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

Percentage Accurate: 95.2% → 97.9%

Time: 13.6s

Alternatives: 16

Speedup: 0.5×

• 37.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lift--.f64 N/A

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

      11. associate--l- N/A

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

      12. lower--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

   4. Applied egg-rr 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 77.8

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

   5. Simplified 77.8%

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

4. Final simplification 99.2%

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

Alternative 2: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + -2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(b, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y -2.0))) (t_2 (* t (- b a))))
   (if (<= t -1.1e-11)
     t_2
     (if (<= t -2.9e-157)
       t_1
       (if (<= t -1.52e-261)
         (+ x a)
         (if (<= t 1.7e-183) t_1 (if (<= t 7.2e+56) (fma b y x) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + -2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.1e-11) {
		tmp = t_2;
	} else if (t <= -2.9e-157) {
		tmp = t_1;
	} else if (t <= -1.52e-261) {
		tmp = x + a;
	} else if (t <= 1.7e-183) {
		tmp = t_1;
	} else if (t <= 7.2e+56) {
		tmp = fma(b, y, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + -2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.1e-11)
		tmp = t_2;
	elseif (t <= -2.9e-157)
		tmp = t_1;
	elseif (t <= -1.52e-261)
		tmp = Float64(x + a);
	elseif (t <= 1.7e-183)
		tmp = t_1;
	elseif (t <= 7.2e+56)
		tmp = fma(b, y, x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e-11], t$95$2, If[LessEqual[t, -2.9e-157], t$95$1, If[LessEqual[t, -1.52e-261], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.7e-183], t$95$1, If[LessEqual[t, 7.2e+56], N[(b * y + x), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1000000000000001e-11 or 7.19999999999999996e56 < t

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 72.8

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

   5. Simplified 72.8%

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

   if -1.1000000000000001e-11 < t < -2.89999999999999988e-157 or -1.5200000000000001e-261 < t < 1.70000000000000007e-183

   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 b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 58.5

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

   5. Simplified 58.5%

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

   6. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. lower-+.f64 N/A

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

      4. metadata-eval 58.5

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

   8. Simplified 58.5%

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

   if -2.89999999999999988e-157 < t < -1.5200000000000001e-261

   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 z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. distribute-neg-in N/A

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

      20. metadata-eval N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 67.5

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

   5. Simplified 67.5%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 48.2

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

   8. Simplified 48.2%

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

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{x + a} \]

       2. lower-+.f64 48.2

          \[\leadsto \color{blue}{x + a} \]

   11. Simplified 48.2%

       \[\leadsto \color{blue}{x + a} \]

   if 1.70000000000000007e-183 < t < 7.19999999999999996e56

   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. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lift--.f64 N/A

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

      11. associate--l- N/A

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

      12. lower--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-*.f64 N/A

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

      8. cancel-sign-sub-inv N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 64.4

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

   7. Simplified 64.4%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 57.6

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

   10. Simplified 57.6%

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

Alternative 3: 79.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+141}:\\ \;\;\;\;x - \mathsf{fma}\left(y + -1, z, t \cdot \left(a - b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t + -2, b, y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6e-11)
   (* b (+ y (+ t -2.0)))
   (if (<= b 8.5e-49)
     (fma a (- 1.0 t) (fma z (- 1.0 y) x))
     (if (<= b 7.2e+141)
       (- x (fma (+ y -1.0) z (* t (- a b))))
       (fma (+ t -2.0) b (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e-11) {
		tmp = b * (y + (t + -2.0));
	} else if (b <= 8.5e-49) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else if (b <= 7.2e+141) {
		tmp = x - fma((y + -1.0), z, (t * (a - b)));
	} else {
		tmp = fma((t + -2.0), b, (y * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6e-11)
		tmp = Float64(b * Float64(y + Float64(t + -2.0)));
	elseif (b <= 8.5e-49)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	elseif (b <= 7.2e+141)
		tmp = Float64(x - fma(Float64(y + -1.0), z, Float64(t * Float64(a - b))));
	else
		tmp = fma(Float64(t + -2.0), b, Float64(y * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6e-11], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-49], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e+141], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(t * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + -2.0), $MachinePrecision] * b + N[(y * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.59999999999999997e-11

   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 b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 79.0

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

   5. Simplified 79.0%

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

   if -1.59999999999999997e-11 < b < 8.50000000000000069e-49

   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 b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Simplified 94.1%

