
		tmp = x * (y - z);
	} else {
		tmp = z - (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 <= (-16500000000.0d0)) .or. (.not. (x <= 3.4d-31))) then
        tmp = x * (y - z)
    else
        tmp = z - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -16500000000.0) || !(x <= 3.4e-31)) {
		tmp = x * (y - z);
	} else {
		tmp = z - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -16500000000.0) or not (x <= 3.4e-31):
		tmp = x * (y - z)
	else:
		tmp = z - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -16500000000.0) || !(x <= 3.4e-31))
		tmp = Float64(x * Float64(y - z));
	else
		tmp = Float64(z - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -16500000000.0) || ~((x <= 3.4e-31)))
		tmp = x * (y - z);
	else
		tmp = z - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -16500000000.0], N[Not[LessEqual[x, 3.4e-31]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(z - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e10 or 3.4000000000000001e-31 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. +-commutative 98.2%

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

      3. unsub-neg 98.2%

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

   4. Simplified 98.2%

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

   if -1.65e10 < x < 3.4000000000000001e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.3%

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

   3. Taylor expanded in x around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-rgt-neg-out 76.3%

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

      3. +-commutative 76.3%

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

      4. distribute-rgt-neg-out 76.3%

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

      5. unsub-neg 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16500000000 \lor \neg \left(x \leq 3.4 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot z\\ \end{array} \]

Alternative 7: 61.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-31}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.25e-14) (* x y) (if (<= x 5.2e-31) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.25e-14) {
		tmp = x * y;
	} else if (x <= 5.2e-31) {
		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 <= (-2.25d-14)) then
        tmp = x * y
    else if (x <= 5.2d-31) 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 <= -2.25e-14) {
		tmp = x * y;
	} else if (x <= 5.2e-31) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.25e-14:
		tmp = x * y
	elif x <= 5.2e-31:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.25e-14)
		tmp = Float64(x * y);
	elseif (x <= 5.2e-31)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.25e-14)
		tmp = x * y;
	elseif (x <= 5.2e-31)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.25e-14], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.2e-31], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2499999999999999e-14 or 5.19999999999999991e-31 < x

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 49.1%

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

   if -2.2499999999999999e-14 < x < 5.19999999999999991e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.2%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-31}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 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 97.6%

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

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 97.6%

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

   1. *-commutative 97.6%

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

   2. neg-mul-1 97.6%

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

   3. distribute-lft-in 97.6%

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

   4. *-rgt-identity 97.6%

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

   5. associate-+l+ 97.6%

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

   6. +-commutative 97.6%

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

   7. distribute-rgt-neg-out 97.6%

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

   8. unsub-neg 97.6%

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

   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 9: 36.6% 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 97.6%

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

2. Taylor expanded in x around 0 38.0%

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

3. Final simplification 38.0%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023221 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))