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

Percentage Accurate: 95.2% → 97.8%

Time: 9.8s

Alternatives: 15

Speedup: 1.2×

• 36.7% 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: 95.2% 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: 97.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 y around 0

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. +-commutative N/A

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

   4. distribute-neg-in N/A

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

   5. mul-1-neg N/A

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

   6. remove-double-neg N/A

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

   7. associate-+l+ N/A

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

   8. *-commutative N/A

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

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

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

   10. mul-1-neg N/A

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

   11. lower-fma.f64 N/A

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

5. Applied rewrites 97.3%

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

Alternative 2: 42.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+307}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 10^{+285}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 -2e+307)
     (* (- a) t)
     (if (<= t_1 1e+285) (+ (+ z x) a) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -2e+307) {
		tmp = -a * t;
	} else if (t_1 <= 1e+285) {
		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) :: t_1
    real(8) :: tmp
    t_1 = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
    if (t_1 <= (-2d+307)) then
        tmp = -a * t
    else if (t_1 <= 1d+285) 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 t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -2e+307) {
		tmp = -a * t;
	} else if (t_1 <= 1e+285) {
		tmp = (z + x) + a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= -2e+307:
		tmp = -a * t
	elif t_1 <= 1e+285:
		tmp = (z + x) + a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= -2e+307)
		tmp = Float64(Float64(-a) * t);
	elseif (t_1 <= 1e+285)
		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)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= -2e+307)
		tmp = -a * t;
	elseif (t_1 <= 1e+285)
		tmp = (z + x) + a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -2e+307], N[((-a) * t), $MachinePrecision], If[LessEqual[t$95$1, 1e+285], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 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)) < -1.99999999999999997e307

   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 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 61.8

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 40.7%

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

   if -1.99999999999999997e307 < (+.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)) < 9.9999999999999998e284

   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 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 81.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 64.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 52.5%

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

   if 9.9999999999999998e284 < (+.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 77.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lower-+.f64 58.1

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

   5. Applied rewrites 58.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 29.5%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 36.4%

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

Alternative 3: 41.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;t\_1 \leq 10^{+285}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 (- INFINITY))
     (* (- y) z)
     (if (<= t_1 1e+285) (+ (+ z x) a) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -y * z;
	} else if (t_1 <= 1e+285) {
		tmp = (z + x) + a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -y * z;
	} else if (t_1 <= 1e+285) {
		tmp = (z + x) + a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -y * z
	elif t_1 <= 1e+285:
		tmp = (z + x) + a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(-y) * z);
	elseif (t_1 <= 1e+285)
		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)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -y * z;
	elseif (t_1 <= 1e+285)
		tmp = (z + x) + a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, (-Infinity)], N[((-y) * z), $MachinePrecision], If[LessEqual[t$95$1, 1e+285], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. neg-mul-1 N/A

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

      4. +-commutative N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 34.3

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

   5. Applied rewrites 34.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 33.9%

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

   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)) < 9.9999999999999998e284

   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 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 81.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 63.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 52.2%

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

   if 9.9999999999999998e284 < (+.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 77.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lower-+.f64 58.1

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

   5. Applied rewrites 58.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 29.5%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 36.4%

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

Alternative 4: 87.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+78} \lor \neg \left(t \leq 2 \cdot 10^{+14}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + \mathsf{fma}\left(t - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.8e+78) (not (<= t 2e+14)))
   (fma (- 1.0 t) a (+ z (fma (- t 2.0) b x)))
   (fma (- 1.0 y) z (+ a (fma (- y 2.0) b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.8e+78) || !(t <= 2e+14)) {
		tmp = fma((1.0 - t), a, (z + fma((t - 2.0), b, x)));
	} else {
		tmp = fma((1.0 - y), z, (a + fma((y - 2.0), b, x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.8e+78) || !(t <= 2e+14))
		tmp = fma(Float64(1.0 - t), a, Float64(z + fma(Float64(t - 2.0), b, x)));
	else
		tmp = fma(Float64(1.0 - y), z, Float64(a + fma(Float64(y - 2.0), b, x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.8e+78], N[Not[LessEqual[t, 2e+14]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.80000000000000014e78 or 2e14 < t

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 85.7%

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

   if -6.80000000000000014e78 < t < 2e14

   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 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 93.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+78} \lor \neg \left(t \leq 2 \cdot 10^{+14}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + \mathsf{fma}\left(t - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, x\right) + a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)) (t_2 (* (- b a) t)))
   (if (<= t -2e+54)
     t_2
     (if (<= t -1.7e-14)
       t_1
       (if (<= t 3.2e-79) (+ (fma -2.0 b x) a) (if (<= t 2e+14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -2e+54) {
		tmp = t_2;
	} else if (t <= -1.7e-14) {
		tmp = t_1;
	} else if (t <= 3.2e-79) {
		tmp = fma(-2.0, b, x) + a;
	} else if (t <= 2e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -2e+54)
		tmp = t_2;
	elseif (t <= -1.7e-14)
		tmp = t_1;
	elseif (t <= 3.2e-79)
		tmp = Float64(fma(-2.0, b, x) + a);
	elseif (t <= 2e+14)
		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[(b - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2e+54], t$95$2, If[LessEqual[t, -1.7e-14], t$95$1, If[LessEqual[t, 3.2e-79], N[(N[(-2.0 * b + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 2e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0000000000000002e54 or 2e14 < t

