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

Percentage Accurate: 95.4% → 97.6%

Time: 10.8s

Alternatives: 21

Speedup: 1.2×

• 35.5% 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: 95.4% 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: 97.6% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 98.0%

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

6. Final simplification 98.0%

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

Alternative 2: 43.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)\\ t_2 := \left(-y\right) \cdot z\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+306}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* (- (+ t y) 2.0) b) (- (- x (* (- y 1.0) z)) (* (- t 1.0) a))))
        (t_2 (* (- y) z)))
   (if (<= t_1 -4e+304) t_2 (if (<= t_1 1e+306) (+ (+ z x) a) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a));
	double t_2 = -y * z;
	double tmp;
	if (t_1 <= -4e+304) {
		tmp = t_2;
	} else if (t_1 <= 1e+306) {
		tmp = (z + x) + a;
	} 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 = (((t + y) - 2.0d0) * b) + ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a))
    t_2 = -y * z
    if (t_1 <= (-4d+304)) then
        tmp = t_2
    else if (t_1 <= 1d+306) then
        tmp = (z + x) + a
    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 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a));
	double t_2 = -y * z;
	double tmp;
	if (t_1 <= -4e+304) {
		tmp = t_2;
	} else if (t_1 <= 1e+306) {
		tmp = (z + x) + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a))
	t_2 = -y * z
	tmp = 0
	if t_1 <= -4e+304:
		tmp = t_2
	elif t_1 <= 1e+306:
		tmp = (z + x) + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(t + y) - 2.0) * b) + Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)))
	t_2 = Float64(Float64(-y) * z)
	tmp = 0.0
	if (t_1 <= -4e+304)
		tmp = t_2;
	elseif (t_1 <= 1e+306)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a));
	t_2 = -y * z;
	tmp = 0.0;
	if (t_1 <= -4e+304)
		tmp = t_2;
	elseif (t_1 <= 1e+306)
		tmp = (z + x) + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-y) * z), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+304], t$95$2, If[LessEqual[t$95$1, 1e+306], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -3.9999999999999998e304 or 1.00000000000000002e306 < (+.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 87.5%

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

   3. Taylor expanded in 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. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      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 36.4

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

   5. Applied rewrites 36.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 36.2%

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

   if -3.9999999999999998e304 < (+.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)) < 1.00000000000000002e306

   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 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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 59.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 49.5%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \leq -4 \cdot 10^{+304}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \leq 10^{+306}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \mathsf{fma}\left(-1, t + y, 2\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + x\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+19}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b) (fma -1.0 (+ t y) 2.0))))
   (if (<= b -3e+43)
     t_1
     (if (<= b 1.2e-25)
       (fma (- 1.0 t) a (+ z x))
       (if (<= b 7e+19)
         (* (- b z) y)
         (if (<= b 1.05e+94) (fma (- 1.0 y) z (+ a x)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -b * fma(-1.0, (t + y), 2.0);
	double tmp;
	if (b <= -3e+43) {
		tmp = t_1;
	} else if (b <= 1.2e-25) {
		tmp = fma((1.0 - t), a, (z + x));
	} else if (b <= 7e+19) {
		tmp = (b - z) * y;
	} else if (b <= 1.05e+94) {
		tmp = fma((1.0 - y), z, (a + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-b) * fma(-1.0, Float64(t + y), 2.0))
	tmp = 0.0
	if (b <= -3e+43)
		tmp = t_1;
	elseif (b <= 1.2e-25)
		tmp = fma(Float64(1.0 - t), a, Float64(z + x));
	elseif (b <= 7e+19)
		tmp = Float64(Float64(b - z) * y);
	elseif (b <= 1.05e+94)
		tmp = fma(Float64(1.0 - y), z, Float64(a + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-b) * N[(-1.0 * N[(t + y), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+43], t$95$1, If[LessEqual[b, 1.2e-25], N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+19], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[b, 1.05e+94], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.00000000000000017e43 or 1.04999999999999995e94 < 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 x around 0

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

   5. Applied rewrites 94.4%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 74.6%

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

   if -3.00000000000000017e43 < b < 1.20000000000000005e-25

   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 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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 74.2%