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

   if 8.50000000000000069e-49 < b < 7.2000000000000003e141

   1. Initial program 97.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lift--.f64 N/A

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

      11. associate--l- N/A

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

      12. lower--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

   4. Applied egg-rr 97.4%

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

   5. Taylor expanded in t around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. lower--.f64 78.4

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

   7. Simplified 78.4%

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

   if 7.2000000000000003e141 < b

   1. Initial program 92.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 87.5

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

   5. Simplified 87.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 87.5

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

   7. Applied egg-rr 87.5%

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

Alternative 4: 36.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + -2\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(b, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;-t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y -2.0))))
   (if (<= t -3.5e+43)
     (* t b)
     (if (<= t -2.9e-157)
       t_1
       (if (<= t -1.52e-261)
         (+ x a)
         (if (<= t 1.7e-183)
           t_1
           (if (<= t 7.8e+139) (fma b y x) (- (* t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + -2.0);
	double tmp;
	if (t <= -3.5e+43) {
		tmp = t * b;
	} else if (t <= -2.9e-157) {
		tmp = t_1;
	} else if (t <= -1.52e-261) {
		tmp = x + a;
	} else if (t <= 1.7e-183) {
		tmp = t_1;
	} else if (t <= 7.8e+139) {
		tmp = fma(b, y, x);
	} else {
		tmp = -(t * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + -2.0))
	tmp = 0.0
	if (t <= -3.5e+43)
		tmp = Float64(t * b);
	elseif (t <= -2.9e-157)
		tmp = t_1;
	elseif (t <= -1.52e-261)
		tmp = Float64(x + a);
	elseif (t <= 1.7e-183)
		tmp = t_1;
	elseif (t <= 7.8e+139)
		tmp = fma(b, y, x);
	else
		tmp = Float64(-Float64(t * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+43], N[(t * b), $MachinePrecision], If[LessEqual[t, -2.9e-157], t$95$1, If[LessEqual[t, -1.52e-261], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.7e-183], t$95$1, If[LessEqual[t, 7.8e+139], N[(b * y + x), $MachinePrecision], (-N[(t * a), $MachinePrecision])]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.5000000000000001e43

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 82.8

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

   5. Simplified 82.8%

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

   6. Taylor expanded in b around inf

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

      1. lower-*.f64 51.3

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

   8. Simplified 51.3%

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

   if -3.5000000000000001e43 < t < -2.89999999999999988e-157 or -1.5200000000000001e-261 < t < 1.70000000000000007e-183

   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 b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 54.0

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

   5. Simplified 54.0%

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

   6. Taylor expanded in t around 0

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. lower-+.f64 N/A

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

      4. metadata-eval 52.9

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

   8. Simplified 52.9%

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

   if -2.89999999999999988e-157 < t < -1.5200000000000001e-261

   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 z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. distribute-neg-in N/A

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

      20. metadata-eval N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 67.5

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

   5. Simplified 67.5%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 48.2

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

   8. Simplified 48.2%

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

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{x + a} \]

       2. lower-+.f64 48.2

          \[\leadsto \color{blue}{x + a} \]

   11. Simplified 48.2%

       \[\leadsto \color{blue}{x + a} \]

   if 1.70000000000000007e-183 < t < 7.80000000000000012e139

   1. Initial program 98.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lift--.f64 N/A

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

      11. associate--l- N/A

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

      12. lower--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. +-commutative N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. lower-*.f64 N/A

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

      8. cancel-sign-sub-inv N/A

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

      9. metadata-eval N/A

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

      10. *-lft-identity N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 60.0

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

   7. Simplified 60.0%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. cancel-sign-sub N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 53.5

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

   10. Simplified 53.5%

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

   if 7.80000000000000012e139 < t

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 71.7

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

   5. Simplified 71.7%

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

   6. Taylor expanded in b around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 45.0

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

   8. Simplified 45.0%

      \[\leadsto \color{blue}{t \cdot \left(-a\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+43}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-183}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(b, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;-t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.38 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(y, b - z, \mathsf{fma}\left(b, t + -2, x + z\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.38e-11)
   (fma y (- b z) (fma b (+ t -2.0) (+ x z)))
   (if (<= b 1.12e-38)
     (fma a (- 1.0 t) (fma z (- 1.0 y) x))
     (fma b (+ y (+ t -2.0)) (fma a (- 1.0 t) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.38e-11) {
		tmp = fma(y, (b - z), fma(b, (t + -2.0), (x + z)));
	} else if (b <= 1.12e-38) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = fma(b, (y + (t + -2.0)), fma(a, (1.0 - t), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.38e-11)
		tmp = fma(y, Float64(b - z), fma(b, Float64(t + -2.0), Float64(x + z)));
	elseif (b <= 1.12e-38)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = fma(b, Float64(y + Float64(t + -2.0)), fma(a, Float64(1.0 - t), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.38e-11], N[(y * N[(b - z), $MachinePrecision] + N[(b * N[(t + -2.0), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e-38], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.38e-11

