Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Percentage Accurate: 99.9% → 99.8%

Time: 7.1s

Alternatives: 9

Speedup: 1.0×

• 29.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. flip-+ 65.8%

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

   2. clear-num 65.8%

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

   3. fma-neg 65.8%

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

   4. pow2 65.8%

      \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(x, y, -z\right)}{\color{blue}{{\left(x \cdot y\right)}^{2}} - z \cdot z}} \cdot y + t \]

3. Applied egg-rr 65.8%

   \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, -z\right)}{{\left(x \cdot y\right)}^{2} - z \cdot z}}} \cdot y + t \]
4. Step-by-step derivation

   1. clear-num 65.8%

      \[\leadsto \color{blue}{\frac{{\left(x \cdot y\right)}^{2} - z \cdot z}{\mathsf{fma}\left(x, y, -z\right)}} \cdot y + t \]

   2. *-commutative 65.8%

      \[\leadsto \frac{{\color{blue}{\left(y \cdot x\right)}}^{2} - z \cdot z}{\mathsf{fma}\left(x, y, -z\right)} \cdot y + t \]

   3. pow2 65.8%

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

   4. fma-neg 65.8%

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

   5. *-commutative 65.8%

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

   6. flip-+ 99.9%

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

   7. add-sqr-sqrt 51.5%

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

   8. sqrt-prod 77.1%

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

   9. sqr-neg 77.1%

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

   10. sqrt-unprod 36.7%

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

   11. add-sqr-sqrt 75.2%

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

   12. sub-neg 75.2%

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

   13. *-un-lft-identity 75.2%

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

   14. prod-diff 75.2%

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

   15. add-sqr-sqrt 36.7%

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

   16. sqrt-unprod 77.1%

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

   17. sqr-neg 77.1%

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

   18. sqrt-prod 51.5%

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

   19. add-sqr-sqrt 100.0%

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

5. Applied egg-rr 100.0%

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

   1. fma-udef 100.0%

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

   2. *-rgt-identity 100.0%

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

   3. *-rgt-identity 100.0%

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

   4. *-rgt-identity 100.0%

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

   5. fma-neg 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 2: 80.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+140} \lor \neg \left(y \leq -1.1 \cdot 10^{+104} \lor \neg \left(y \leq -1.7 \cdot 10^{+80}\right) \land y \leq 2.5 \cdot 10^{+61}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.8e+140)
         (not
          (or (<= y -1.1e+104) (and (not (<= y -1.7e+80)) (<= y 2.5e+61)))))
   (* y (* y x))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.8e+140) || !((y <= -1.1e+104) || (!(y <= -1.7e+80) && (y <= 2.5e+61)))) {
		tmp = y * (y * x);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.8d+140)) .or. (.not. (y <= (-1.1d+104)) .or. (.not. (y <= (-1.7d+80))) .and. (y <= 2.5d+61))) then
        tmp = y * (y * x)
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.8e+140) || !((y <= -1.1e+104) || (!(y <= -1.7e+80) && (y <= 2.5e+61)))) {
		tmp = y * (y * x);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.8e+140) or not ((y <= -1.1e+104) or (not (y <= -1.7e+80) and (y <= 2.5e+61))):
		tmp = y * (y * x)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.8e+140) || !((y <= -1.1e+104) || (!(y <= -1.7e+80) && (y <= 2.5e+61))))
		tmp = Float64(y * Float64(y * x));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.8e+140) || ~(((y <= -1.1e+104) || (~((y <= -1.7e+80)) && (y <= 2.5e+61)))))
		tmp = y * (y * x);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.8e+140], N[Not[Or[LessEqual[y, -1.1e+104], And[N[Not[LessEqual[y, -1.7e+80]], $MachinePrecision], LessEqual[y, 2.5e+61]]]], $MachinePrecision]], N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999998e140 or -1.1e104 < y < -1.69999999999999996e80 or 2.50000000000000009e61 < y

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 96.4%

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

   5. Taylor expanded in y around inf 81.7%

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

   if -5.7999999999999998e140 < y < -1.1e104 or -1.69999999999999996e80 < y < 2.50000000000000009e61

