Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.1% → 96.4%

Time: 11.0s

Alternatives: 21

Speedup: 1.2×

• 36.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (- b z) y (+ (fma (- t 2.0) b z) (fma (- 1.0 t) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((b - z), y, (fma((t - 2.0), b, z) + fma((1.0 - t), a, x)));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(b - z), y, Float64(fma(Float64(t - 2.0), b, z) + fma(Float64(1.0 - t), a, x)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(b - z), $MachinePrecision] * y + N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.1%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

5. Applied rewrites 97.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)\right)} \]
6. Add Preprocessing

Alternative 2: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-292}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -9.2e+125)
     t_1
     (if (<= b -1.8e+86)
       (* (- b a) t)
       (if (<= b -1.95e-292)
         (fma (- 1.0 y) z (+ a x))
         (if (<= b 2.65e+150) (+ (fma (- 1.0 t) a z) x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -9.2e+125) {
		tmp = t_1;
	} else if (b <= -1.8e+86) {
		tmp = (b - a) * t;
	} else if (b <= -1.95e-292) {
		tmp = fma((1.0 - y), z, (a + x));
	} else if (b <= 2.65e+150) {
		tmp = fma((1.0 - t), a, z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -9.2e+125)
		tmp = t_1;
	elseif (b <= -1.8e+86)
		tmp = Float64(Float64(b - a) * t);
	elseif (b <= -1.95e-292)
		tmp = fma(Float64(1.0 - y), z, Float64(a + x));
	elseif (b <= 2.65e+150)
		tmp = Float64(fma(Float64(1.0 - t), a, z) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9.2e+125], t$95$1, If[LessEqual[b, -1.8e+86], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[b, -1.95e-292], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.65e+150], N[(N[(N[(1.0 - t), $MachinePrecision] * a + z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.20000000000000051e125 or 2.65000000000000007e150 < b

   1. Initial program 86.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 89.4

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 89.4%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   if -9.20000000000000051e125 < b < -1.80000000000000003e86

   1. Initial program 71.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 100.0

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -1.80000000000000003e86 < b < -1.95e-292

   1. Initial program 98.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 86.7%

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

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 76.0%

       \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]

   if -1.95e-292 < b < 2.65000000000000007e150

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) + x} \]

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - \color{blue}{\left(-1 \cdot z - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)}\right) + x \]

      4. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} + x \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right) + x\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} \]

      7. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(t - 2\right) \cdot b} + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{1} \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{z}\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right)\right) \]

      18. fp-cancel-sign-sub-inv N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)} \]

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.8%

      \[\leadsto \mathsf{fma}\left(1 - t, a, z\right) + \color{blue}{x} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -26 \lor \neg \left(t \leq 7 \cdot 10^{+112}\right):\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -26.0) (not (<= t 7e+112)))
   (+ (fma (- t 2.0) b z) (fma (- 1.0 t) a x))
   (fma (- y 2.0) b (- x (fma (- y 1.0) z (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -26.0) || !(t <= 7e+112)) {
		tmp = fma((t - 2.0), b, z) + fma((1.0 - t), a, x);
	} else {
		tmp = fma((y - 2.0), b, (x - fma((y - 1.0), z, -a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -26.0) || !(t <= 7e+112))
		tmp = Float64(fma(Float64(t - 2.0), b, z) + fma(Float64(1.0 - t), a, x));
	else
		tmp = fma(Float64(y - 2.0), b, Float64(x - fma(Float64(y - 1.0), z, Float64(-a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -26.0], N[Not[LessEqual[t, 7e+112]], $MachinePrecision]], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -26 or 6.99999999999999994e112 < t

   1. Initial program 94.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) + x} \]

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - \color{blue}{\left(-1 \cdot z - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)}\right) + x \]

      4. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} + x \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right) + x\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} \]

      7. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(t - 2\right) \cdot b} + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{1} \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{z}\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right)\right) \]