   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 a around 0

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

   5. Simplified 94.2%

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

   if -1.38e-11 < b < 1.1200000000000001e-38

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Simplified 93.1%

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

   if 1.1200000000000001e-38 < b

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. distribute-neg-in N/A

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

      20. metadata-eval N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 88.2

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

   5. Simplified 88.2%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.38 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(y, b - z, \mathsf{fma}\left(b, t + -2, x + z\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \mathsf{fma}\left(y + -1, z, t \cdot \left(a - b\right)\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (fma (+ y -1.0) z (* t (- a b))))))
   (if (<= z -9.2e+75)
     t_1
     (if (<= z 1.35e+80) (fma b (+ y (+ t -2.0)) (fma a (- 1.0 t) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - fma((y + -1.0), z, (t * (a - b)));
	double tmp;
	if (z <= -9.2e+75) {
		tmp = t_1;
	} else if (z <= 1.35e+80) {
		tmp = fma(b, (y + (t + -2.0)), fma(a, (1.0 - t), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - fma(Float64(y + -1.0), z, Float64(t * Float64(a - b))))
	tmp = 0.0
	if (z <= -9.2e+75)
		tmp = t_1;
	elseif (z <= 1.35e+80)
		tmp = fma(b, Float64(y + Float64(t + -2.0)), fma(a, Float64(1.0 - t), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(t * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+75], t$95$1, If[LessEqual[z, 1.35e+80], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.1999999999999994e75 or 1.34999999999999991e80 < z

   1. Initial program 93.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lift--.f64 N/A

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

      11. associate--l- N/A

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

      12. lower--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in t around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. lower--.f64 90.0

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

   7. Simplified 90.0%

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

   if -9.1999999999999994e75 < z < 1.34999999999999991e80

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. distribute-neg-in N/A

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

      20. metadata-eval N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 90.9

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

   5. Simplified 90.9%

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

Alternative 7: 79.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+138}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t + -2, b, y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6e-11)
   (* b (+ y (+ t -2.0)))
   (if (<= b 4.2e+138)
     (fma a (- 1.0 t) (fma z (- 1.0 y) x))
     (fma (+ t -2.0) b (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e-11) {
		tmp = b * (y + (t + -2.0));
	} else if (b <= 4.2e+138) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = fma((t + -2.0), b, (y * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6e-11)
		tmp = Float64(b * Float64(y + Float64(t + -2.0)));
	elseif (b <= 4.2e+138)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = fma(Float64(t + -2.0), b, Float64(y * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6e-11], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+138], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(N[(t + -2.0), $MachinePrecision] * b + N[(y * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.59999999999999997e-11

   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 b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 79.0

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

   5. Simplified 79.0%

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

   if -1.59999999999999997e-11 < b < 4.20000000000000014e138

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Simplified 86.8%

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

   if 4.20000000000000014e138 < b

   1. Initial program 92.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 85.8

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

   5. Simplified 85.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 85.9

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

   7. Applied egg-rr 85.9%

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

Alternative 8: 31.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+51}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-302}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-86}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+141}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7e+51)
   (* t b)
   (if (<= t -6.8e-302)
     (+ x a)
     (if (<= t 2.7e-86) (* y b) (if (<= t 5e+141) (+ x z) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7e+51) {
		tmp = t * b;
	} else if (t <= -6.8e-302) {
		tmp = x + a;
	} else if (t <= 2.7e-86) {
		tmp = y * b;
	} else if (t <= 5e+141) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	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 <= (-7d+51)) then
        tmp = t * b
    else if (t <= (-6.8d-302)) then
        tmp = x + a
    else if (t <= 2.7d-86) then
        tmp = y * b
    else if (t <= 5d+141) then
        tmp = x + z
    else
        tmp = t * b
    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 <= -7e+51) {
		tmp = t * b;
	} else if (t <= -6.8e-302) {
		tmp = x + a;
	} else if (t <= 2.7e-86) {
		tmp = y * b;
	} else if (t <= 5e+141) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7e+51:
		tmp = t * b
	elif t <= -6.8e-302:
		tmp = x + a
	elif t <= 2.7e-86:
		tmp = y * b
	elif t <= 5e+141:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7e+51)
		tmp = Float64(t * b);
	elseif (t <= -6.8e-302)
		tmp = Float64(x + a);
	elseif (t <= 2.7e-86)
		tmp = Float64(y * b);
	elseif (t <= 5e+141)
		tmp = Float64(x + z);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7e+51)
		tmp = t * b;
	elseif (t <= -6.8e-302)
		tmp = x + a;
	elseif (t <= 2.7e-86)
		tmp = y * b;
	elseif (t <= 5e+141)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7e+51], N[(t * b), $MachinePrecision], If[LessEqual[t, -6.8e-302], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.7e-86], N[(y * b), $MachinePrecision], If[LessEqual[t, 5e+141], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7e51 or 5.00000000000000025e141 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 80.6

