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

Percentage Accurate: 99.9% → 99.9%

Time: 6.0s

Alternatives: 6

Speedup: 1.3×

• 29.1% 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: 99.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lower-fma.f64 100.0

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

   4. lift-+.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ t_2 := \mathsf{fma}\left(x, y, z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+144}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)) (t_2 (* (fma x y z) y)))
   (if (<= t_1 -2e+30) t_2 (if (<= t_1 1e+144) (fma z y t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double t_2 = fma(x, y, z) * y;
	double tmp;
	if (t_1 <= -2e+30) {
		tmp = t_2;
	} else if (t_1 <= 1e+144) {
		tmp = fma(z, y, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	t_2 = Float64(fma(x, y, z) * y)
	tmp = 0.0
	if (t_1 <= -2e+30)
		tmp = t_2;
	elseif (t_1 <= 1e+144)
		tmp = fma(z, y, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y + z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+30], t$95$2, If[LessEqual[t$95$1, 1e+144], N[(z * y + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -2e30 or 1.00000000000000002e144 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 95.0

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

   5. Applied rewrites 95.0%

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

   if -2e30 < (*.f64 (+.f64 (*.f64 x y) z) y) < 1.00000000000000002e144

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 94.1

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

   5. Applied rewrites 94.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ t_2 := \left(x \cdot y\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+144}:\\ \;\;\;\;\mathsf{fma}\left(z, y, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)) (t_2 (* (* x y) y)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 1e+144) (fma z y t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double t_2 = (x * y) * y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+144) {
		tmp = fma(z, y, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	t_2 = Float64(Float64(x * y) * y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+144)
		tmp = fma(z, y, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+144], N[(z * y + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -inf.0 or 1.00000000000000002e144 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 98.8

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \left(x \cdot y\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 83.6%

      \[\leadsto \left(x \cdot y\right) \cdot y \]

   if -inf.0 < (*.f64 (+.f64 (*.f64 x y) z) y) < 1.00000000000000002e144

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 87.3

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

   5. Applied rewrites 87.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 52.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+69}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+154}:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)))
   (if (<= t_1 -2e+69) (* z y) (if (<= t_1 5e+154) (* 1.0 t) (* z y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if (t_1 <= -2e+69) {
		tmp = z * y;
	} else if (t_1 <= 5e+154) {
		tmp = 1.0 * t;
	} else {
		tmp = z * 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) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) + z) * y
    if (t_1 <= (-2d+69)) then
        tmp = z * y
    else if (t_1 <= 5d+154) then
        tmp = 1.0d0 * t
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if (t_1 <= -2e+69) {
		tmp = z * y;
	} else if (t_1 <= 5e+154) {
		tmp = 1.0 * t;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * y) + z) * y
	tmp = 0
	if t_1 <= -2e+69:
		tmp = z * y
	elif t_1 <= 5e+154:
		tmp = 1.0 * t
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	tmp = 0.0
	if (t_1 <= -2e+69)
		tmp = Float64(z * y);
	elseif (t_1 <= 5e+154)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * y) + z) * y;
	tmp = 0.0;
	if (t_1 <= -2e+69)
		tmp = z * y;
	elseif (t_1 <= 5e+154)
		tmp = 1.0 * t;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+69], N[(z * y), $MachinePrecision], If[LessEqual[t$95$1, 5e+154], N[(1.0 * t), $MachinePrecision], N[(z * y), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -2.0000000000000001e69 or 5.00000000000000004e154 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 35.2

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

   5. Applied rewrites 35.2%

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

   if -2.0000000000000001e69 < (*.f64 (+.f64 (*.f64 x y) z) y) < 5.00000000000000004e154

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 100.0

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in t around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. sub-neg N/A

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

      6. associate-/l* N/A

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

      7. associate-*r* N/A

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

      8. metadata-eval N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-fma.f64 93.5

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

   7. Applied rewrites 93.5%

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

   8. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 93.5

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

   10. Applied rewrites 93.5%

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

   11. Taylor expanded in t around inf

       \[\leadsto 1 \cdot t \]
   12. Step-by-step derivation

   13. Applied rewrites 75.4%

       \[\leadsto 1 \cdot t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 65.9% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 66.4

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

5. Applied rewrites 66.4%

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

Alternative 6: 29.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ z \cdot y \end{array} \]

FPCore

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

C

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

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 = z * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 25.9

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

5. Applied rewrites 25.9%

   \[\leadsto \color{blue}{z \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024249 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))