      18. fp-cancel-sign-sub-inv N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 85.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)} \]

   if -26 < t < 6.99999999999999994e112

   1. Initial program 93.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(y - 2\right) \cdot b} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y - 2, b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -1 \cdot a\right)}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(\color{blue}{y - 1}, z, -1 \cdot a\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{\mathsf{neg}\left(a\right)}\right)\right) \]

      12. lower-neg.f64 91.3

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{-a}\right)\right) \]

   5. Applied rewrites 91.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -26 \lor \neg \left(t \leq 7 \cdot 10^{+112}\right):\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -4.25 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-180}:\\ \;\;\;\;\mathsf{fma}\left(1, z, a + x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -4.25e+46)
     t_1
     (if (<= t -2.2e-60)
       (* (- b z) y)
       (if (<= t 2.45e-180)
         (fma 1.0 z (+ a x))
         (if (<= t 5e+117) (fma (- 1.0 y) z x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -4.25e+46) {
		tmp = t_1;
	} else if (t <= -2.2e-60) {
		tmp = (b - z) * y;
	} else if (t <= 2.45e-180) {
		tmp = fma(1.0, z, (a + x));
	} else if (t <= 5e+117) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -4.25e+46)
		tmp = t_1;
	elseif (t <= -2.2e-60)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 2.45e-180)
		tmp = fma(1.0, z, Float64(a + x));
	elseif (t <= 5e+117)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.25e+46], t$95$1, If[LessEqual[t, -2.2e-60], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 2.45e-180], N[(1.0 * z + N[(a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+117], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.2499999999999998e46 or 4.99999999999999983e117 < t

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 77.0

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 77.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -4.2499999999999998e46 < t < -2.1999999999999999e-60

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.1

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

   5. Applied rewrites 54.1%

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

   if -2.1999999999999999e-60 < t < 2.4500000000000001e-180

   1. Initial program 96.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 66.5%

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

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 66.5%

       \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]

   12. Taylor expanded in y around 0

       \[\leadsto \mathsf{fma}\left(1, z, a + x\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 56.1%

       \[\leadsto \mathsf{fma}\left(1, z, a + x\right) \]

   if 2.4500000000000001e-180 < t < 4.99999999999999983e117

   1. Initial program 87.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 96.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 69.5%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 63.4%

       \[\leadsto \mathsf{fma}\left(1 - y, z, x\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 87.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+104} \lor \neg \left(b \leq 9.8 \cdot 10^{+66}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.6e+104) (not (<= b 9.8e+66)))
   (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))
   (fma (- 1.0 y) z (fma (- 1.0 t) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+104) || !(b <= 9.8e+66)) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.6e+104) || !(b <= 9.8e+66))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.6e+104], N[Not[LessEqual[b, 9.8e+66]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.60000000000000001e104 or 9.7999999999999995e66 < b

   1. Initial program 87.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right) + x\right) + b \cdot \left(\left(t + y\right) - 2\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} + b \cdot \left(\left(t + y\right) - 2\right) \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + b \cdot \left(\left(t + y\right) - 2\right) \]

      6. associate-+l- N/A

         \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) - b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. distribute-lft-out-- N/A

         \[\leadsto x - \left(\color{blue}{\left(a \cdot t - a \cdot 1\right)} - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x - \left(\left(a \cdot t - \color{blue}{1 \cdot a}\right) - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto x - \left(\color{blue}{\left(a \cdot t + \left(\mathsf{neg}\left(1\right)\right) \cdot a\right)} - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto x - \left(\left(a \cdot t + \color{blue}{-1} \cdot a\right) - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto x - \left(\color{blue}{\left(-1 \cdot a + a \cdot t\right)} - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto x - \left(\left(-1 \cdot a + \color{blue}{1 \cdot \left(a \cdot t\right)}\right) - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto x - \left(\left(-1 \cdot a + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot \left(a \cdot t\right)\right) - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto x - \left(\color{blue}{\left(-1 \cdot a - -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. distribute-lft-out-- N/A