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

   5. Simplified 80.6%

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

   6. Taylor expanded in b around inf

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

      1. lower-*.f64 46.8

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

   8. Simplified 46.8%

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

   if -7e51 < t < -6.8e-302

   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 z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. distribute-neg-in N/A

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

      20. metadata-eval N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 75.2

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

   5. Simplified 75.2%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 38.1

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

   8. Simplified 38.1%

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

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{x + a} \]

       2. lower-+.f64 34.2

          \[\leadsto \color{blue}{x + a} \]

   11. Simplified 34.2%

       \[\leadsto \color{blue}{x + a} \]

   if -6.8e-302 < t < 2.69999999999999992e-86

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 54.7

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

   5. Simplified 54.7%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 41.6

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

   8. Simplified 41.6%

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

   if 2.69999999999999992e-86 < t < 5.00000000000000025e141

   1. Initial program 97.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lift--.f64 N/A

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

      11. associate--l- N/A

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

      12. lower--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

   4. Applied egg-rr 97.5%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 69.3

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

   7. Simplified 69.3%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   9. Step-by-step derivation

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

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

      2. metadata-eval N/A

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity N/A

         \[\leadsto x + \color{blue}{z} \]

      4. lower-+.f64 47.9

         \[\leadsto \color{blue}{x + z} \]

   10. Simplified 47.9%

       \[\leadsto \color{blue}{x + z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+51}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-302}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-86}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+141}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -980000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+56}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -980000000.0)
     t_1
     (if (<= t 1.15e-85) (* y (- b z)) (if (<= t 3e+56) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -980000000.0) {
		tmp = t_1;
	} else if (t <= 1.15e-85) {
		tmp = y * (b - z);
	} else if (t <= 3e+56) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-980000000.0d0)) then
        tmp = t_1
    else if (t <= 1.15d-85) then
        tmp = y * (b - z)
    else if (t <= 3d+56) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -980000000.0) {
		tmp = t_1;
	} else if (t <= 1.15e-85) {
		tmp = y * (b - z);
	} else if (t <= 3e+56) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -980000000.0:
		tmp = t_1
	elif t <= 1.15e-85:
		tmp = y * (b - z)
	elif t <= 3e+56:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -980000000.0)
		tmp = t_1;
	elseif (t <= 1.15e-85)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 3e+56)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -980000000.0)
		tmp = t_1;
	elseif (t <= 1.15e-85)
		tmp = y * (b - z);
	elseif (t <= 3e+56)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -980000000.0], t$95$1, If[LessEqual[t, 1.15e-85], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+56], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.8e8 or 3.00000000000000006e56 < 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 t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 74.4

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

   5. Simplified 74.4%

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

   if -9.8e8 < t < 1.15e-85

   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. lower-*.f64 N/A

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

      2. lower--.f64 47.6

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

   5. Simplified 47.6%

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

   if 1.15e-85 < t < 3.00000000000000006e56

   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. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lift--.f64 N/A

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

      11. associate--l- N/A

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

      12. lower--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 81.2

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

   7. Simplified 81.2%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   9. Step-by-step derivation

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

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

      2. metadata-eval N/A

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity N/A

         \[\leadsto x + \color{blue}{z} \]

      4. lower-+.f64 62.6

         \[\leadsto \color{blue}{x + z} \]

   10. Simplified 62.6%

       \[\leadsto \color{blue}{x + z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 66.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+56}:\\ \;\;\;\;a + \mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.05e+21)
     t_1
     (if (<= t 7.2e+56) (+ a (fma b (+ y -2.0) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.05e+21) {
		tmp = t_1;
	} else if (t <= 7.2e+56) {
		tmp = a + fma(b, (y + -2.0), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.05e+21)
		tmp = t_1;
	elseif (t <= 7.2e+56)
		tmp = Float64(a + fma(b, Float64(y + -2.0), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+21], t$95$1, If[LessEqual[t, 7.2e+56], N[(a + N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e21 or 7.19999999999999996e56 < 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 t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 74.4