   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 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 70.8

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

   5. Applied rewrites 70.8%

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

   if -2.0000000000000002e54 < t < -1.70000000000000001e-14 or 3.19999999999999988e-79 < t < 2e14

   1. Initial program 97.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 58.8

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

   5. Applied rewrites 58.8%

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

   if -1.70000000000000001e-14 < t < 3.19999999999999988e-79

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 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 68.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 59.6%

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

Alternative 6: 54.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-83}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)) (t_2 (* (- b a) t)))
   (if (<= t -2e+54)
     t_2
     (if (<= t -4.6e-222)
       t_1
       (if (<= t 1.55e-83) (+ (+ z x) a) (if (<= t 2e+14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -2e+54) {
		tmp = t_2;
	} else if (t <= -4.6e-222) {
		tmp = t_1;
	} else if (t <= 1.55e-83) {
		tmp = (z + x) + a;
	} else if (t <= 2e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (b - z) * y
    t_2 = (b - a) * t
    if (t <= (-2d+54)) then
        tmp = t_2
    else if (t <= (-4.6d-222)) then
        tmp = t_1
    else if (t <= 1.55d-83) then
        tmp = (z + x) + a
    else if (t <= 2d+14) then
        tmp = t_1
    else
        tmp = t_2
    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 - z) * y;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -2e+54) {
		tmp = t_2;
	} else if (t <= -4.6e-222) {
		tmp = t_1;
	} else if (t <= 1.55e-83) {
		tmp = (z + x) + a;
	} else if (t <= 2e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	t_2 = (b - a) * t
	tmp = 0
	if t <= -2e+54:
		tmp = t_2
	elif t <= -4.6e-222:
		tmp = t_1
	elif t <= 1.55e-83:
		tmp = (z + x) + a
	elif t <= 2e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -2e+54)
		tmp = t_2;
	elseif (t <= -4.6e-222)
		tmp = t_1;
	elseif (t <= 1.55e-83)
		tmp = Float64(Float64(z + x) + a);
	elseif (t <= 2e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	t_2 = (b - a) * t;
	tmp = 0.0;
	if (t <= -2e+54)
		tmp = t_2;
	elseif (t <= -4.6e-222)
		tmp = t_1;
	elseif (t <= 1.55e-83)
		tmp = (z + x) + a;
	elseif (t <= 2e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2e+54], t$95$2, If[LessEqual[t, -4.6e-222], t$95$1, If[LessEqual[t, 1.55e-83], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 2e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0000000000000002e54 or 2e14 < t

   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 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 70.8

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

   5. Applied rewrites 70.8%

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

   if -2.0000000000000002e54 < t < -4.6000000000000003e-222 or 1.54999999999999996e-83 < t < 2e14

   1. Initial program 98.5%

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

   3. Taylor expanded in 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 51.0

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

   5. Applied rewrites 51.0%

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

   if -4.6000000000000003e-222 < t < 1.54999999999999996e-83

   1. Initial program 98.4%

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

   3. Taylor expanded in 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 b around 0

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

   8. Applied rewrites 73.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 59.8%

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

Alternative 7: 81.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+125} \lor \neg \left(b \leq 3.3 \cdot 10^{+63}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.2e+125) (not (<= b 3.3e+63)))
   (* (- (+ t y) 2.0) b)
   (fma (- 1.0 y) z (fma (- 1.0 t) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.2e+125) || !(b <= 3.3e+63)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.2e+125) || !(b <= 3.3e+63))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.2e+125], N[Not[LessEqual[b, 3.3e+63]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.20000000000000006e125 or 3.3000000000000002e63 < b

   1. Initial program 87.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lower-+.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if -5.20000000000000006e125 < b < 3.3000000000000002e63