          \[\leadsto x - \left(\color{blue}{-1 \cdot \left(a - a \cdot t\right)} - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. *-rgt-identity N/A

          \[\leadsto x - \left(-1 \cdot \left(\color{blue}{a \cdot 1} - a \cdot t\right) - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      17. distribute-lft-out-- N/A

          \[\leadsto x - \left(-1 \cdot \color{blue}{\left(a \cdot \left(1 - t\right)\right)} - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      18. mul-1-neg N/A

          \[\leadsto x - \left(\color{blue}{\left(\mathsf{neg}\left(a \cdot \left(1 - t\right)\right)\right)} - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      19. distribute-lft-neg-out N/A

          \[\leadsto x - \left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right) \cdot \left(1 - t\right)} - b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   5. Applied rewrites 90.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   if -3.60000000000000001e104 < b < 9.7999999999999995e66

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 86.7%

      \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, \mathsf{fma}\left(1 - t, a, x\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+104} \lor \neg \left(b \leq 9.8 \cdot 10^{+66}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 40.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-a, t, a\right)\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+126}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-306}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- a) t a)))
   (if (<= b -6.4e+126)
     (* (- y 2.0) b)
     (if (<= b -2.6e+57)
       t_1
       (if (<= b -2.65e-306)
         (* (- 1.0 y) z)
         (if (<= b 2.6e+47) t_1 (* (- t 2.0) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-a, t, a);
	double tmp;
	if (b <= -6.4e+126) {
		tmp = (y - 2.0) * b;
	} else if (b <= -2.6e+57) {
		tmp = t_1;
	} else if (b <= -2.65e-306) {
		tmp = (1.0 - y) * z;
	} else if (b <= 2.6e+47) {
		tmp = t_1;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-a), t, a)
	tmp = 0.0
	if (b <= -6.4e+126)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= -2.6e+57)
		tmp = t_1;
	elseif (b <= -2.65e-306)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (b <= 2.6e+47)
		tmp = t_1;
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t + a), $MachinePrecision]}, If[LessEqual[b, -6.4e+126], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -2.6e+57], t$95$1, If[LessEqual[b, -2.65e-306], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, 2.6e+47], t$95$1, N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.3999999999999995e126

   1. Initial program 85.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(y - 2\right) \cdot b} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y - 2, b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -1 \cdot a\right)}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(\color{blue}{y - 1}, z, -1 \cdot a\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{\mathsf{neg}\left(a\right)}\right)\right) \]

      12. lower-neg.f64 71.2

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{-a}\right)\right) \]

   5. Applied rewrites 71.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y - 2\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 69.5%

      \[\leadsto \left(y - 2\right) \cdot \color{blue}{b} \]

   if -6.3999999999999995e126 < b < -2.6e57 or -2.6499999999999999e-306 < b < 2.60000000000000003e47

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      3. lower--.f64 40.4

         \[\leadsto \color{blue}{\left(1 - t\right)} \cdot a \]

   5. Applied rewrites 40.4%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 40.4%

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

   if -2.6e57 < b < -2.6499999999999999e-306

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.1

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

   5. Applied rewrites 51.1%

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

   if 2.60000000000000003e47 < b

   1. Initial program 90.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 72.6

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 72.6%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 47.9%

       \[\leadsto \left(t - 2\right) \cdot b \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 82.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+104} \lor \neg \left(b \leq 2.65 \cdot 10^{+150}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.5e+104) (not (<= b 2.65e+150)))
   (* (- (+ t y) 2.0) b)
   (fma (- 1.0 y) z (fma (- 1.0 t) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.5e+104) || !(b <= 2.65e+150)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.5e+104) || !(b <= 2.65e+150))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.5e+104], N[Not[LessEqual[b, 2.65e+150]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.50000000000000017e104 or 2.65000000000000007e150 < b