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

   5. Simplified 74.4%

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

   if -1.05e21 < t < 7.19999999999999996e56

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. distribute-neg-in N/A

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

      20. metadata-eval N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 74.6

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

   5. Simplified 74.6%

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

   6. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval 72.9

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

   8. Simplified 72.9%

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

Alternative 11: 34.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+51}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-91}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+141}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7e+51)
   (* t b)
   (if (<= t 2.25e-91) (+ x a) (if (<= t 5e+141) (+ x z) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7e+51) {
		tmp = t * b;
	} else if (t <= 2.25e-91) {
		tmp = x + a;
	} else if (t <= 5e+141) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	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 <= (-7d+51)) then
        tmp = t * b
    else if (t <= 2.25d-91) then
        tmp = x + a
    else if (t <= 5d+141) then
        tmp = x + z
    else
        tmp = t * b
    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 <= -7e+51) {
		tmp = t * b;
	} else if (t <= 2.25e-91) {
		tmp = x + a;
	} else if (t <= 5e+141) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7e+51:
		tmp = t * b
	elif t <= 2.25e-91:
		tmp = x + a
	elif t <= 5e+141:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7e+51)
		tmp = Float64(t * b);
	elseif (t <= 2.25e-91)
		tmp = Float64(x + a);
	elseif (t <= 5e+141)
		tmp = Float64(x + z);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7e+51)
		tmp = t * b;
	elseif (t <= 2.25e-91)
		tmp = x + a;
	elseif (t <= 5e+141)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7e+51], N[(t * b), $MachinePrecision], If[LessEqual[t, 2.25e-91], N[(x + a), $MachinePrecision], If[LessEqual[t, 5e+141], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7e51 or 5.00000000000000025e141 < t

   1. Initial program 91.6%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 80.6

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

   5. Simplified 80.6%

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

   6. Taylor expanded in b around inf

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

      1. lower-*.f64 46.8

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

   8. Simplified 46.8%

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

   if -7e51 < t < 2.24999999999999988e-91

   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 z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. distribute-neg-in N/A

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

      20. metadata-eval N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 75.4

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

   5. Simplified 75.4%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 33.3

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

   8. Simplified 33.3%

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

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{x + a} \]

       2. lower-+.f64 30.7

          \[\leadsto \color{blue}{x + a} \]

   11. Simplified 30.7%

       \[\leadsto \color{blue}{x + a} \]

   if 2.24999999999999988e-91 < t < 5.00000000000000025e141

   1. Initial program 97.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lift--.f64 N/A

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

      11. associate--l- N/A

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

      12. lower--.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 71.4

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   9. Step-by-step derivation

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

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

      2. metadata-eval N/A

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity N/A

         \[\leadsto x + \color{blue}{z} \]

      4. lower-+.f64 46.9

         \[\leadsto \color{blue}{x + z} \]

   10. Simplified 46.9%

       \[\leadsto \color{blue}{x + z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+51}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-91}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+141}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -1.38 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 700000000:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -1.38e-11) t_1 (if (<= b 700000000.0) (fma a (- 1.0 t) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -1.38e-11) {
		tmp = t_1;
	} else if (b <= 700000000.0) {
		tmp = fma(a, (1.0 - t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -1.38e-11)
		tmp = t_1;
	elseif (b <= 700000000.0)
		tmp = fma(a, Float64(1.0 - t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.38e-11], t$95$1, If[LessEqual[b, 700000000.0], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.38e-11 or 7e8 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 76.8

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

   5. Simplified 76.8%

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

   if -1.38e-11 < b < 7e8

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. distribute-neg-in N/A

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

      20. metadata-eval N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 69.4

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

   5. Simplified 69.4%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x\right) \]

      18. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

      19. lower--.f64 62.3

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

   8. Simplified 62.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 39.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(b, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;-t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.6e+78) (* t b) (if (<= t 7.8e+139) (fma b y x) (- (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.6e+78) {
		tmp = t * b;
	} else if (t <= 7.8e+139) {
		tmp = fma(b, y, x);
	} else {
		tmp = -(t * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.6e+78)
		tmp = Float64(t * b);
	elseif (t <= 7.8e+139)
		tmp = fma(b, y, x);
	else
		tmp = Float64(-Float64(t * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.6e+78], N[(t * b), $MachinePrecision], If[LessEqual[t, 7.8e+139], N[(b * y + x), $MachinePrecision], (-N[(t * a), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if t < -8.59999999999999962e78