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.9%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+140} \lor \neg \left(y \leq -1.1 \cdot 10^{+104} \lor \neg \left(y \leq -1.7 \cdot 10^{+80}\right) \land y \leq 2.5 \cdot 10^{+61}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 3: 65.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 122:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* y x))))
   (if (<= y -1.9e-25)
     t_1
     (if (<= y 1.18e-24) t (if (<= y 122.0) (* y z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (y * x);
	double tmp;
	if (y <= -1.9e-25) {
		tmp = t_1;
	} else if (y <= 1.18e-24) {
		tmp = t;
	} else if (y <= 122.0) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (y * x)
    if (y <= (-1.9d-25)) then
        tmp = t_1
    else if (y <= 1.18d-24) then
        tmp = t
    else if (y <= 122.0d0) then
        tmp = y * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (y * x);
	double tmp;
	if (y <= -1.9e-25) {
		tmp = t_1;
	} else if (y <= 1.18e-24) {
		tmp = t;
	} else if (y <= 122.0) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (y * x)
	tmp = 0
	if y <= -1.9e-25:
		tmp = t_1
	elif y <= 1.18e-24:
		tmp = t
	elif y <= 122.0:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(y * x))
	tmp = 0.0
	if (y <= -1.9e-25)
		tmp = t_1;
	elseif (y <= 1.18e-24)
		tmp = t;
	elseif (y <= 122.0)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (y * x);
	tmp = 0.0;
	if (y <= -1.9e-25)
		tmp = t_1;
	elseif (y <= 1.18e-24)
		tmp = t;
	elseif (y <= 122.0)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e-25], t$95$1, If[LessEqual[y, 1.18e-24], t, If[LessEqual[y, 122.0], N[(y * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8999999999999999e-25 or 122 < y

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 85.5%

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

   5. Taylor expanded in y around inf 64.3%

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

   if -1.8999999999999999e-25 < y < 1.18e-24

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 70.7%

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

   if 1.18e-24 < y < 122

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 89.3%

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

   5. Taylor expanded in y around 0 78.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 122:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 4: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-25} \lor \neg \left(y \leq 3.3 \cdot 10^{-22}\right):\\ \;\;\;\;y \cdot \left(y \cdot x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e-25) (not (<= y 3.3e-22)))
   (* y (+ (* y x) z))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e-25) || !(y <= 3.3e-22)) {
		tmp = y * ((y * x) + z);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.8d-25)) .or. (.not. (y <= 3.3d-22))) then
        tmp = y * ((y * x) + z)
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e-25) || !(y <= 3.3e-22)) {
		tmp = y * ((y * x) + z);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e-25) or not (y <= 3.3e-22):
		tmp = y * ((y * x) + z)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e-25) || !(y <= 3.3e-22))
		tmp = Float64(y * Float64(Float64(y * x) + z));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.8e-25) || ~((y <= 3.3e-22)))
		tmp = y * ((y * x) + z);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e-25], N[Not[LessEqual[y, 3.3e-22]], $MachinePrecision]], N[(y * N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e-25 or 3.3000000000000001e-22 < y

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 86.3%

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

   if -1.8e-25 < y < 3.3000000000000001e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-25} \lor \neg \left(y \leq 3.3 \cdot 10^{-22}\right):\\ \;\;\;\;y \cdot \left(y \cdot x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+173} \lor \neg \left(z \leq 52000\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.5e+173) (not (<= z 52000.0)))
   (+ t (* y z))
   (+ t (* x (* y y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e+173) || !(z <= 52000.0)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (x * (y * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.5d+173)) .or. (.not. (z <= 52000.0d0))) then
        tmp = t + (y * z)
    else
        tmp = t + (x * (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e+173) || !(z <= 52000.0)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (x * (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.5e+173) or not (z <= 52000.0):
		tmp = t + (y * z)
	else:
		tmp = t + (x * (y * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.5e+173) || !(z <= 52000.0))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(x * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.5e+173) || ~((z <= 52000.0)))
		tmp = t + (y * z);
	else
		tmp = t + (x * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.5e+173], N[Not[LessEqual[z, 52000.0]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999999e173 or 52000 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.0%

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

   if -3.4999999999999999e173 < z < 52000

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. fma-def 99.9%

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

   4. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. *-commutative 99.9%

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

      3. flip-+ 79.1%

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

      4. unpow2 79.1%

         \[\leadsto \frac{\color{blue}{{\left(x \cdot y\right)}^{2}} - z \cdot z}{x \cdot y - z} \cdot y + t \]

      5. unsub-neg 79.1%

         \[\leadsto \frac{{\left(x \cdot y\right)}^{2} - z \cdot z}{\color{blue}{x \cdot y + \left(-z\right)}} \cdot y + t \]

      6. fma-udef 79.1%

         \[\leadsto \frac{{\left(x \cdot y\right)}^{2} - z \cdot z}{\color{blue}{\mathsf{fma}\left(x, y, -z\right)}} \cdot y + t \]