   1. Initial program 86.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 92.5%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 87.9

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 87.9%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   if -5.50000000000000017e104 < b < 2.65000000000000007e150

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.4%

      \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, \mathsf{fma}\left(1 - t, a, x\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+104} \lor \neg \left(b \leq 2.65 \cdot 10^{+150}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-220}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \left(1 - t\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -5e+104)
     t_1
     (if (<= b 1.3e-220)
       (fma (- 1.0 y) z (* (- 1.0 t) a))
       (if (<= b 2.65e+150) (+ (fma (- 1.0 t) a z) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -5e+104) {
		tmp = t_1;
	} else if (b <= 1.3e-220) {
		tmp = fma((1.0 - y), z, ((1.0 - t) * a));
	} else if (b <= 2.65e+150) {
		tmp = fma((1.0 - t), a, z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -5e+104)
		tmp = t_1;
	elseif (b <= 1.3e-220)
		tmp = fma(Float64(1.0 - y), z, Float64(Float64(1.0 - t) * a));
	elseif (b <= 2.65e+150)
		tmp = Float64(fma(Float64(1.0 - t), a, z) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5e+104], t$95$1, If[LessEqual[b, 1.3e-220], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.65e+150], N[(N[(N[(1.0 - t), $MachinePrecision] * a + z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.9999999999999997e104 or 2.65000000000000007e150 < b

   1. Initial program 86.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 92.5%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 87.9

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 87.9%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   if -4.9999999999999997e104 < b < 1.3e-220

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 89.4%

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

   9. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(1 - y, z, a \cdot \left(1 - t\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 77.8%

       \[\leadsto \mathsf{fma}\left(1 - y, z, \left(1 - t\right) \cdot a\right) \]

   if 1.3e-220 < b < 2.65000000000000007e150

   1. Initial program 97.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) + x} \]

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - \color{blue}{\left(-1 \cdot z - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)}\right) + x \]

      4. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} + x \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right) + x\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} \]

      7. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(t - 2\right) \cdot b} + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{1} \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{z}\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

      15. distribute-lft-out-- N/A

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right)\right) \]

      18. fp-cancel-sign-sub-inv N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)} \]

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 67.9%

      \[\leadsto \mathsf{fma}\left(1 - t, a, z\right) + \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 67.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -9.2e+125)
     t_1
     (if (<= b -1.8e+86)
       (* (- b a) t)
       (if (<= b 2.65e+150) (fma (- 1.0 y) z (+ a x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -9.2e+125) {
		tmp = t_1;
	} else if (b <= -1.8e+86) {
		tmp = (b - a) * t;
	} else if (b <= 2.65e+150) {
		tmp = fma((1.0 - y), z, (a + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -9.2e+125)
		tmp = t_1;
	elseif (b <= -1.8e+86)
		tmp = Float64(Float64(b - a) * t);
	elseif (b <= 2.65e+150)
		tmp = fma(Float64(1.0 - y), z, Float64(a + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9.2e+125], t$95$1, If[LessEqual[b, -1.8e+86], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[b, 2.65e+150], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.20000000000000051e125 or 2.65000000000000007e150 < b

   1. Initial program 86.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 89.4

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 89.4%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   if -9.20000000000000051e125 < b < -1.80000000000000003e86

   1. Initial program 71.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 100.0

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -1.80000000000000003e86 < b < 2.65000000000000007e150

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.1%

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

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 67.4%

       \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 60.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -9.2e+125)
     t_1
     (if (<= b -1.8e+86)
       (* (- b a) t)
       (if (<= b 2.65e+150) (fma (- 1.0 y) z x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -9.2e+125) {
		tmp = t_1;
	} else if (b <= -1.8e+86) {
		tmp = (b - a) * t;
	} else if (b <= 2.65e+150) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -9.2e+125)
		tmp = t_1;
	elseif (b <= -1.8e+86)
		tmp = Float64(Float64(b - a) * t);
	elseif (b <= 2.65e+150)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9.2e+125], t$95$1, If[LessEqual[b, -1.8e+86], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[b, 2.65e+150], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.20000000000000051e125 or 2.65000000000000007e150 < b