   1. Initial program 94.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

      2. lower--.f64 89.2

         \[\leadsto t \cdot \color{blue}{\left(b - a\right)} \]

   5. Simplified 89.2%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. lower-*.f64 54.1

         \[\leadsto \color{blue}{b \cdot t} \]

   8. Simplified 54.1%

      \[\leadsto \color{blue}{b \cdot t} \]

   if -8.59999999999999962e78 < t < 7.80000000000000012e139

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. associate-+l- N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      10. lift--.f64 N/A

          \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      11. associate--l- N/A

          \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      12. lower--.f64 N/A

          \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      13. lift-*.f64 N/A

          \[\leadsto x - \left(\color{blue}{\left(y - 1\right) \cdot z} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto x - \color{blue}{\mathsf{fma}\left(y - 1, z, \left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a - \left(y + \left(t + -2\right)\right) \cdot b\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \color{blue}{y \cdot \left(z - b\right)} \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x - y \cdot \color{blue}{\left(z + \left(\mathsf{neg}\left(b\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto x - y \cdot \left(z + \color{blue}{-1 \cdot b}\right) \]

      3. +-commutative N/A

         \[\leadsto x - y \cdot \color{blue}{\left(-1 \cdot b + z\right)} \]

      4. *-lft-identity N/A

         \[\leadsto x - y \cdot \left(-1 \cdot b + \color{blue}{1 \cdot z}\right) \]

      5. metadata-eval N/A

         \[\leadsto x - y \cdot \left(-1 \cdot b + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot z\right) \]

      6. cancel-sign-sub-inv N/A

         \[\leadsto x - y \cdot \color{blue}{\left(-1 \cdot b - -1 \cdot z\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{y \cdot \left(-1 \cdot b - -1 \cdot z\right)} \]

      8. cancel-sign-sub-inv N/A

         \[\leadsto x - y \cdot \color{blue}{\left(-1 \cdot b + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} \]

      9. metadata-eval N/A

         \[\leadsto x - y \cdot \left(-1 \cdot b + \color{blue}{1} \cdot z\right) \]

      10. *-lft-identity N/A

          \[\leadsto x - y \cdot \left(-1 \cdot b + \color{blue}{z}\right) \]

      11. +-commutative N/A

          \[\leadsto x - y \cdot \color{blue}{\left(z + -1 \cdot b\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x - y \cdot \left(z + \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \]

      13. sub-neg N/A

          \[\leadsto x - y \cdot \color{blue}{\left(z - b\right)} \]

      14. lower--.f64 57.3

          \[\leadsto x - y \cdot \color{blue}{\left(z - b\right)} \]

   7. Simplified 57.3%

      \[\leadsto x - \color{blue}{y \cdot \left(z - b\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x - -1 \cdot \left(b \cdot y\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto x - \color{blue}{\left(-1 \cdot b\right) \cdot y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot y \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{x + b \cdot y} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{b \cdot y + x} \]

      5. lower-fma.f64 42.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, y, x\right)} \]

   10. Simplified 42.5%

       \[\leadsto \color{blue}{\mathsf{fma}\left(b, y, x\right)} \]

   if 7.80000000000000012e139 < t

   1. Initial program 87.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

      2. lower--.f64 71.7

         \[\leadsto t \cdot \color{blue}{\left(b - a\right)} \]

   5. Simplified 71.7%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot a\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot a\right)} \]

      4. mul-1-neg N/A

         \[\leadsto t \cdot \color{blue}{\left(\mathsf{neg}\left(a\right)\right)} \]

      5. lower-neg.f64 45.0

         \[\leadsto t \cdot \color{blue}{\left(-a\right)} \]

   8. Simplified 45.0%

      \[\leadsto \color{blue}{t \cdot \left(-a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(b, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;-t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+138}:\\ \;\;\;\;\mathsf{fma}\left(b, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.6e+78) (* t b) (if (<= t 4.1e+138) (fma b y x) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.6e+78) {
		tmp = t * b;
	} else if (t <= 4.1e+138) {
		tmp = fma(b, y, x);
	} else {
		tmp = t * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.6e+78)
		tmp = Float64(t * b);
	elseif (t <= 4.1e+138)
		tmp = fma(b, y, x);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.6e+78], N[(t * b), $MachinePrecision], If[LessEqual[t, 4.1e+138], N[(b * y + x), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.59999999999999962e78 or 4.0999999999999998e138 < t

