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

Percentage Accurate: 95.6% → 98.0%

Time: 10.4s

Alternatives: 17

Speedup: 0.5×

• 36.1% 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: 95.6% 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: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* b (- (+ t y) 2.0)) (- (- x (* z (- y 1.0))) (* a (- t 1.0))))))
   (if (<= t_1 INFINITY) t_1 (* (- b z) y))))

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (b - z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (b - z) * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(t + y) - 2.0)) + Float64(Float64(x - Float64(z * Float64(y - 1.0))) - Float64(a * Float64(t - 1.0))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(b - z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (b - z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

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

   3. Taylor expanded in y around 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 63.2

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

   5. Applied rewrites 63.2%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq \infty:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, x\right)\\ t_2 := \left(b - a\right) \cdot t\\ t_3 := \mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-297}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-106}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{-9}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 9200000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z x))
        (t_2 (* (- b a) t))
        (t_3 (fma (- y 2.0) b x)))
   (if (<= t -7.2e+35)
     t_2
     (if (<= t -1.35e-176)
       t_1
       (if (<= t -1.02e-297)
         t_3
         (if (<= t 6.5e-106)
           (+ (+ z x) a)
           (if (<= t 3.35e-9) t_3 (if (<= t 9200000000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, x);
	double t_2 = (b - a) * t;
	double t_3 = fma((y - 2.0), b, x);
	double tmp;
	if (t <= -7.2e+35) {
		tmp = t_2;
	} else if (t <= -1.35e-176) {
		tmp = t_1;
	} else if (t <= -1.02e-297) {
		tmp = t_3;
	} else if (t <= 6.5e-106) {
		tmp = (z + x) + a;
	} else if (t <= 3.35e-9) {
		tmp = t_3;
	} else if (t <= 9200000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, x)
	t_2 = Float64(Float64(b - a) * t)
	t_3 = fma(Float64(y - 2.0), b, x)
	tmp = 0.0
	if (t <= -7.2e+35)
		tmp = t_2;
	elseif (t <= -1.35e-176)
		tmp = t_1;
	elseif (t <= -1.02e-297)
		tmp = t_3;
	elseif (t <= 6.5e-106)
		tmp = Float64(Float64(z + x) + a);
	elseif (t <= 3.35e-9)
		tmp = t_3;
	elseif (t <= 9200000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[t, -7.2e+35], t$95$2, If[LessEqual[t, -1.35e-176], t$95$1, If[LessEqual[t, -1.02e-297], t$95$3, If[LessEqual[t, 6.5e-106], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 3.35e-9], t$95$3, If[LessEqual[t, 9200000000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.2000000000000001e35 or 9.2e12 < t

   1. Initial program 91.0%

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

   3. Taylor expanded in 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 68.3

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

   5. Applied rewrites 68.3%

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

   if -7.2000000000000001e35 < t < -1.3499999999999999e-176 or 3.34999999999999981e-9 < t < 9.2e12

   1. Initial program 95.9%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 85.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 66.5%

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

   if -1.3499999999999999e-176 < t < -1.0200000000000001e-297 or 6.4999999999999997e-106 < t < 3.34999999999999981e-9

   1. Initial program 96.1%

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

   3. Taylor expanded in t around 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 86.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 76.2%

       \[\leadsto \mathsf{fma}\left(y - 2, b, x\right) \]

   if -1.0200000000000001e-297 < t < 6.4999999999999997e-106

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 78.2%

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

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 70.9%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 56.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + x\right) + a\\ t_2 := \left(b - a\right) \cdot t\\ t_3 := \mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.85:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-297}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2850000000000:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ z x) a)) (t_2 (* (- b a) t)) (t_3 (fma (- y 2.0) b x)))
   (if (<= t -1.8e+105)
     t_2
     (if (<= t -1.85)
       (* (- b z) y)
       (if (<= t -1.42e-176)
         t_1
         (if (<= t -1.02e-297)
           t_3
           (if (<= t 6.5e-106) t_1 (if (<= t 2850000000000.0) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + x) + a;
	double t_2 = (b - a) * t;
	double t_3 = fma((y - 2.0), b, x);
	double tmp;
	if (t <= -1.8e+105) {
		tmp = t_2;
	} else if (t <= -1.85) {
		tmp = (b - z) * y;
	} else if (t <= -1.42e-176) {
		tmp = t_1;
	} else if (t <= -1.02e-297) {
		tmp = t_3;
	} else if (t <= 6.5e-106) {
		tmp = t_1;
	} else if (t <= 2850000000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + x) + a)
	t_2 = Float64(Float64(b - a) * t)
	t_3 = fma(Float64(y - 2.0), b, x)
	tmp = 0.0
	if (t <= -1.8e+105)
		tmp = t_2;
	elseif (t <= -1.85)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= -1.42e-176)
		tmp = t_1;
	elseif (t <= -1.02e-297)
		tmp = t_3;
	elseif (t <= 6.5e-106)
		tmp = t_1;
	elseif (t <= 2850000000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[t, -1.8e+105], t$95$2, If[LessEqual[t, -1.85], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, -1.42e-176], t$95$1, If[LessEqual[t, -1.02e-297], t$95$3, If[LessEqual[t, 6.5e-106], t$95$1, If[LessEqual[t, 2850000000000.0], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.7999999999999999e105 or 2.85e12 < t

