Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 8

Speedup: 1.0×

• 20.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 60.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+269}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+242}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+175}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+79}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-20}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+142}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -1.55e+269)
     (* y z)
     (if (<= z -2.15e+242)
       t_0
       (if (<= z -1.65e+175)
         (* y z)
         (if (<= z -6.2e+79)
           t_0
           (if (<= z -3e-20)
             (* y z)
             (if (<= z 1.0) x (if (<= z 1.35e+142) t_0 (* y z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -1.55e+269) {
		tmp = y * z;
	} else if (z <= -2.15e+242) {
		tmp = t_0;
	} else if (z <= -1.65e+175) {
		tmp = y * z;
	} else if (z <= -6.2e+79) {
		tmp = t_0;
	} else if (z <= -3e-20) {
		tmp = y * z;
	} else if (z <= 1.0) {
		tmp = x;
	} else if (z <= 1.35e+142) {
		tmp = t_0;
	} else {
		tmp = y * 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) :: t_0
    real(8) :: tmp
    t_0 = x * -z
    if (z <= (-1.55d+269)) then
        tmp = y * z
    else if (z <= (-2.15d+242)) then
        tmp = t_0
    else if (z <= (-1.65d+175)) then
        tmp = y * z
    else if (z <= (-6.2d+79)) then
        tmp = t_0
    else if (z <= (-3d-20)) then
        tmp = y * z
    else if (z <= 1.0d0) then
        tmp = x
    else if (z <= 1.35d+142) then
        tmp = t_0
    else
        tmp = y * z
    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 (z <= -1.55e+269) {
		tmp = y * z;
	} else if (z <= -2.15e+242) {
		tmp = t_0;
	} else if (z <= -1.65e+175) {
		tmp = y * z;
	} else if (z <= -6.2e+79) {
		tmp = t_0;
	} else if (z <= -3e-20) {
		tmp = y * z;
	} else if (z <= 1.0) {
		tmp = x;
	} else if (z <= 1.35e+142) {
		tmp = t_0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -1.55e+269:
		tmp = y * z
	elif z <= -2.15e+242:
		tmp = t_0
	elif z <= -1.65e+175:
		tmp = y * z
	elif z <= -6.2e+79:
		tmp = t_0
	elif z <= -3e-20:
		tmp = y * z
	elif z <= 1.0:
		tmp = x
	elif z <= 1.35e+142:
		tmp = t_0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -1.55e+269)
		tmp = Float64(y * z);
	elseif (z <= -2.15e+242)
		tmp = t_0;
	elseif (z <= -1.65e+175)
		tmp = Float64(y * z);
	elseif (z <= -6.2e+79)
		tmp = t_0;
	elseif (z <= -3e-20)
		tmp = Float64(y * z);
	elseif (z <= 1.0)
		tmp = x;
	elseif (z <= 1.35e+142)
		tmp = t_0;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -1.55e+269)
		tmp = y * z;
	elseif (z <= -2.15e+242)
		tmp = t_0;
	elseif (z <= -1.65e+175)
		tmp = y * z;
	elseif (z <= -6.2e+79)
		tmp = t_0;
	elseif (z <= -3e-20)
		tmp = y * z;
	elseif (z <= 1.0)
		tmp = x;
	elseif (z <= 1.35e+142)
		tmp = t_0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.55e+269], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.15e+242], t$95$0, If[LessEqual[z, -1.65e+175], N[(y * z), $MachinePrecision], If[LessEqual[z, -6.2e+79], t$95$0, If[LessEqual[z, -3e-20], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.0], x, If[LessEqual[z, 1.35e+142], t$95$0, N[(y * z), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000001e269 or -2.1500000000000002e242 < z < -1.6500000000000001e175 or -6.1999999999999998e79 < z < -3.00000000000000029e-20 or 1.34999999999999991e142 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 97.2%

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

   4. Applied egg-rr 97.2%

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

      1. associate-+r+ 97.2%

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

      2. distribute-rgt-neg-out 97.2%

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

      3. unsub-neg 97.2%

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

      4. +-commutative 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around inf 70.9%

      \[\leadsto \color{blue}{y \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 70.9%

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

   9. Simplified 70.9%

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

   if -1.55000000000000001e269 < z < -2.1500000000000002e242 or -1.6500000000000001e175 < z < -6.1999999999999998e79 or 1 < z < 1.34999999999999991e142