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

   if 1.20000000000000005e-25 < b < 7e19

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.5

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

   5. Applied rewrites 77.5%

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

   if 7e19 < b < 1.04999999999999995e94

   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 94.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 79.7%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+43}:\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, t + y, 2\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + x\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+19}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, t + y, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 42.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ t_2 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-308}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-173}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)) (t_2 (* (- 1.0 y) z)))
   (if (<= z -1.1e+87)
     t_2
     (if (<= z -2.8e+23)
       t_1
       (if (<= z 6.5e-308)
         (+ (+ z x) a)
         (if (<= z 5.8e-173) (* (- y 2.0) b) (if (<= z 6e+31) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double t_2 = (1.0 - y) * z;
	double tmp;
	if (z <= -1.1e+87) {
		tmp = t_2;
	} else if (z <= -2.8e+23) {
		tmp = t_1;
	} else if (z <= 6.5e-308) {
		tmp = (z + x) + a;
	} else if (z <= 5.8e-173) {
		tmp = (y - 2.0) * b;
	} else if (z <= 6e+31) {
		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 = (1.0d0 - t) * a
    t_2 = (1.0d0 - y) * z
    if (z <= (-1.1d+87)) then
        tmp = t_2
    else if (z <= (-2.8d+23)) then
        tmp = t_1
    else if (z <= 6.5d-308) then
        tmp = (z + x) + a
    else if (z <= 5.8d-173) then
        tmp = (y - 2.0d0) * b
    else if (z <= 6d+31) 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 = (1.0 - t) * a;
	double t_2 = (1.0 - y) * z;
	double tmp;
	if (z <= -1.1e+87) {
		tmp = t_2;
	} else if (z <= -2.8e+23) {
		tmp = t_1;
	} else if (z <= 6.5e-308) {
		tmp = (z + x) + a;
	} else if (z <= 5.8e-173) {
		tmp = (y - 2.0) * b;
	} else if (z <= 6e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - t) * a
	t_2 = (1.0 - y) * z
	tmp = 0
	if z <= -1.1e+87:
		tmp = t_2
	elif z <= -2.8e+23:
		tmp = t_1
	elif z <= 6.5e-308:
		tmp = (z + x) + a
	elif z <= 5.8e-173:
		tmp = (y - 2.0) * b
	elif z <= 6e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	t_2 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -1.1e+87)
		tmp = t_2;
	elseif (z <= -2.8e+23)
		tmp = t_1;
	elseif (z <= 6.5e-308)
		tmp = Float64(Float64(z + x) + a);
	elseif (z <= 5.8e-173)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (z <= 6e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - t) * a;
	t_2 = (1.0 - y) * z;
	tmp = 0.0;
	if (z <= -1.1e+87)
		tmp = t_2;
	elseif (z <= -2.8e+23)
		tmp = t_1;
	elseif (z <= 6.5e-308)
		tmp = (z + x) + a;
	elseif (z <= 5.8e-173)
		tmp = (y - 2.0) * b;
	elseif (z <= 6e+31)
		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[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.1e+87], t$95$2, If[LessEqual[z, -2.8e+23], t$95$1, If[LessEqual[z, 6.5e-308], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[z, 5.8e-173], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[z, 6e+31], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1e87 or 5.99999999999999978e31 < z

   1. Initial program 93.5%

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

   3. Taylor expanded in 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. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      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 66.2

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

   5. Applied rewrites 66.2%

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

   if -1.1e87 < z < -2.8e23 or 5.7999999999999997e-173 < z < 5.99999999999999978e31

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 51.7

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

   5. Applied rewrites 51.7%

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

   if -2.8e23 < z < 6.4999999999999999e-308

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 77.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 51.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 40.7%