   1. Initial program 90.3%

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

   3. Taylor expanded in 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 74.2

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

   5. Applied rewrites 74.2%

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

   if -1.7999999999999999e105 < t < -1.8500000000000001

   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 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 55.8

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

   5. Applied rewrites 55.8%

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

   if -1.8500000000000001 < t < -1.42000000000000009e-176 or -1.0200000000000001e-297 < t < 6.4999999999999997e-106

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 69.6%

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

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 62.1%

       \[\leadsto \left(z + x\right) + a \]

   if -1.42000000000000009e-176 < t < -1.0200000000000001e-297 or 6.4999999999999997e-106 < t < 2.85e12

   1. Initial program 96.5%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 79.8%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 70.9%

       \[\leadsto \mathsf{fma}\left(y - 2, b, x\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 87.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.05 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))))
   (if (<= b -7.6e+62)
     t_1
     (if (<= b 4.05e+40) (fma (- 1.0 y) z (fma (- 1.0 t) a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	double tmp;
	if (b <= -7.6e+62) {
		tmp = t_1;
	} else if (b <= 4.05e+40) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x))
	tmp = 0.0
	if (b <= -7.6e+62)
		tmp = t_1;
	elseif (b <= 4.05e+40)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.6e+62], t$95$1, If[LessEqual[b, 4.05e+40], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.59999999999999967e62 or 4.0499999999999999e40 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in z around 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 88.7

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

   5. Applied rewrites 88.7%

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

   if -7.59999999999999967e62 < b < 4.0499999999999999e40

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 90.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 4.05 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.85:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 5200000000000:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.8e+105)
     t_1
     (if (<= t -1.85)
       (* (- b z) y)
       (if (<= t 5200000000000.0) (+ (+ (fma -2.0 b z) x) a) 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 <= -1.8e+105) {
		tmp = t_1;
	} else if (t <= -1.85) {
		tmp = (b - z) * y;
	} else if (t <= 5200000000000.0) {
		tmp = (fma(-2.0, b, z) + x) + a;
	} 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 <= -1.8e+105)
		tmp = t_1;
	elseif (t <= -1.85)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 5200000000000.0)
		tmp = Float64(Float64(fma(-2.0, b, z) + x) + a);
	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, -1.8e+105], t$95$1, If[LessEqual[t, -1.85], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 5200000000000.0], N[(N[(N[(-2.0 * b + z), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7999999999999999e105 or 5.2e12 < t

   1. Initial program 90.3%

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

   3. Taylor expanded in 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 74.2

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

   5. Applied rewrites 74.2%

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

   if -1.7999999999999999e105 < t < -1.8500000000000001

   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 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 55.8

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

   5. Applied rewrites 55.8%

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

   if -1.8500000000000001 < t < 5.2e12

   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 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 98.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.7%

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

Alternative 6: 82.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -1.5e+150)
     t_1
     (if (<= b 4e+122) (fma (- 1.0 y) z (fma (- 1.0 t) a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -1.5e+150) {
		tmp = t_1;
	} else if (b <= 4e+122) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -1.5e+150)
		tmp = t_1;
	elseif (b <= 4e+122)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.5e+150], t$95$1, If[LessEqual[b, 4e+122], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.50000000000000006e150 or 4.00000000000000006e122 < b

   1. Initial program 82.7%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 84.3

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

   5. Applied rewrites 84.3%

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

   if -1.50000000000000006e150 < b < 4.00000000000000006e122

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 84.1%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+150}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -2.6e+136)
     t_1
     (if (<= b -1.12e-181)
       (fma (- 1.0 t) a x)
       (if (<= b 1.15e+84) (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 * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.6e+136) {
		tmp = t_1;
	} else if (b <= -1.12e-181) {
		tmp = fma((1.0 - t), a, x);
	} else if (b <= 1.15e+84) {
		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(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -2.6e+136)
		tmp = t_1;
	elseif (b <= -1.12e-181)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (b <= 1.15e+84)
		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[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+136], t$95$1, If[LessEqual[b, -1.12e-181], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[b, 1.15e+84], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6000000000000001e136 or 1.1499999999999999e84 < b