      7. associate-/r/ 77.9%

         \[\leadsto \color{blue}{\frac{{\left(x \cdot y\right)}^{2} - z \cdot z}{\frac{\mathsf{fma}\left(x, y, -z\right)}{y}}} + t \]

      8. associate-/l* 76.8%

         \[\leadsto \color{blue}{\frac{\left({\left(x \cdot y\right)}^{2} - z \cdot z\right) \cdot y}{\mathsf{fma}\left(x, y, -z\right)}} + t \]

      9. frac-2neg 76.8%

         \[\leadsto \color{blue}{\frac{-\left({\left(x \cdot y\right)}^{2} - z \cdot z\right) \cdot y}{-\mathsf{fma}\left(x, y, -z\right)}} + t \]

   6. Applied egg-rr 76.8%

      \[\leadsto \color{blue}{\frac{y \cdot \left(-{\left(\mathsf{fma}\left(y, x, z\right)\right)}^{2}\right)}{-\mathsf{fma}\left(y, x, z\right)}} + t \]
   7. Step-by-step derivation

      1. distribute-rgt-neg-out 76.8%

         \[\leadsto \frac{\color{blue}{-y \cdot {\left(\mathsf{fma}\left(y, x, z\right)\right)}^{2}}}{-\mathsf{fma}\left(y, x, z\right)} + t \]

      2. distribute-neg-frac 76.8%

         \[\leadsto \color{blue}{\left(-\frac{y \cdot {\left(\mathsf{fma}\left(y, x, z\right)\right)}^{2}}{-\mathsf{fma}\left(y, x, z\right)}\right)} + t \]

      3. associate-/l* 79.0%

         \[\leadsto \left(-\color{blue}{\frac{y}{\frac{-\mathsf{fma}\left(y, x, z\right)}{{\left(\mathsf{fma}\left(y, x, z\right)\right)}^{2}}}}\right) + t \]

      4. distribute-neg-frac 79.0%

         \[\leadsto \color{blue}{\frac{-y}{\frac{-\mathsf{fma}\left(y, x, z\right)}{{\left(\mathsf{fma}\left(y, x, z\right)\right)}^{2}}}} + t \]

      5. distribute-frac-neg 79.0%

         \[\leadsto \frac{-y}{\color{blue}{-\frac{\mathsf{fma}\left(y, x, z\right)}{{\left(\mathsf{fma}\left(y, x, z\right)\right)}^{2}}}} + t \]

      6. unpow2 79.0%

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

      7. associate-/r* 90.3%

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

      8. *-inverses 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 86.4%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} + t \]
   10. Step-by-step derivation

       1. unpow2 86.4%

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

       2. *-commutative 86.4%

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

   11. Simplified 86.4%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot y\right)} + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+173} \lor \neg \left(z \leq 52000\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 6: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+172} \lor \neg \left(z \leq 1200\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e+172) (not (<= z 1200.0)))
   (+ t (* y z))
   (+ t (* y (* y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+172) || !(z <= 1200.0)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (y * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.8d+172)) .or. (.not. (z <= 1200.0d0))) then
        tmp = t + (y * z)
    else
        tmp = t + (y * (y * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+172) || !(z <= 1200.0)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (y * x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e+172) or not (z <= 1200.0):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (y * x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e+172) || !(z <= 1200.0))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(y * Float64(y * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.8e+172) || ~((z <= 1200.0)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (y * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e+172], N[Not[LessEqual[z, 1200.0]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999997e172 or 1200 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.0%

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

   if -3.7999999999999997e172 < z < 1200

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 91.2%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot y + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+172} \lor \neg \left(z \leq 1200\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 8: 51.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+85}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e+85) (* y z) (if (<= z 1.38e+45) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+85) {
		tmp = y * z;
	} else if (z <= 1.38e+45) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.9d+85)) then
        tmp = y * z
    else if (z <= 1.38d+45) then
        tmp = t
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+85) {
		tmp = y * z;
	} else if (z <= 1.38e+45) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e+85:
		tmp = y * z
	elif z <= 1.38e+45:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e+85)
		tmp = Float64(y * z);
	elseif (z <= 1.38e+45)
		tmp = t;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.9e+85)
		tmp = y * z;
	elseif (z <= 1.38e+45)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e+85], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.38e+45], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999997e85 or 1.3799999999999999e45 < z

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 77.8%

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

   5. Taylor expanded in y around 0 61.3%

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

   if -2.89999999999999997e85 < z < 1.3799999999999999e45

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

      2. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 50.0%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+85}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 9: 37.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 99.9%

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

   1. fma-def 99.9%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around 0 40.4%

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

5. Final simplification 40.4%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))