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

   if 6.4999999999999999e-308 < z < 5.7999999999999997e-173

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 73.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 71.7%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 56.6%

       \[\leadsto \left(y - 2\right) \cdot \color{blue}{b} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, z + x\right)\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.66 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + x\right) + a\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a (+ z x))) (t_2 (* (- b a) t)))
   (if (<= t -1.66e+143)
     t_2
     (if (<= t -3.4e-15)
       t_1
       (if (<= t 3.2e-31)
         (+ (+ (fma -2.0 b z) x) a)
         (if (<= t 1.25e+104) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, (z + x));
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -1.66e+143) {
		tmp = t_2;
	} else if (t <= -3.4e-15) {
		tmp = t_1;
	} else if (t <= 3.2e-31) {
		tmp = (fma(-2.0, b, z) + x) + a;
	} else if (t <= 1.25e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, Float64(z + x))
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.66e+143)
		tmp = t_2;
	elseif (t <= -3.4e-15)
		tmp = t_1;
	elseif (t <= 3.2e-31)
		tmp = Float64(Float64(fma(-2.0, b, z) + x) + a);
	elseif (t <= 1.25e+104)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.66e+143], t$95$2, If[LessEqual[t, -3.4e-15], t$95$1, If[LessEqual[t, 3.2e-31], N[(N[(N[(-2.0 * b + z), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 1.25e+104], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.66000000000000007e143 or 1.2499999999999999e104 < t

   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 81.3

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

   5. Applied rewrites 81.3%

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

   if -1.66000000000000007e143 < t < -3.4e-15 or 3.20000000000000018e-31 < t < 1.2499999999999999e104

   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 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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 79.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 69.1%

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

   if -3.4e-15 < t < 3.20000000000000018e-31

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 62.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 62.5%

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

Alternative 6: 54.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.28 \cdot 10^{-179}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-239}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -5.5e+74)
     t_1
     (if (<= t -1.28e-179)
       (+ (+ z x) a)
       (if (<= t -1.5e-239)
         (* (- b z) y)
         (if (<= t 8.5e-22) (+ (fma -2.0 b x) a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -5.5e+74) {
		tmp = t_1;
	} else if (t <= -1.28e-179) {
		tmp = (z + x) + a;
	} else if (t <= -1.5e-239) {
		tmp = (b - z) * y;
	} else if (t <= 8.5e-22) {
		tmp = fma(-2.0, b, x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -5.5e+74)
		tmp = t_1;
	elseif (t <= -1.28e-179)
		tmp = Float64(Float64(z + x) + a);
	elseif (t <= -1.5e-239)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 8.5e-22)
		tmp = Float64(fma(-2.0, b, x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.5e+74], t$95$1, If[LessEqual[t, -1.28e-179], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, -1.5e-239], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 8.5e-22], N[(N[(-2.0 * b + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.5000000000000003e74 or 8.5000000000000001e-22 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.3

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

   5. Applied rewrites 68.3%

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

   if -5.5000000000000003e74 < t < -1.28000000000000006e-179

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0

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

      1. 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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 61.9%

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

   if -1.28000000000000006e-179 < t < -1.4999999999999999e-239

   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 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 67.8

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

   5. Applied rewrites 67.8%

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

   if -1.4999999999999999e-239 < t < 8.5000000000000001e-22

   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 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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 64.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 64.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 42.8%

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

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 56.4%

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

Alternative 7: 86.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a (+ (fma (- t 2.0) b x) z))))
   (if (<= t -8.5e+78)
     t_1
     (if (<= t 5.8e-20) (fma (- 1.0 y) z (+ (fma (- y 2.0) b x) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, (fma((t - 2.0), b, x) + z));
	double tmp;
	if (t <= -8.5e+78) {
		tmp = t_1;
	} else if (t <= 5.8e-20) {
		tmp = fma((1.0 - y), z, (fma((y - 2.0), b, x) + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, Float64(fma(Float64(t - 2.0), b, x) + z))
	tmp = 0.0
	if (t <= -8.5e+78)
		tmp = t_1;
	elseif (t <= 5.8e-20)
		tmp = fma(Float64(1.0 - y), z, Float64(fma(Float64(y - 2.0), b, x) + a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+78], t$95$1, If[LessEqual[t, 5.8e-20], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000079e78 or 5.8e-20 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 84.0%

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

   if -8.50000000000000079e78 < t < 5.8e-20

   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 97.9%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.4e+21)
   (fma (- (+ t y) 2.0) b (* (- z) y))
   (if (<= y 2.4e-11)
     (fma (- 1.0 t) a (+ (fma (- t 2.0) b x) z))
     (fma (- 1.0 t) a (fma (- 1.0 y) z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.4e+21) {
		tmp = fma(((t + y) - 2.0), b, (-z * y));
	} else if (y <= 2.4e-11) {
		tmp = fma((1.0 - t), a, (fma((t - 2.0), b, x) + z));
	} else {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.4e+21)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(-z) * y));
	elseif (y <= 2.4e-11)
		tmp = fma(Float64(1.0 - t), a, Float64(fma(Float64(t - 2.0), b, x) + z));
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.4e+21], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-z) * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-11], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4e21