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

      2. lower--.f64 81.1

         \[\leadsto t \cdot \color{blue}{\left(b - a\right)} \]

   5. Simplified 81.1%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. lower-*.f64 46.2

         \[\leadsto \color{blue}{b \cdot t} \]

   8. Simplified 46.2%

      \[\leadsto \color{blue}{b \cdot t} \]

   if -8.59999999999999962e78 < t < 4.0999999999999998e138

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. associate-+l- N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      10. lift--.f64 N/A

          \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      11. associate--l- N/A

          \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      12. lower--.f64 N/A

          \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      13. lift-*.f64 N/A

          \[\leadsto x - \left(\color{blue}{\left(y - 1\right) \cdot z} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto x - \color{blue}{\mathsf{fma}\left(y - 1, z, \left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a - \left(y + \left(t + -2\right)\right) \cdot b\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \color{blue}{y \cdot \left(z - b\right)} \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x - y \cdot \color{blue}{\left(z + \left(\mathsf{neg}\left(b\right)\right)\right)} \]

      2. mul-1-neg N/A

         \[\leadsto x - y \cdot \left(z + \color{blue}{-1 \cdot b}\right) \]

      3. +-commutative N/A

         \[\leadsto x - y \cdot \color{blue}{\left(-1 \cdot b + z\right)} \]

      4. *-lft-identity N/A

         \[\leadsto x - y \cdot \left(-1 \cdot b + \color{blue}{1 \cdot z}\right) \]

      5. metadata-eval N/A

         \[\leadsto x - y \cdot \left(-1 \cdot b + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot z\right) \]

      6. cancel-sign-sub-inv N/A

         \[\leadsto x - y \cdot \color{blue}{\left(-1 \cdot b - -1 \cdot z\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{y \cdot \left(-1 \cdot b - -1 \cdot z\right)} \]

      8. cancel-sign-sub-inv N/A

         \[\leadsto x - y \cdot \color{blue}{\left(-1 \cdot b + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} \]

      9. metadata-eval N/A

         \[\leadsto x - y \cdot \left(-1 \cdot b + \color{blue}{1} \cdot z\right) \]

      10. *-lft-identity N/A

          \[\leadsto x - y \cdot \left(-1 \cdot b + \color{blue}{z}\right) \]

      11. +-commutative N/A

          \[\leadsto x - y \cdot \color{blue}{\left(z + -1 \cdot b\right)} \]

      12. mul-1-neg N/A

          \[\leadsto x - y \cdot \left(z + \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \]

      13. sub-neg N/A

          \[\leadsto x - y \cdot \color{blue}{\left(z - b\right)} \]

      14. lower--.f64 57.6

          \[\leadsto x - y \cdot \color{blue}{\left(z - b\right)} \]

   7. Simplified 57.6%

      \[\leadsto x - \color{blue}{y \cdot \left(z - b\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x - -1 \cdot \left(b \cdot y\right)} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto x - \color{blue}{\left(-1 \cdot b\right) \cdot y} \]

      2. mul-1-neg N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(b\right)\right)} \cdot y \]

      3. cancel-sign-sub N/A

         \[\leadsto \color{blue}{x + b \cdot y} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{b \cdot y + x} \]

      5. lower-fma.f64 42.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, y, x\right)} \]

   10. Simplified 42.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(b, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+138}:\\ \;\;\;\;\mathsf{fma}\left(b, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+122}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-70}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7e+122) (+ x a) (if (<= a 1.4e-70) (+ x z) (+ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7e+122) {
		tmp = x + a;
	} else if (a <= 1.4e-70) {
		tmp = x + z;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-7d+122)) then
        tmp = x + a
    else if (a <= 1.4d-70) then
        tmp = x + z
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7e+122) {
		tmp = x + a;
	} else if (a <= 1.4e-70) {
		tmp = x + z;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7e+122:
		tmp = x + a
	elif a <= 1.4e-70:
		tmp = x + z
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7e+122)
		tmp = Float64(x + a);
	elseif (a <= 1.4e-70)
		tmp = Float64(x + z);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7e+122)
		tmp = x + a;
	elseif (a <= 1.4e-70)
		tmp = x + z;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7e+122], N[(x + a), $MachinePrecision], If[LessEqual[a, 1.4e-70], N[(x + z), $MachinePrecision], N[(x + a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.00000000000000028e122 or 1.4e-70 < a