   1. Initial program 86.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 89.4

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 89.4%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   if -9.20000000000000051e125 < b < -1.80000000000000003e86

   1. Initial program 71.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 100.0

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -1.80000000000000003e86 < b < 2.65000000000000007e150

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.1%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 55.3%

       \[\leadsto \mathsf{fma}\left(1 - y, z, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 55.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -4.25 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-175}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -4.25e+46)
     t_1
     (if (<= t -1.22e-175)
       (* (- b z) y)
       (if (<= t 5e+117) (fma (- 1.0 y) z x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -4.25e+46) {
		tmp = t_1;
	} else if (t <= -1.22e-175) {
		tmp = (b - z) * y;
	} else if (t <= 5e+117) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -4.25e+46)
		tmp = t_1;
	elseif (t <= -1.22e-175)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 5e+117)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.25e+46], t$95$1, If[LessEqual[t, -1.22e-175], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 5e+117], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2499999999999998e46 or 4.99999999999999983e117 < t

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 77.0

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 77.0%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -4.2499999999999998e46 < t < -1.2200000000000001e-175

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 48.1

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

   5. Applied rewrites 48.1%

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

   if -1.2200000000000001e-175 < t < 4.99999999999999983e117

   1. Initial program 93.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 98.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.1%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 56.1%

       \[\leadsto \mathsf{fma}\left(1 - y, z, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 47.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -0.039:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-291}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+111}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -0.039)
     t_1
     (if (<= t 4.5e-291)
       (* (- y 2.0) b)
       (if (<= t 4.5e+111) (* (- 1.0 y) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -0.039) {
		tmp = t_1;
	} else if (t <= 4.5e-291) {
		tmp = (y - 2.0) * b;
	} else if (t <= 4.5e+111) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-0.039d0)) then
        tmp = t_1
    else if (t <= 4.5d-291) then
        tmp = (y - 2.0d0) * b
    else if (t <= 4.5d+111) then
        tmp = (1.0d0 - 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 a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -0.039) {
		tmp = t_1;
	} else if (t <= 4.5e-291) {
		tmp = (y - 2.0) * b;
	} else if (t <= 4.5e+111) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -0.039:
		tmp = t_1
	elif t <= 4.5e-291:
		tmp = (y - 2.0) * b
	elif t <= 4.5e+111:
		tmp = (1.0 - y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -0.039)
		tmp = t_1;
	elseif (t <= 4.5e-291)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 4.5e+111)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -0.039)
		tmp = t_1;
	elseif (t <= 4.5e-291)
		tmp = (y - 2.0) * b;
	elseif (t <= 4.5e+111)
		tmp = (1.0 - y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -0.039], t$95$1, If[LessEqual[t, 4.5e-291], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 4.5e+111], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.0389999999999999999 or 4.50000000000000001e111 < t

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 73.4

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 73.4%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -0.0389999999999999999 < t < 4.49999999999999974e-291

   1. Initial program 96.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(y - 2\right) \cdot b} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y - 2, b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -1 \cdot a\right)}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(\color{blue}{y - 1}, z, -1 \cdot a\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{\mathsf{neg}\left(a\right)}\right)\right) \]

      12. lower-neg.f64 96.1

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{-a}\right)\right) \]