   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 y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 74.0

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

   5. Applied rewrites 74.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 75.9

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 75.9

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

   7. Applied rewrites 75.9%

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

   if -4.4e21 < y < 2.4000000000000001e-11

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 98.6%

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

   if 2.4000000000000001e-11 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 72.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + x\right) + a\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.28 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-270}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 2020:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ z x) a)) (t_2 (* (- b a) t)))
   (if (<= t -5.5e+74)
     t_2
     (if (<= t -1.28e-179)
       t_1
       (if (<= t 3.5e-270) (* (- b z) y) (if (<= t 2020.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + x) + a;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -5.5e+74) {
		tmp = t_2;
	} else if (t <= -1.28e-179) {
		tmp = t_1;
	} else if (t <= 3.5e-270) {
		tmp = (b - z) * y;
	} else if (t <= 2020.0) {
		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 = (z + x) + a
    t_2 = (b - a) * t
    if (t <= (-5.5d+74)) then
        tmp = t_2
    else if (t <= (-1.28d-179)) then
        tmp = t_1
    else if (t <= 3.5d-270) then
        tmp = (b - z) * y
    else if (t <= 2020.0d0) 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 = (z + x) + a;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -5.5e+74) {
		tmp = t_2;
	} else if (t <= -1.28e-179) {
		tmp = t_1;
	} else if (t <= 3.5e-270) {
		tmp = (b - z) * y;
	} else if (t <= 2020.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + x) + a
	t_2 = (b - a) * t
	tmp = 0
	if t <= -5.5e+74:
		tmp = t_2
	elif t <= -1.28e-179:
		tmp = t_1
	elif t <= 3.5e-270:
		tmp = (b - z) * y
	elif t <= 2020.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + x) + a)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -5.5e+74)
		tmp = t_2;
	elseif (t <= -1.28e-179)
		tmp = t_1;
	elseif (t <= 3.5e-270)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 2020.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + x) + a;
	t_2 = (b - a) * t;
	tmp = 0.0;
	if (t <= -5.5e+74)
		tmp = t_2;
	elseif (t <= -1.28e-179)
		tmp = t_1;
	elseif (t <= 3.5e-270)
		tmp = (b - z) * y;
	elseif (t <= 2020.0)
		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[(z + x), $MachinePrecision] + a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.5e+74], t$95$2, If[LessEqual[t, -1.28e-179], t$95$1, If[LessEqual[t, 3.5e-270], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 2020.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5000000000000003e74 or 2020 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in 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 69.4

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

   5. Applied rewrites 69.4%

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

   if -5.5000000000000003e74 < t < -1.28000000000000006e-179 or 3.49999999999999994e-270 < t < 2020

   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

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 58.2%

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

   if -1.28000000000000006e-179 < t < 3.49999999999999994e-270

   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 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 51.5

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

   5. Applied rewrites 51.5%

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

Alternative 10: 73.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -8.5e+78)
     t_1
     (if (<= t 3.2e-31)
       (fma 1.0 z (+ (fma (- y 2.0) b x) a))
       (if (<= t 1.25e+104) (fma (- 1.0 t) a (+ z x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -8.5e+78) {
		tmp = t_1;
	} else if (t <= 3.2e-31) {
		tmp = fma(1.0, z, (fma((y - 2.0), b, x) + a));
	} else if (t <= 1.25e+104) {
		tmp = fma((1.0 - t), a, (z + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -8.5e+78)
		tmp = t_1;
	elseif (t <= 3.2e-31)
		tmp = fma(1.0, z, Float64(fma(Float64(y - 2.0), b, x) + a));
	elseif (t <= 1.25e+104)
		tmp = fma(Float64(1.0 - t), a, Float64(z + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -8.5e+78], t$95$1, If[LessEqual[t, 3.2e-31], N[(1.0 * z + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+104], N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.50000000000000079e78 or 1.2499999999999999e104 < t