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

   8. Applied rewrites 93.0%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+125} \lor \neg \left(b \leq 3.3 \cdot 10^{+63}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-175}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+60}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -5e+125)
     t_1
     (if (<= b -2.5e-175)
       (fma -2.0 b (fma (- 1.0 t) a x))
       (if (<= b 3.6e+60) (+ (fma (- 1.0 y) z x) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -5e+125) {
		tmp = t_1;
	} else if (b <= -2.5e-175) {
		tmp = fma(-2.0, b, fma((1.0 - t), a, x));
	} else if (b <= 3.6e+60) {
		tmp = fma((1.0 - y), z, x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -5e+125)
		tmp = t_1;
	elseif (b <= -2.5e-175)
		tmp = fma(-2.0, b, fma(Float64(1.0 - t), a, x));
	elseif (b <= 3.6e+60)
		tmp = Float64(fma(Float64(1.0 - y), 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[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5e+125], t$95$1, If[LessEqual[b, -2.5e-175], N[(-2.0 * b + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+60], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.99999999999999962e125 or 3.59999999999999968e60 < b

   1. Initial program 87.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lower-+.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if -4.99999999999999962e125 < b < -2.5e-175

   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 y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. sub-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. *-commutative N/A

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

      20. mul-1-neg N/A

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

      21. remove-double-neg N/A

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

   8. Applied rewrites 82.0%

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

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(t - 2, b, x + a \cdot \left(1 - t\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 74.0%

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

   12. Taylor expanded in t around 0

       \[\leadsto \mathsf{fma}\left(-2, b, \mathsf{fma}\left(1 - t, a, x\right)\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 71.9%

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

   if -2.5e-175 < b < 3.59999999999999968e60

   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 75.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 72.1%

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

Alternative 9: 44.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.05 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-16}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+30}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 2.0) b)))
   (if (<= b -3.05e+50)
     t_1
     (if (<= b 1.9e-16) (+ (+ z x) a) (if (<= b 4.5e+30) (* (- a) t) 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 <= -3.05e+50) {
		tmp = t_1;
	} else if (b <= 1.9e-16) {
		tmp = (z + x) + a;
	} else if (b <= 4.5e+30) {
		tmp = -a * t;
	} 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 <= (-3.05d+50)) then
        tmp = t_1
    else if (b <= 1.9d-16) then
        tmp = (z + x) + a
    else if (b <= 4.5d+30) then
        tmp = -a * t
    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 <= -3.05e+50) {
		tmp = t_1;
	} else if (b <= 1.9e-16) {
		tmp = (z + x) + a;
	} else if (b <= 4.5e+30) {
		tmp = -a * t;
	} 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 <= -3.05e+50:
		tmp = t_1
	elif b <= 1.9e-16:
		tmp = (z + x) + a
	elif b <= 4.5e+30:
		tmp = -a * t
	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 <= -3.05e+50)
		tmp = t_1;
	elseif (b <= 1.9e-16)
		tmp = Float64(Float64(z + x) + a);
	elseif (b <= 4.5e+30)
		tmp = Float64(Float64(-a) * t);
	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 <= -3.05e+50)
		tmp = t_1;
	elseif (b <= 1.9e-16)
		tmp = (z + x) + a;
	elseif (b <= 4.5e+30)
		tmp = -a * t;
	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, -3.05e+50], t$95$1, If[LessEqual[b, 1.9e-16], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[b, 4.5e+30], N[((-a) * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.05000000000000013e50 or 4.49999999999999995e30 < b

   1. Initial program 88.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lower-+.f64 75.7

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 55.7%

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

   if -3.05000000000000013e50 < b < 1.90000000000000006e-16

   1. Initial program 98.4%

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

   3. Taylor expanded in 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 75.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 73.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 50.2%

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

   if 1.90000000000000006e-16 < b < 4.49999999999999995e30

   1. Initial program 90.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 61.3

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

   5. Applied rewrites 61.3%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 61.0%

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

Alternative 10: 69.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+125} \lor \neg \left(b \leq 3.6 \cdot 10^{+60}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.2e+125) (not (<= b 3.6e+60)))
   (* (- (+ t y) 2.0) b)
   (+ (fma (- 1.0 y) z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.2e+125) || !(b <= 3.6e+60)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = fma((1.0 - y), z, x) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.2e+125) || !(b <= 3.6e+60))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = Float64(fma(Float64(1.0 - y), z, x) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.2e+125], N[Not[LessEqual[b, 3.6e+60]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.2000000000000001e125 or 3.59999999999999968e60 < b

   1. Initial program 87.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lower-+.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if -4.2000000000000001e125 < b < 3.59999999999999968e60

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0

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

      1. 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 73.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+125} \lor \neg \left(b \leq 3.6 \cdot 10^{+60}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+14} \lor \neg \left(t \leq 8.2 \cdot 10^{+45}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e+14) (not (<= t 8.2e+45)))
   (* (- b a) t)
   (+ (+ (fma -2.0 b z) x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e+14) || !(t <= 8.2e+45)) {
		tmp = (b - a) * t;
	} else {
		tmp = (fma(-2.0, b, z) + x) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5e+14) || !(t <= 8.2e+45))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(fma(-2.0, b, z) + x) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5e+14], N[Not[LessEqual[t, 8.2e+45]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(N[(-2.0 * b + z), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5e14 or 8.20000000000000025e45 < t