   5. Applied rewrites 96.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y - 2\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 39.6%

      \[\leadsto \left(y - 2\right) \cdot \color{blue}{b} \]

   if 4.49999999999999974e-291 < t < 4.50000000000000001e111

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.4

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

   5. Applied rewrites 44.4%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 39.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 2.0) b)))
   (if (<= b -6.4e+126)
     t_1
     (if (<= b 1e+47) (fma (- a) t a) (if (<= b 2.1e+227) t_1 (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double tmp;
	if (b <= -6.4e+126) {
		tmp = t_1;
	} else if (b <= 1e+47) {
		tmp = fma(-a, t, a);
	} else if (b <= 2.1e+227) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 2.0) * b)
	tmp = 0.0
	if (b <= -6.4e+126)
		tmp = t_1;
	elseif (b <= 1e+47)
		tmp = fma(Float64(-a), t, a);
	elseif (b <= 2.1e+227)
		tmp = t_1;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -6.4e+126], t$95$1, If[LessEqual[b, 1e+47], N[((-a) * t + a), $MachinePrecision], If[LessEqual[b, 2.1e+227], t$95$1, N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.3999999999999995e126 or 1e47 < b < 2.10000000000000019e227

   1. Initial program 87.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(y - 2\right) \cdot b} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y - 2, b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -1 \cdot a\right)}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(\color{blue}{y - 1}, z, -1 \cdot a\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{\mathsf{neg}\left(a\right)}\right)\right) \]

      12. lower-neg.f64 72.3

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{-a}\right)\right) \]

   5. Applied rewrites 72.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y - 2\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.4%

      \[\leadsto \left(y - 2\right) \cdot \color{blue}{b} \]

   if -6.3999999999999995e126 < b < 1e47

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      3. lower--.f64 34.0

         \[\leadsto \color{blue}{\left(1 - t\right)} \cdot a \]

   5. Applied rewrites 34.0%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 34.0%

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

   if 2.10000000000000019e227 < b

   1. Initial program 92.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 90.6

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 90.6%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   10. Step-by-step derivation

   11. Applied rewrites 66.8%

       \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 50.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.25 \cdot 10^{+46} \lor \neg \left(t \leq 7 \cdot 10^{+112}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.25e+46) (not (<= t 7e+112))) (* (- b a) t) (* (- b z) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.25e+46) || !(t <= 7e+112)) {
		tmp = (b - a) * t;
	} else {
		tmp = (b - z) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.25d+46)) .or. (.not. (t <= 7d+112))) then
        tmp = (b - a) * t
    else
        tmp = (b - z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.25e+46) || !(t <= 7e+112)) {
		tmp = (b - a) * t;
	} else {
		tmp = (b - z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.25e+46) or not (t <= 7e+112):
		tmp = (b - a) * t
	else:
		tmp = (b - z) * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.25e+46) || !(t <= 7e+112))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(b - z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.25e+46) || ~((t <= 7e+112)))
		tmp = (b - a) * t;
	else
		tmp = (b - z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.25e+46], N[Not[LessEqual[t, 7e+112]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.2499999999999998e46 or 6.99999999999999994e112 < t

   1. Initial program 94.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

      3. lower--.f64 76.2

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 76.2%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   if -4.2499999999999998e46 < t < 6.99999999999999994e112

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.9

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

   5. Applied rewrites 44.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.25 \cdot 10^{+46} \lor \neg \left(t \leq 7 \cdot 10^{+112}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+126}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.4e+126)
   (* (- y 2.0) b)
   (if (<= b 2.6e+47) (fma (- a) t a) (* (- t 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.4e+126) {
		tmp = (y - 2.0) * b;
	} else if (b <= 2.6e+47) {
		tmp = fma(-a, t, a);
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.4e+126)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= 2.6e+47)
		tmp = fma(Float64(-a), t, a);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.4e+126], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 2.6e+47], N[((-a) * t + a), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.3999999999999995e126

   1. Initial program 85.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(y - 2\right) \cdot b} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y - 2, b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -1 \cdot a\right)}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(\color{blue}{y - 1}, z, -1 \cdot a\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{\mathsf{neg}\left(a\right)}\right)\right) \]