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.7

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

   5. Applied rewrites 76.7%

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

   if -8.50000000000000079e78 < t < 3.20000000000000018e-31

   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 t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 80.0%

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

   if 3.20000000000000018e-31 < t < 1.2499999999999999e104

   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 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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 67.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+78}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(1, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, t + y, 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.5e+43)
   (fma (- (+ t y) 2.0) b (* (- z) y))
   (if (<= b 6.5e+151)
     (fma (- 1.0 t) a (fma (- 1.0 y) z x))
     (* (- b) (fma -1.0 (+ t y) 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.5e+43) {
		tmp = fma(((t + y) - 2.0), b, (-z * y));
	} else if (b <= 6.5e+151) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = -b * fma(-1.0, (t + y), 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.5e+43)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(-z) * y));
	elseif (b <= 6.5e+151)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = Float64(Float64(-b) * fma(-1.0, Float64(t + y), 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.5e+43], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-z) * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+151], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], N[((-b) * N[(-1.0 * N[(t + y), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.50000000000000008e43

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 77.2

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

   5. Applied rewrites 77.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 81.3

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 81.3

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

   7. Applied rewrites 81.3%

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

   if -1.50000000000000008e43 < b < 6.5000000000000002e151

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.1%

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

   if 6.5000000000000002e151 < b

   1. Initial program 92.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.0%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 88.4%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, t + y, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-b\right) \cdot \mathsf{fma}\left(-1, t + y, 2\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b) (fma -1.0 (+ t y) 2.0))))
   (if (<= b -6e+43)
     t_1
     (if (<= b 6.5e+151) (fma (- 1.0 t) a (fma (- 1.0 y) z x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -b * fma(-1.0, (t + y), 2.0);
	double tmp;
	if (b <= -6e+43) {
		tmp = t_1;
	} else if (b <= 6.5e+151) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-b) * fma(-1.0, Float64(t + y), 2.0))
	tmp = 0.0
	if (b <= -6e+43)
		tmp = t_1;
	elseif (b <= 6.5e+151)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-b) * N[(-1.0 * N[(t + y), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+43], t$95$1, If[LessEqual[b, 6.5e+151], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.00000000000000033e43 or 6.5000000000000002e151 < 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 x around 0

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

   5. Applied rewrites 94.6%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 80.0%

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

   if -6.00000000000000033e43 < b < 6.5000000000000002e151

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.1%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+43}:\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, t + y, 2\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \mathsf{fma}\left(-1, t + y, 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.3e+76)
     t_1
     (if (<= t 1.56e+31) (fma (- 1.0 y) z (+ a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.3e+76) {
		tmp = t_1;
	} else if (t <= 1.56e+31) {
		tmp = fma((1.0 - y), z, (a + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.3e+76)
		tmp = t_1;
	elseif (t <= 1.56e+31)
		tmp = fma(Float64(1.0 - y), z, Float64(a + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.3e+76], t$95$1, If[LessEqual[t, 1.56e+31], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e76 or 1.56000000000000004e31 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   if -1.3e76 < t < 1.56000000000000004e31

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 95.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 69.2%

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

Alternative 14: 61.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2020:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -5.5e+74) t_1 (if (<= t 2020.0) (+ (+ (fma -2.0 b z) x) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -5.5e+74) {
		tmp = t_1;
	} else if (t <= 2020.0) {
		tmp = (fma(-2.0, b, z) + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -5.5e+74)
		tmp = t_1;
	elseif (t <= 2020.0)
		tmp = Float64(Float64(fma(-2.0, b, z) + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.5e+74], t$95$1, If[LessEqual[t, 2020.0], N[(N[(N[(-2.0 * b + z), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5000000000000003e74 or 2020 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in 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 69.4

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

   5. Applied rewrites 69.4%

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

   if -5.5000000000000003e74 < t < 2020

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 64.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 62.8%

