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

Percentage Accurate: 98.1% → 100.0%

Time: 6.4s

Alternatives: 7

Speedup: 1.3×

• 21.6% 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 96.1%

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

   1. *-commutative 96.1%

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

   2. distribute-lft-out-- 96.1%

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

   3. *-rgt-identity 96.1%

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

   4. cancel-sign-sub-inv 96.1%

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

   5. +-commutative 96.1%

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

   6. associate-+r+ 96.1%

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

   7. +-commutative 96.1%

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

   8. *-commutative 96.1%

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

   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: 61.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+265}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+160}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+117}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+90}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.86 \cdot 10^{-69}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-24}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= x -6.5e+265)
     (* x y)
     (if (<= x -5.5e+160)
       t_0
       (if (<= x -3.2e+117)
         (* x y)
         (if (<= x -1.15e+90)
           t_0
           (if (<= x -1.86e-69)
             (* x y)
             (if (<= x 1.65e-24) z (if (<= x 2.7e+48) (* x y) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (x <= -6.5e+265) {
		tmp = x * y;
	} else if (x <= -5.5e+160) {
		tmp = t_0;
	} else if (x <= -3.2e+117) {
		tmp = x * y;
	} else if (x <= -1.15e+90) {
		tmp = t_0;
	} else if (x <= -1.86e-69) {
		tmp = x * y;
	} else if (x <= 1.65e-24) {
		tmp = z;
	} else if (x <= 2.7e+48) {
		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 <= (-6.5d+265)) then
        tmp = x * y
    else if (x <= (-5.5d+160)) then
        tmp = t_0
    else if (x <= (-3.2d+117)) then
        tmp = x * y
    else if (x <= (-1.15d+90)) then
        tmp = t_0
    else if (x <= (-1.86d-69)) then
        tmp = x * y
    else if (x <= 1.65d-24) then
        tmp = z
    else if (x <= 2.7d+48) 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 <= -6.5e+265) {
		tmp = x * y;
	} else if (x <= -5.5e+160) {
		tmp = t_0;
	} else if (x <= -3.2e+117) {
		tmp = x * y;
	} else if (x <= -1.15e+90) {
		tmp = t_0;
	} else if (x <= -1.86e-69) {
		tmp = x * y;
	} else if (x <= 1.65e-24) {
		tmp = z;
	} else if (x <= 2.7e+48) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if x <= -6.5e+265:
		tmp = x * y
	elif x <= -5.5e+160:
		tmp = t_0
	elif x <= -3.2e+117:
		tmp = x * y
	elif x <= -1.15e+90:
		tmp = t_0
	elif x <= -1.86e-69:
		tmp = x * y
	elif x <= 1.65e-24:
		tmp = z
	elif x <= 2.7e+48:
		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 <= -6.5e+265)
		tmp = Float64(x * y);
	elseif (x <= -5.5e+160)
		tmp = t_0;
	elseif (x <= -3.2e+117)
		tmp = Float64(x * y);
	elseif (x <= -1.15e+90)
		tmp = t_0;
	elseif (x <= -1.86e-69)
		tmp = Float64(x * y);
	elseif (x <= 1.65e-24)
		tmp = z;
	elseif (x <= 2.7e+48)
		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 <= -6.5e+265)
		tmp = x * y;
	elseif (x <= -5.5e+160)
		tmp = t_0;
	elseif (x <= -3.2e+117)
		tmp = x * y;
	elseif (x <= -1.15e+90)
		tmp = t_0;
	elseif (x <= -1.86e-69)
		tmp = x * y;
	elseif (x <= 1.65e-24)
		tmp = z;
	elseif (x <= 2.7e+48)
		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, -6.5e+265], N[(x * y), $MachinePrecision], If[LessEqual[x, -5.5e+160], t$95$0, If[LessEqual[x, -3.2e+117], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.15e+90], t$95$0, If[LessEqual[x, -1.86e-69], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.65e-24], z, If[LessEqual[x, 2.7e+48], N[(x * y), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.50000000000000034e265 or -5.5e160 < x < -3.20000000000000005e117 or -1.15e90 < x < -1.86e-69 or 1.64999999999999992e-24 < x < 2.70000000000000004e48

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      2. distribute-lft-out-- 97.0%

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

      3. *-rgt-identity 97.0%

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

      4. cancel-sign-sub-inv 97.0%

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

      5. +-commutative 97.0%

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

      6. associate-+r+ 97.0%

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

      7. +-commutative 97.0%

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

      8. *-commutative 97.0%

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

      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. Taylor expanded in y around inf 67.0%

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

   if -6.50000000000000034e265 < x < -5.5e160 or -3.20000000000000005e117 < x < -1.15e90 or 2.70000000000000004e48 < x

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

      2. distribute-lft-out-- 91.0%

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

      3. *-rgt-identity 91.0%

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

      4. cancel-sign-sub-inv 91.0%

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

      5. +-commutative 91.0%

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

      6. associate-+r+ 91.0%

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

      7. +-commutative 91.0%

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

      8. *-commutative 91.0%

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

      9. distribute-rgt-out 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 99.9%

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

   6. Taylor expanded in y around 0 67.0%

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

      1. associate-*r* 67.0%

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

      2. mul-1-neg 67.0%

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

   8. Simplified 67.0%

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

   if -1.86e-69 < x < 1.64999999999999992e-24

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-out-- 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. *-commutative 100.0%