      12. lower-neg.f64 71.2

          \[\leadsto \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, \color{blue}{-a}\right)\right) \]

   5. Applied rewrites 71.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(y - 2\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 69.5%

      \[\leadsto \left(y - 2\right) \cdot \color{blue}{b} \]

   if -6.3999999999999995e126 < b < 2.60000000000000003e47

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      3. lower--.f64 34.0

         \[\leadsto \color{blue}{\left(1 - t\right)} \cdot a \]

   5. Applied rewrites 34.0%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 34.0%

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

   if 2.60000000000000003e47 < b

   1. Initial program 90.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 72.6

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 72.6%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 47.9%

       \[\leadsto \left(t - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 35.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+125}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4e+125) (* b y) (if (<= b 1.42e+48) (fma (- a) t a) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4e+125) {
		tmp = b * y;
	} else if (b <= 1.42e+48) {
		tmp = fma(-a, t, a);
	} else {
		tmp = b * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4e+125)
		tmp = Float64(b * y);
	elseif (b <= 1.42e+48)
		tmp = fma(Float64(-a), t, a);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4e+125], N[(b * y), $MachinePrecision], If[LessEqual[b, 1.42e+48], N[((-a) * t + a), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.9999999999999997e125

   1. Initial program 85.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 89.8%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 88.1

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 88.1%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 57.3%

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

   if -3.9999999999999997e125 < b < 1.42e48

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      3. lower--.f64 34.2

         \[\leadsto \color{blue}{\left(1 - t\right)} \cdot a \]

   5. Applied rewrites 34.2%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 34.2%

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

   if 1.42e48 < b

   1. Initial program 90.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 72.6

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 72.6%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   10. Step-by-step derivation

   11. Applied rewrites 35.7%

       \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 29.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-5} \lor \neg \left(t \leq 2.05 \cdot 10^{+60}\right):\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.1e-5) (not (<= t 2.05e+60))) (* (- t) a) (* b y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.1e-5) || !(t <= 2.05e+60)) {
		tmp = -t * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.1d-5)) .or. (.not. (t <= 2.05d+60))) then
        tmp = -t * a
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.1e-5) || !(t <= 2.05e+60)) {
		tmp = -t * a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.1e-5) or not (t <= 2.05e+60):
		tmp = -t * a
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.1e-5) || !(t <= 2.05e+60))
		tmp = Float64(Float64(-t) * a);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.1e-5) || ~((t <= 2.05e+60)))
		tmp = -t * a;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.1e-5], N[Not[LessEqual[t, 2.05e+60]], $MachinePrecision]], N[((-t) * a), $MachinePrecision], N[(b * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.09999999999999988e-5 or 2.05e60 < t

   1. Initial program 93.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      3. lower--.f64 41.7

         \[\leadsto \color{blue}{\left(1 - t\right)} \cdot a \]

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   6. Taylor expanded in t around inf

      \[\leadsto \left(-1 \cdot t\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 41.2%

      \[\leadsto \left(-t\right) \cdot a \]

   if -2.09999999999999988e-5 < t < 2.05e60

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 38.5

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 38.5%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 28.3%

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

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-5} \lor \neg \left(t \leq 2.05 \cdot 10^{+60}\right):\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 26.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-54}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-6}:\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.15e-54) (* b y) (if (<= y 6.5e-6) (* 1.0 z) (* (- y) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.15e-54) {
		tmp = b * y;
	} else if (y <= 6.5e-6) {
		tmp = 1.0 * z;
	} else {
		tmp = -y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.15d-54)) then
        tmp = b * y
    else if (y <= 6.5d-6) then
        tmp = 1.0d0 * z
    else
        tmp = -y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.15e-54) {
		tmp = b * y;
	} else if (y <= 6.5e-6) {
		tmp = 1.0 * z;
	} else {
		tmp = -y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.15e-54:
		tmp = b * y
	elif y <= 6.5e-6:
		tmp = 1.0 * z
	else:
		tmp = -y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.15e-54)
		tmp = Float64(b * y);
	elseif (y <= 6.5e-6)
		tmp = Float64(1.0 * z);
	else
		tmp = Float64(Float64(-y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.15e-54)
		tmp = b * y;
	elseif (y <= 6.5e-6)
		tmp = 1.0 * z;
	else
		tmp = -y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.15e-54], N[(b * y), $MachinePrecision], If[LessEqual[y, 6.5e-6], N[(1.0 * z), $MachinePrecision], N[((-y) * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1499999999999999e-54