   1. Initial program 85.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -2.6000000000000001e136 < b < -1.11999999999999997e-181

   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 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 73.3

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

   5. Applied rewrites 73.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 58.1%

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

   if -1.11999999999999997e-181 < b < 1.1499999999999999e84

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 88.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 59.9%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+136}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-181}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a + x\right)\\ \mathbf{elif}\;t \leq 9200000000000:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -5.1e+60)
     t_1
     (if (<= t 3.1e-8)
       (fma (- y 2.0) b (+ a x))
       (if (<= t 9200000000000.0) (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 <= -5.1e+60) {
		tmp = t_1;
	} else if (t <= 3.1e-8) {
		tmp = fma((y - 2.0), b, (a + x));
	} else if (t <= 9200000000000.0) {
		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 <= -5.1e+60)
		tmp = t_1;
	elseif (t <= 3.1e-8)
		tmp = fma(Float64(y - 2.0), b, Float64(a + x));
	elseif (t <= 9200000000000.0)
		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, -5.1e+60], t$95$1, If[LessEqual[t, 3.1e-8], N[(N[(y - 2.0), $MachinePrecision] * b + N[(a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9200000000000.0], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.09999999999999996e60 or 9.2e12 < t

   1. Initial program 90.3%

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

   3. Taylor expanded in 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 70.6

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

   5. Applied rewrites 70.6%

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

   if -5.09999999999999996e60 < t < 3.1e-8

   1. Initial program 96.3%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 95.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 70.4%

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

   if 3.1e-8 < t < 9.2e12

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 100.0%

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

Alternative 9: 54.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-201}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+93}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -6.8e+49)
     t_1
     (if (<= y 6.2e-201)
       (fma (- 1.0 t) a x)
       (if (<= y 3e+93) (* (- b a) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -6.8e+49) {
		tmp = t_1;
	} else if (y <= 6.2e-201) {
		tmp = fma((1.0 - t), a, x);
	} else if (y <= 3e+93) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -6.8e+49)
		tmp = t_1;
	elseif (y <= 6.2e-201)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (y <= 3e+93)
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -6.8e+49], t$95$1, If[LessEqual[y, 6.2e-201], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[y, 3e+93], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.8000000000000001e49 or 2.99999999999999978e93 < y

   1. Initial program 88.5%

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

   3. Taylor expanded in y around 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 75.1

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

   5. Applied rewrites 75.1%

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

   if -6.8000000000000001e49 < y < 6.1999999999999998e-201

   1. Initial program 98.8%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 87.6

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

   5. Applied rewrites 87.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 59.3%

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

   if 6.1999999999999998e-201 < y < 2.99999999999999978e93

   1. Initial program 94.7%

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

   3. Taylor expanded in 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 50.2

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

   5. Applied rewrites 50.2%

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

Alternative 10: 53.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-249}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 5200000000000:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.8e+105)
     t_1
     (if (<= t -9e-249)
       (* (- b z) y)
       (if (<= t 5200000000000.0) (+ (+ z x) a) 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 <= -1.8e+105) {
		tmp = t_1;
	} else if (t <= -9e-249) {
		tmp = (b - z) * y;
	} else if (t <= 5200000000000.0) {
		tmp = (z + x) + a;
	} 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 <= (-1.8d+105)) then
        tmp = t_1
    else if (t <= (-9d-249)) then
        tmp = (b - z) * y
    else if (t <= 5200000000000.0d0) then
        tmp = (z + x) + a
    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 <= -1.8e+105) {
		tmp = t_1;
	} else if (t <= -9e-249) {
		tmp = (b - z) * y;
	} else if (t <= 5200000000000.0) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -1.8e+105:
		tmp = t_1
	elif t <= -9e-249:
		tmp = (b - z) * y
	elif t <= 5200000000000.0:
		tmp = (z + x) + a
	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 <= -1.8e+105)
		tmp = t_1;
	elseif (t <= -9e-249)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 5200000000000.0)
		tmp = Float64(Float64(z + x) + a);
	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 <= -1.8e+105)
		tmp = t_1;
	elseif (t <= -9e-249)
		tmp = (b - z) * y;
	elseif (t <= 5200000000000.0)
		tmp = (z + x) + a;
	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, -1.8e+105], t$95$1, If[LessEqual[t, -9e-249], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 5200000000000.0], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7999999999999999e105 or 5.2e12 < t