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

      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. Taylor expanded in x around 0 75.8%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+265}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+117}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -1.86 \cdot 10^{-69}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-24}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-68} \lor \neg \left(x \leq 1.2 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e-68) (not (<= x 1.2e-24))) (* x (- y z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e-68) || !(x <= 1.2e-24)) {
		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 <= (-1.7d-68)) .or. (.not. (x <= 1.2d-24))) 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 <= -1.7e-68) || !(x <= 1.2e-24)) {
		tmp = x * (y - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e-68) or not (x <= 1.2e-24):
		tmp = x * (y - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e-68) || !(x <= 1.2e-24))
		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 <= -1.7e-68) || ~((x <= 1.2e-24)))
		tmp = x * (y - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e-68], N[Not[LessEqual[x, 1.2e-24]], $MachinePrecision]], N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000009e-68 or 1.1999999999999999e-24 < x

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. distribute-lft-out-- 93.6%

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

      3. *-rgt-identity 93.6%

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

      4. cancel-sign-sub-inv 93.6%

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

      5. +-commutative 93.6%

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

      6. associate-+r+ 93.6%

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

      7. +-commutative 93.6%

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

      8. *-commutative 93.6%

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

      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. Taylor expanded in x around inf 96.5%

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

   if -1.70000000000000009e-68 < x < 1.1999999999999999e-24

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-out-- 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. *-commutative 100.0%

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

      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. Taylor expanded in x around 0 75.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-68} \lor \neg \left(x \leq 1.2 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+15} \lor \neg \left(x \leq 4.2 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e+15) (not (<= x 4.2e-7))) (* x (- y z)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e+15) || !(x <= 4.2e-7)) {
		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 <= (-9d+15)) .or. (.not. (x <= 4.2d-7))) 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 <= -9e+15) || !(x <= 4.2e-7)) {
		tmp = x * (y - z);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e+15) or not (x <= 4.2e-7):
		tmp = x * (y - z)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e+15) || !(x <= 4.2e-7))
		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 <= -9e+15) || ~((x <= 4.2e-7)))
		tmp = x * (y - z);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e+15], N[Not[LessEqual[x, 4.2e-7]], $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 < -9e15 or 4.2e-7 < x

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

      2. distribute-lft-out-- 92.9%

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

      3. *-rgt-identity 92.9%

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

      4. cancel-sign-sub-inv 92.9%

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

      5. +-commutative 92.9%

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

      6. associate-+r+ 92.9%

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

      7. +-commutative 92.9%

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

      8. *-commutative 92.9%

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

      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. Taylor expanded in x around inf 99.9%

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

   if -9e15 < x < 4.2e-7

   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 99.5%

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

      1. mul-1-neg 99.5%

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

      2. *-commutative 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

   7. Simplified 99.5%

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

      1. *-commutative 99.5%

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

      2. cancel-sign-sub 99.5%

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

      3. *-commutative 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

   9. Applied egg-rr 99.5%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+15} \lor \neg \left(x \leq 4.2 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-68} \lor \neg \left(x \leq 7 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e-68) (not (<= x 7e-24))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e-68) || !(x <= 7e-24)) {
		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 <= (-1.7d-68)) .or. (.not. (x <= 7d-24))) 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 <= -1.7e-68) || !(x <= 7e-24)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e-68) or not (x <= 7e-24):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e-68) || !(x <= 7e-24))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.7e-68) || ~((x <= 7e-24)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e-68], N[Not[LessEqual[x, 7e-24]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000009e-68 or 6.9999999999999993e-24 < x

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. distribute-lft-out-- 93.6%

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

      3. *-rgt-identity 93.6%

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

      4. cancel-sign-sub-inv 93.6%

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

      5. +-commutative 93.6%

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

      6. associate-+r+ 93.6%

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

      7. +-commutative 93.6%

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

      8. *-commutative 93.6%

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

      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. Taylor expanded in y around inf 49.6%

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

   if -1.70000000000000009e-68 < x < 6.9999999999999993e-24

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-out-- 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. *-commutative 100.0%

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

      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. Taylor expanded in x around 0 75.8%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-68} \lor \neg \left(x \leq 7 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

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 96.1%

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

   1. +-commutative 96.1%

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

   2. remove-double-neg 96.1%

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

   3. distribute-rgt-neg-out 96.1%

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

   4. neg-sub0 96.1%

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

   5. neg-sub0 96.1%

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

   6. *-commutative 96.1%

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

   7. distribute-lft-neg-in 96.1%

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

   8. remove-double-neg 96.1%

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

   9. distribute-rgt-out-- 96.1%

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

   10. *-lft-identity 96.1%

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

   11. associate-+l- 96.1%

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

   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 7: 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 96.1%

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

   1. *-commutative 96.1%

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

   2. distribute-lft-out-- 96.1%

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

   3. *-rgt-identity 96.1%

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

   4. cancel-sign-sub-inv 96.1%

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

   5. +-commutative 96.1%

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

   6. associate-+r+ 96.1%

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

   7. +-commutative 96.1%

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

   8. *-commutative 96.1%

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

   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. Taylor expanded in x around 0 32.8%

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

6. Final simplification 32.8%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))