   1. Initial program 88.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 95.6%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 49.3

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 39.5%

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

   if -1.1499999999999999e-54 < y < 6.4999999999999996e-6

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 29.0

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

   5. Applied rewrites 29.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 29.0%

      \[\leadsto 1 \cdot z \]

   if 6.4999999999999996e-6 < y

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 40.6

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

   5. Applied rewrites 40.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 40.2%

      \[\leadsto \left(-y\right) \cdot z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 25.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-54} \lor \neg \left(y \leq 6.5 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e-54) (not (<= y 6.5e-6))) (* b y) (* 1.0 z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e-54) || !(y <= 6.5e-6)) {
		tmp = b * y;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.15d-54)) .or. (.not. (y <= 6.5d-6))) then
        tmp = b * y
    else
        tmp = 1.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e-54) || !(y <= 6.5e-6)) {
		tmp = b * y;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.15e-54) or not (y <= 6.5e-6):
		tmp = b * y
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e-54) || !(y <= 6.5e-6))
		tmp = Float64(b * y);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.15e-54) || ~((y <= 6.5e-6)))
		tmp = b * y;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e-54], N[Not[LessEqual[y, 6.5e-6]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999e-54 or 6.4999999999999996e-6 < y

   1. Initial program 90.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 45.4

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 45.4%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 36.2%

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

   if -1.1499999999999999e-54 < y < 6.4999999999999996e-6

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 29.0

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

   5. Applied rewrites 29.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 29.0%

      \[\leadsto 1 \cdot z \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-54} \lor \neg \left(y \leq 6.5 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -24000000000000 \lor \neg \left(y \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -24000000000000.0) (not (<= y 3.4e+50))) (* b y) (* b t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -24000000000000.0) || !(y <= 3.4e+50)) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-24000000000000.0d0)) .or. (.not. (y <= 3.4d+50))) then
        tmp = b * y
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -24000000000000.0) || !(y <= 3.4e+50)) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -24000000000000.0) or not (y <= 3.4e+50):
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -24000000000000.0) || !(y <= 3.4e+50))
		tmp = Float64(b * y);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -24000000000000.0) || ~((y <= 3.4e+50)))
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -24000000000000.0], N[Not[LessEqual[y, 3.4e+50]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e13 or 3.3999999999999998e50 < y

   1. Initial program 89.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 46.3

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 46.3%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 40.2%

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

   if -2.4e13 < y < 3.3999999999999998e50

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

   5. Applied rewrites 98.4%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. lower-+.f64 30.2

         \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

   8. Applied rewrites 30.2%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   10. Step-by-step derivation

   11. Applied rewrites 21.2%

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

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -24000000000000 \lor \neg \left(y \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 17.4% accurate, 6.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(b * t), $MachinePrecision]

Derivation

1. Initial program 94.1%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]

5. Applied rewrites 97.7%

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

6. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   3. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

   4. lower-+.f64 38.2

      \[\leadsto \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b \]

8. Applied rewrites 38.2%

   \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

9. Taylor expanded in t around inf

   \[\leadsto b \cdot \color{blue}{t} \]
10. Step-by-step derivation

11. Applied rewrites 15.6%

    \[\leadsto b \cdot \color{blue}{t} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))