   1. Initial program 90.3%

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

   3. Taylor expanded in 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 74.2

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

   5. Applied rewrites 74.2%

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

   if -1.7999999999999999e105 < t < -8.99999999999999962e-249

   1. Initial program 95.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 50.3

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

   5. Applied rewrites 50.3%

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

   if -8.99999999999999962e-249 < t < 5.2e12

   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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 68.7%

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

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 54.6%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 69.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -6.8e+65)
     t_1
     (if (<= b 1.15e+84) (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 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -6.8e+65) {
		tmp = t_1;
	} else if (b <= 1.15e+84) {
		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(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -6.8e+65)
		tmp = t_1;
	elseif (b <= 1.15e+84)
		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[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+65], t$95$1, If[LessEqual[b, 1.15e+84], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.7999999999999999e65 or 1.1499999999999999e84 < b

   1. Initial program 87.4%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 74.3

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

   5. Applied rewrites 74.3%

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

   if -6.7999999999999999e65 < b < 1.1499999999999999e84

   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 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 70.9%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5200000000000:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -6.6e+30) t_1 (if (<= t 5200000000000.0) (+ (+ z x) a) 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 <= -6.6e+30) {
		tmp = t_1;
	} else if (t <= 5200000000000.0) {
		tmp = (z + x) + a;
	} 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 <= (-6.6d+30)) then
        tmp = t_1
    else if (t <= 5200000000000.0d0) then
        tmp = (z + x) + a
    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 <= -6.6e+30) {
		tmp = t_1;
	} else if (t <= 5200000000000.0) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -6.6e+30:
		tmp = t_1
	elif t <= 5200000000000.0:
		tmp = (z + x) + a
	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 <= -6.6e+30)
		tmp = t_1;
	elseif (t <= 5200000000000.0)
		tmp = Float64(Float64(z + x) + a);
	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 <= -6.6e+30)
		tmp = t_1;
	elseif (t <= 5200000000000.0)
		tmp = (z + x) + a;
	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, -6.6e+30], t$95$1, If[LessEqual[t, 5200000000000.0], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.60000000000000053e30 or 5.2e12 < t

   1. Initial program 91.0%

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

   3. Taylor expanded in 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 68.3

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

   5. Applied rewrites 68.3%

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

   if -6.60000000000000053e30 < t < 5.2e12

   1. Initial program 96.3%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 97.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.3%

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

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 49.4%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 45.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+124}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 2.0) b)))
   (if (<= b -1.8e+102) t_1 (if (<= b 1.7e+124) (+ (+ z x) a) t_1))))

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 <= -1.8e+102) {
		tmp = t_1;
	} else if (b <= 1.7e+124) {
		tmp = (z + x) + a;
	} 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 = (y - 2.0d0) * b
    if (b <= (-1.8d+102)) then
        tmp = t_1
    else if (b <= 1.7d+124) then
        tmp = (z + x) + a
    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 = (y - 2.0) * b;
	double tmp;
	if (b <= -1.8e+102) {
		tmp = t_1;
	} else if (b <= 1.7e+124) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y - 2.0) * b
	tmp = 0
	if b <= -1.8e+102:
		tmp = t_1
	elif b <= 1.7e+124:
		tmp = (z + x) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 2.0) * b)
	tmp = 0.0
	if (b <= -1.8e+102)
		tmp = t_1;
	elseif (b <= 1.7e+124)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.8e+102)
		tmp = t_1;
	elseif (b <= 1.7e+124)
		tmp = (z + x) + a;
	else
		tmp = t_1;
	end
	tmp_2 = 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, -1.8e+102], t$95$1, If[LessEqual[b, 1.7e+124], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8000000000000001e102 or 1.7e124 < b

   1. Initial program 85.1%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 78.5

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 53.6%

      \[\leadsto \left(y - 2\right) \cdot b \]

   if -1.8000000000000001e102 < b < 1.7e124

   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 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 46.5%