   1. Initial program 89.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 70.4

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

   5. Applied rewrites 70.4%

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

   if -5e14 < t < 8.20000000000000025e45

   1. Initial program 98.4%

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

   3. Taylor expanded in 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 96.5%

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

   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 60.7%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+14} \lor \neg \left(t \leq 8.2 \cdot 10^{+45}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+14} \lor \neg \left(t \leq 8.2 \cdot 10^{+45}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e+14) (not (<= t 8.2e+45))) (* (- b a) t) (+ (+ z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e+14) || !(t <= 8.2e+45)) {
		tmp = (b - a) * t;
	} else {
		tmp = (z + x) + a;
	}
	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 <= (-5d+14)) .or. (.not. (t <= 8.2d+45))) then
        tmp = (b - a) * t
    else
        tmp = (z + x) + a
    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 <= -5e+14) || !(t <= 8.2e+45)) {
		tmp = (b - a) * t;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5e+14) or not (t <= 8.2e+45):
		tmp = (b - a) * t
	else:
		tmp = (z + x) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5e+14) || !(t <= 8.2e+45))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(z + x) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5e+14) || ~((t <= 8.2e+45)))
		tmp = (b - a) * t;
	else
		tmp = (z + x) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5e+14], N[Not[LessEqual[t, 8.2e+45]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5e14 or 8.20000000000000025e45 < t

   1. Initial program 89.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 70.4

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

   5. Applied rewrites 70.4%

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

   if -5e14 < t < 8.20000000000000025e45

   1. Initial program 98.4%

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

   3. Taylor expanded in 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 96.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 66.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 45.9%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+14} \lor \neg \left(t \leq 8.2 \cdot 10^{+45}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+129} \lor \neg \left(b \leq 1.9 \cdot 10^{+63}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.7e+129) (not (<= b 1.9e+63))) (* b t) (+ (+ z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.7e+129) || !(b <= 1.9e+63)) {
		tmp = b * t;
	} else {
		tmp = (z + x) + a;
	}
	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 ((b <= (-2.7d+129)) .or. (.not. (b <= 1.9d+63))) then
        tmp = b * t
    else
        tmp = (z + x) + a
    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 ((b <= -2.7e+129) || !(b <= 1.9e+63)) {
		tmp = b * t;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.7e+129) or not (b <= 1.9e+63):
		tmp = b * t
	else:
		tmp = (z + x) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.7e+129) || !(b <= 1.9e+63))
		tmp = Float64(b * t);
	else
		tmp = Float64(Float64(z + x) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.7e+129) || ~((b <= 1.9e+63)))
		tmp = b * t;
	else
		tmp = (z + x) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.7e+129], N[Not[LessEqual[b, 1.9e+63]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.7000000000000001e129 or 1.9000000000000001e63 < 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. lower-+.f64 82.4

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

   5. Applied rewrites 82.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 33.3%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 45.8%

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

   if -2.7000000000000001e129 < b < 1.9000000000000001e63

   1. Initial program 97.5%

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

   3. Taylor expanded in 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 73.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 67.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 44.1%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+129} \lor \neg \left(b \leq 1.9 \cdot 10^{+63}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 33.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.3 \cdot 10^{+122} \lor \neg \left(b \leq 3.3 \cdot 10^{+61}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.3e+122) (not (<= b 3.3e+61))) (* b t) (+ a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.3e+122) || !(b <= 3.3e+61)) {
		tmp = b * t;
	} else {
		tmp = a + x;
	}
	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 ((b <= (-5.3d+122)) .or. (.not. (b <= 3.3d+61))) then
        tmp = b * t
    else
        tmp = a + x
    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 ((b <= -5.3e+122) || !(b <= 3.3e+61)) {
		tmp = b * t;
	} else {
		tmp = a + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.3e+122) or not (b <= 3.3e+61):
		tmp = b * t
	else:
		tmp = a + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.3e+122) || !(b <= 3.3e+61))
		tmp = Float64(b * t);
	else
		tmp = Float64(a + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.3e+122) || ~((b <= 3.3e+61)))
		tmp = b * t;
	else
		tmp = a + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.3e+122], N[Not[LessEqual[b, 3.3e+61]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(a + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.3e122 or 3.2999999999999998e61 < b

   1. Initial program 87.0%

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

   3. Taylor expanded in 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. lower-+.f64 81.3

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 32.7%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 44.6%

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

   if -5.3e122 < b < 3.2999999999999998e61

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 73.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 34.3%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.3 \cdot 10^{+122} \lor \neg \left(b \leq 3.3 \cdot 10^{+61}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 24.7% 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 67.9%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 49.5%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 24.5%

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

Reproduce

herbie shell --seed 2024309 
(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)))