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

Alternative 15: 23.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+127}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-177}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-22}:\\ \;\;\;\;1 \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9e+127)
   (* b t)
   (if (<= t -8e-177) (* 1.0 z) (if (<= t 8.5e-22) (* 1.0 a) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+127) {
		tmp = b * t;
	} else if (t <= -8e-177) {
		tmp = 1.0 * z;
	} else if (t <= 8.5e-22) {
		tmp = 1.0 * a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9d+127)) then
        tmp = b * t
    else if (t <= (-8d-177)) then
        tmp = 1.0d0 * z
    else if (t <= 8.5d-22) then
        tmp = 1.0d0 * a
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9e+127) {
		tmp = b * t;
	} else if (t <= -8e-177) {
		tmp = 1.0 * z;
	} else if (t <= 8.5e-22) {
		tmp = 1.0 * a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9e+127:
		tmp = b * t
	elif t <= -8e-177:
		tmp = 1.0 * z
	elif t <= 8.5e-22:
		tmp = 1.0 * a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9e+127)
		tmp = Float64(b * t);
	elseif (t <= -8e-177)
		tmp = Float64(1.0 * z);
	elseif (t <= 8.5e-22)
		tmp = Float64(1.0 * a);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9e+127)
		tmp = b * t;
	elseif (t <= -8e-177)
		tmp = 1.0 * z;
	elseif (t <= 8.5e-22)
		tmp = 1.0 * a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9e+127], N[(b * t), $MachinePrecision], If[LessEqual[t, -8e-177], N[(1.0 * z), $MachinePrecision], If[LessEqual[t, 8.5e-22], N[(1.0 * a), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.00000000000000068e127 or 8.5000000000000001e-22 < t

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.1%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 41.1%

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

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 35.7%

       \[\leadsto b \cdot t \]

   if -9.00000000000000068e127 < t < -7.99999999999999962e-177

   1. Initial program 96.9%

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

   3. Taylor expanded in 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. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      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 42.3

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

   5. Applied rewrites 42.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 26.6%

      \[\leadsto 1 \cdot z \]

   if -7.99999999999999962e-177 < t < 8.5000000000000001e-22

   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 a around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 19.1

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

   5. Applied rewrites 19.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 19.1%

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

Alternative 16: 55.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2020:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -5.5e+74) t_1 (if (<= t 2020.0) (+ (+ z x) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -5.5e+74) {
		tmp = t_1;
	} else if (t <= 2020.0) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-5.5d+74)) then
        tmp = t_1
    else if (t <= 2020.0d0) then
        tmp = (z + x) + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -5.5e+74) {
		tmp = t_1;
	} else if (t <= 2020.0) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -5.5e+74:
		tmp = t_1
	elif t <= 2020.0:
		tmp = (z + x) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -5.5e+74)
		tmp = t_1;
	elseif (t <= 2020.0)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -5.5e+74)
		tmp = t_1;
	elseif (t <= 2020.0)
		tmp = (z + x) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.5e+74], t$95$1, If[LessEqual[t, 2020.0], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5000000000000003e74 or 2020 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in 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 69.4

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

   5. Applied rewrites 69.4%

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

   if -5.5000000000000003e74 < t < 2020

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 64.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 62.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 50.2%

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

Alternative 17: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+128}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+104}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.05e+128)
   (* (- a) t)
   (if (<= t 1.25e+104) (+ (+ z x) a) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e+128) {
		tmp = -a * t;
	} else if (t <= 1.25e+104) {
		tmp = (z + x) + a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.05d+128)) then
        tmp = -a * t
    else if (t <= 1.25d+104) then
        tmp = (z + x) + a
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.05e+128) {
		tmp = -a * t;
	} else if (t <= 1.25e+104) {
		tmp = (z + x) + a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.05e+128:
		tmp = -a * t
	elif t <= 1.25e+104:
		tmp = (z + x) + a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.05e+128)
		tmp = Float64(Float64(-a) * t);
	elseif (t <= 1.25e+104)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.05e+128)
		tmp = -a * t;
	elseif (t <= 1.25e+104)
		tmp = (z + x) + a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.05e+128], N[((-a) * t), $MachinePrecision], If[LessEqual[t, 1.25e+104], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e128

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.6

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

   5. Applied rewrites 75.6%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 54.3%

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

   if -1.05e128 < t < 1.2499999999999999e104

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 68.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 55.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 45.9%