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

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 45.1%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 46.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+79}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 2.0) b)))
   (if (<= b -6.4e+65) t_1 (if (<= b 4.6e+79) (+ (+ z x) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 2.0) * b;
	double tmp;
	if (b <= -6.4e+65) {
		tmp = t_1;
	} else if (b <= 4.6e+79) {
		tmp = (z + x) + a;
	} 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 = (t - 2.0d0) * b
    if (b <= (-6.4d+65)) then
        tmp = t_1
    else if (b <= 4.6d+79) then
        tmp = (z + x) + a
    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 = (t - 2.0) * b;
	double tmp;
	if (b <= -6.4e+65) {
		tmp = t_1;
	} else if (b <= 4.6e+79) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 2.0) * b
	tmp = 0
	if b <= -6.4e+65:
		tmp = t_1
	elif b <= 4.6e+79:
		tmp = (z + x) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 2.0) * b)
	tmp = 0.0
	if (b <= -6.4e+65)
		tmp = t_1;
	elseif (b <= 4.6e+79)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 2.0) * b;
	tmp = 0.0;
	if (b <= -6.4e+65)
		tmp = t_1;
	elseif (b <= 4.6e+79)
		tmp = (z + x) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -6.4e+65], t$95$1, If[LessEqual[b, 4.6e+79], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.40000000000000014e65 or 4.6000000000000001e79 < b

   1. Initial program 87.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 73.6

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

   5. Applied rewrites 73.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 48.6%

      \[\leadsto \left(t - 2\right) \cdot b \]

   if -6.40000000000000014e65 < b < 4.6000000000000001e79

   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 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 47.6%

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

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 46.1%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 43.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+51}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+84}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.05e+51) (* b t) (if (<= t 1.05e+84) (+ (+ z x) a) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e+51) {
		tmp = b * t;
	} else if (t <= 1.05e+84) {
		tmp = (z + x) + a;
	} 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 (t <= (-2.05d+51)) then
        tmp = b * t
    else if (t <= 1.05d+84) then
        tmp = (z + x) + a
    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 (t <= -2.05e+51) {
		tmp = b * t;
	} else if (t <= 1.05e+84) {
		tmp = (z + x) + a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.05e+51:
		tmp = b * t
	elif t <= 1.05e+84:
		tmp = (z + x) + a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.05e+51)
		tmp = Float64(b * t);
	elseif (t <= 1.05e+84)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.05e+51)
		tmp = b * t;
	elseif (t <= 1.05e+84)
		tmp = (z + x) + a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.05e+51], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.05e+84], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05000000000000005e51 or 1.05000000000000009e84 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 50.4

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

   5. Applied rewrites 50.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 43.0%

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

   if -2.05000000000000005e51 < t < 1.05000000000000009e84

   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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 88.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 57.4%

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

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 46.4%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 36.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+51}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+44}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.05e+51) (* b t) (if (<= t 5.7e+44) (+ a x) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.05e+51) {
		tmp = b * t;
	} else if (t <= 5.7e+44) {
		tmp = a + x;
	} 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 (t <= (-2.05d+51)) then
        tmp = b * t
    else if (t <= 5.7d+44) then
        tmp = a + x
    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 (t <= -2.05e+51) {
		tmp = b * t;
	} else if (t <= 5.7e+44) {
		tmp = a + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.05e+51:
		tmp = b * t
	elif t <= 5.7e+44:
		tmp = a + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.05e+51)
		tmp = Float64(b * t);
	elseif (t <= 5.7e+44)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.05e+51)
		tmp = b * t;
	elseif (t <= 5.7e+44)
		tmp = a + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.05e+51], N[(b * t), $MachinePrecision], If[LessEqual[t, 5.7e+44], N[(a + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05000000000000005e51 or 5.7000000000000003e44 < t

   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 b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 47.5

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

   5. Applied rewrites 47.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 40.8%

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

   if -2.05000000000000005e51 < t < 5.7000000000000003e44

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 93.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 65.4%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 38.1%

       \[\leadsto a + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 25.4% accurate, 9.3× speedup

Math

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

FPCore

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

C

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

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 = a + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + x), $MachinePrecision]

Derivation

1. Initial program 93.7%

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

3. Taylor expanded in 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. sub-neg N/A

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

   2. +-commutative N/A

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

   3. +-commutative N/A

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

   4. distribute-neg-in N/A

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

   5. mul-1-neg N/A

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

   6. remove-double-neg N/A

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

   7. associate-+l+ N/A

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

   8. *-commutative N/A

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

   9. distribute-lft-neg-in N/A

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

   10. mul-1-neg N/A

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

   11. lower-fma.f64 N/A

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

   12. sub-neg N/A

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

   13. metadata-eval N/A

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

   14. distribute-lft-in N/A

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

   15. metadata-eval N/A

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

   16. +-commutative N/A

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

   17. neg-mul-1 N/A

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

   18. sub-neg N/A

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

   19. lower--.f64 N/A

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

   20. lower-+.f64 N/A

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

5. Applied rewrites 68.8%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 46.5%

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

9. Taylor expanded in b around 0

   \[\leadsto a + x \]
10. Step-by-step derivation

11. Applied rewrites 25.4%

    \[\leadsto a + x \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024270 
(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)))