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   5. Simplified 65.5%

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

      1. sub-neg 65.5%

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

      2. distribute-rgt-in 65.5%

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

      3. *-un-lft-identity 65.5%

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

      4. distribute-lft-neg-in 65.5%

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

      5. unsub-neg 65.5%

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

   7. Applied egg-rr 65.5%

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

   8. Taylor expanded in z around inf 64.0%

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

      1. mul-1-neg 64.0%

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

      2. distribute-rgt-neg-out 64.0%

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

   10. Simplified 64.0%

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

   if -3.00000000000000029e-20 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 70.6%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+269}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+175}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-20}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+109} \lor \neg \left(y \leq -5.4 \cdot 10^{+74} \lor \neg \left(y \leq -1.8 \cdot 10^{+24}\right) \land y \leq 1.02 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.28e+109)
         (not
          (or (<= y -5.4e+74) (and (not (<= y -1.8e+24)) (<= y 1.02e-20)))))
   (* y z)
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.28e+109) || !((y <= -5.4e+74) || (!(y <= -1.8e+24) && (y <= 1.02e-20)))) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - 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 ((y <= (-1.28d+109)) .or. (.not. (y <= (-5.4d+74)) .or. (.not. (y <= (-1.8d+24))) .and. (y <= 1.02d-20))) then
        tmp = y * z
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.28e+109) || !((y <= -5.4e+74) || (!(y <= -1.8e+24) && (y <= 1.02e-20)))) {
		tmp = y * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.28e+109) or not ((y <= -5.4e+74) or (not (y <= -1.8e+24) and (y <= 1.02e-20))):
		tmp = y * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.28e+109) || !((y <= -5.4e+74) || (!(y <= -1.8e+24) && (y <= 1.02e-20))))
		tmp = Float64(y * z);
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.28e+109) || ~(((y <= -5.4e+74) || (~((y <= -1.8e+24)) && (y <= 1.02e-20)))))
		tmp = y * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.28e+109], N[Not[Or[LessEqual[y, -5.4e+74], And[N[Not[LessEqual[y, -1.8e+24]], $MachinePrecision], LessEqual[y, 1.02e-20]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.28e109 or -5.3999999999999996e74 < y < -1.79999999999999992e24 or 1.02000000000000001e-20 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 97.2%

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

   4. Applied egg-rr 97.2%

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

      1. associate-+r+ 97.2%

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

      2. distribute-rgt-neg-out 97.2%

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

      3. unsub-neg 97.2%

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

      4. +-commutative 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around inf 76.4%

      \[\leadsto \color{blue}{y \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 76.4%

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

   9. Simplified 76.4%

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

   if -1.28e109 < y < -5.3999999999999996e74 or -1.79999999999999992e24 < y < 1.02000000000000001e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+109} \lor \neg \left(y \leq -5.4 \cdot 10^{+74} \lor \neg \left(y \leq -1.8 \cdot 10^{+24}\right) \land y \leq 1.02 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-108} \lor \neg \left(z \leq 62\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e-108) (not (<= z 62.0))) (* (- y x) z) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e-108) || !(z <= 62.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - 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 ((z <= (-1.5d-108)) .or. (.not. (z <= 62.0d0))) then
        tmp = (y - x) * z
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e-108) || !(z <= 62.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e-108) or not (z <= 62.0):
		tmp = (y - x) * z
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e-108) || !(z <= 62.0))
		tmp = Float64(Float64(y - x) * z);
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5e-108) || ~((z <= 62.0)))
		tmp = (y - x) * z;
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e-108], N[Not[LessEqual[z, 62.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999996e-108 or 62 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 98.1%

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

   4. Applied egg-rr 98.1%

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

      1. associate-+r+ 98.1%

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

      2. distribute-rgt-neg-out 98.1%

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

      3. unsub-neg 98.1%

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

      4. +-commutative 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in z around inf 92.3%

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

   if -1.49999999999999996e-108 < z < 62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-108} \lor \neg \left(z \leq 62\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e+24) (not (<= z 1.0))) (* (- y x) z) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+24) || !(z <= 1.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * 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 ((z <= (-1.5d+24)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y - x) * z
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+24) || !(z <= 1.0)) {
		tmp = (y - x) * z;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e+24) or not (z <= 1.0):
		tmp = (y - x) * z
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e+24) || !(z <= 1.0))
		tmp = Float64(Float64(y - x) * z);
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5e+24) || ~((z <= 1.0)))
		tmp = (y - x) * z;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e+24], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999997e24 or 1 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 97.7%

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

   4. Applied egg-rr 97.7%

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

      1. associate-+r+ 97.7%

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

      2. distribute-rgt-neg-out 97.7%

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

      3. unsub-neg 97.7%

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

      4. +-commutative 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in z around inf 99.2%

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

   if -1.49999999999999997e24 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 97.8%

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

      1. *-commutative 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-20} \lor \neg \left(z \leq 10^{-37}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6e-20) (not (<= z 1e-37))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e-20) || !(z <= 1e-37)) {
		tmp = y * z;
	} else {
		tmp = 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 ((z <= (-6d-20)) .or. (.not. (z <= 1d-37))) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6e-20) || !(z <= 1e-37)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6e-20) or not (z <= 1e-37):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6e-20) || !(z <= 1e-37))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6e-20) || ~((z <= 1e-37)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6e-20], N[Not[LessEqual[z, 1e-37]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000057e-20 or 1.00000000000000007e-37 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 97.9%

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

   4. Applied egg-rr 97.9%

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

      1. associate-+r+ 97.9%

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

      2. distribute-rgt-neg-out 97.9%

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

      3. unsub-neg 97.9%

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

      4. +-commutative 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in y around inf 53.3%

      \[\leadsto \color{blue}{y \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 53.3%

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

   9. Simplified 53.3%

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

   if -6.00000000000000057e-20 < z < 1.00000000000000007e-37

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 73.0%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-20} \lor \neg \left(z \leq 10^{-37}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 8: 35.5% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around 0 33.7%

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

4. Final simplification 33.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024054 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))