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

   if 1.2499999999999999e104 < t

   1. Initial program 86.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 58.1%

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

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 55.8%

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

Alternative 18: 41.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+184}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+104}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.65e+184) (* b t) (if (<= t 1.25e+104) (+ (+ z x) a) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.65e+184) {
		tmp = b * t;
	} else if (t <= 1.25e+104) {
		tmp = (z + x) + a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.65d+184)) then
        tmp = b * t
    else if (t <= 1.25d+104) then
        tmp = (z + x) + a
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.65e+184) {
		tmp = b * t;
	} else if (t <= 1.25e+104) {
		tmp = (z + x) + a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.65e+184:
		tmp = b * t
	elif t <= 1.25e+104:
		tmp = (z + x) + a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.65e+184)
		tmp = Float64(b * t);
	elseif (t <= 1.25e+104)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.65e+184)
		tmp = b * t;
	elseif (t <= 1.25e+104)
		tmp = (z + x) + a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.65e+184], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.25e+104], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6499999999999999e184 or 1.2499999999999999e104 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 95.4%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 47.3%

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

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 44.3%

       \[\leadsto b \cdot t \]

   if -1.6499999999999999e184 < t < 1.2499999999999999e104

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 69.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 54.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 44.9%

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

Alternative 19: 24.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+87}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-22}:\\ \;\;\;\;1 \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1e+87) (* b t) (if (<= t 8.5e-22) (* 1.0 a) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e+87) {
		tmp = b * t;
	} else if (t <= 8.5e-22) {
		tmp = 1.0 * a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1d+87)) then
        tmp = b * t
    else if (t <= 8.5d-22) then
        tmp = 1.0d0 * a
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1e+87) {
		tmp = b * t;
	} else if (t <= 8.5e-22) {
		tmp = 1.0 * a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1e+87:
		tmp = b * t
	elif t <= 8.5e-22:
		tmp = 1.0 * a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1e+87)
		tmp = Float64(b * t);
	elseif (t <= 8.5e-22)
		tmp = Float64(1.0 * a);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1e+87)
		tmp = b * t;
	elseif (t <= 8.5e-22)
		tmp = 1.0 * a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1e+87], N[(b * t), $MachinePrecision], If[LessEqual[t, 8.5e-22], N[(1.0 * a), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.9999999999999996e86 or 8.5000000000000001e-22 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.5%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 40.0%

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

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 34.2%

       \[\leadsto b \cdot t \]

   if -9.9999999999999996e86 < t < 8.5000000000000001e-22

   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 a around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 19.5

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

   5. Applied rewrites 19.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 16.3%

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

Alternative 20: 22.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+42}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 2:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.15e+42) (* b t) (if (<= t 2.0) (* -2.0 b) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.15e+42) {
		tmp = b * t;
	} else if (t <= 2.0) {
		tmp = -2.0 * b;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.15d+42)) then
        tmp = b * t
    else if (t <= 2.0d0) then
        tmp = (-2.0d0) * b
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.15e+42) {
		tmp = b * t;
	} else if (t <= 2.0) {
		tmp = -2.0 * b;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.15e+42:
		tmp = b * t
	elif t <= 2.0:
		tmp = -2.0 * b
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.15e+42)
		tmp = Float64(b * t);
	elseif (t <= 2.0)
		tmp = Float64(-2.0 * b);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.15e+42)
		tmp = b * t;
	elseif (t <= 2.0)
		tmp = -2.0 * b;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.15e+42], N[(b * t), $MachinePrecision], If[LessEqual[t, 2.0], N[(-2.0 * b), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e42 or 2 < t

   1. Initial program 92.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 95.9%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 38.9%

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

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 31.9%

       \[\leadsto b \cdot t \]

   if -1.15e42 < t < 2

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      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

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

      21. +-commutative N/A

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

   5. Applied rewrites 64.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 62.7%

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

   9. Taylor expanded in b around inf

      \[\leadsto -2 \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 14.2%

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

Alternative 21: 17.3% accurate, 6.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 98.0%

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

6. Taylor expanded in b around -inf

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

8. Applied rewrites 34.9%

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

9. Taylor expanded in t around inf

   \[\leadsto b \cdot t \]
10. Step-by-step derivation

11. Applied rewrites 16.6%

    \[\leadsto b \cdot t \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024332 
(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)))