   1. Initial program 93.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(\left(t + y\right) - 2\right) + x\right)} - a \cdot \left(t - 1\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, \left(t + y\right) - 2, x - a \cdot \left(t - 1\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(y + t\right)} - 2, x - a \cdot \left(t - 1\right)\right) \]

      5. associate-+r- N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      8. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, y + \left(t + \color{blue}{-2}\right), x - a \cdot \left(t - 1\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x}\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + x\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + x\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x\right)}\right) \]

      15. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, x\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), x\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), x\right)\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), x\right)\right) \]

      19. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, x\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), x\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

      22. lower--.f64 85.3

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

   5. Simplified 85.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + x} \]

      2. sub-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)} + x \]

      3. mul-1-neg N/A

         \[\leadsto a \cdot \left(1 + \color{blue}{-1 \cdot t}\right) + x \]

      4. +-commutative N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot t + 1\right)} + x \]

      5. mul-1-neg N/A

         \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t\right)\right)} + 1\right) + x \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right) + x \]

      7. distribute-neg-in N/A

         \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t + -1\right)\right)\right)} + x \]

      8. metadata-eval N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) + x \]

      9. sub-neg N/A

         \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right)}\right)\right) + x \]

      10. mul-1-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + x \]

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x\right)} \]

      12. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, x\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, x\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, x\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x\right) \]

      18. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

      19. lower--.f64 58.4

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

   8. Simplified 58.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{x + a} \]

       2. lower-+.f64 21.6

          \[\leadsto \color{blue}{x + a} \]

   11. Simplified 21.6%

       \[\leadsto \color{blue}{x + a} \]

   if -7.00000000000000028e122 < a < 1.4e-70

   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. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right)} \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. lift--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      7. lift--.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right)} \cdot b \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

      9. associate-+l- N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      10. lift--.f64 N/A

          \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      11. associate--l- N/A

          \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      12. lower--.f64 N/A

          \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      13. lift-*.f64 N/A

          \[\leadsto x - \left(\color{blue}{\left(y - 1\right) \cdot z} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto x - \color{blue}{\mathsf{fma}\left(y - 1, z, \left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a - \left(y + \left(t + -2\right)\right) \cdot b\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \mathsf{fma}\left(y + -1, z, \color{blue}{-1 \cdot \left(b \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \mathsf{fma}\left(y + -1, z, \color{blue}{\mathsf{neg}\left(b \cdot y\right)}\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto x - \mathsf{fma}\left(y + -1, z, \color{blue}{b \cdot \left(\mathsf{neg}\left(y\right)\right)}\right) \]

      3. mul-1-neg N/A

         \[\leadsto x - \mathsf{fma}\left(y + -1, z, b \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x - \mathsf{fma}\left(y + -1, z, \color{blue}{b \cdot \left(-1 \cdot y\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto x - \mathsf{fma}\left(y + -1, z, b \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

      6. lower-neg.f64 65.1

         \[\leadsto x - \mathsf{fma}\left(y + -1, z, b \cdot \color{blue}{\left(-y\right)}\right) \]

   7. Simplified 65.1%

      \[\leadsto x - \mathsf{fma}\left(y + -1, z, \color{blue}{b \cdot \left(-y\right)}\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - -1 \cdot z} \]
   9. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(-1\right)\right) \cdot z} \]

      2. metadata-eval N/A

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity N/A

         \[\leadsto x + \color{blue}{z} \]

      4. lower-+.f64 34.5

         \[\leadsto \color{blue}{x + z} \]

   10. Simplified 34.5%

       \[\leadsto \color{blue}{x + z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 24.3% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ x + a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ x a))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + a;
}

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 + a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + a;
}

Python

def code(x, y, z, t, a, b):
	return x + a

Julia

function code(x, y, z, t, a, b)
	return Float64(x + a)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + a), $MachinePrecision]

Derivation

1. Initial program 96.4%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\left(b \cdot \left(\left(t + y\right) - 2\right) + x\right)} - a \cdot \left(t - 1\right) \]

   2. associate--l+ N/A

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, \left(t + y\right) - 2, x - a \cdot \left(t - 1\right)\right)} \]

   4. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(y + t\right)} - 2, x - a \cdot \left(t - 1\right)\right) \]

   5. associate-+r- N/A

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

   6. lower-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

   8. lower-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(b, y + \left(t + \color{blue}{-2}\right), x - a \cdot \left(t - 1\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x}\right) \]

   12. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + x\right) \]

   13. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + x\right) \]

   14. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x\right)}\right) \]

   15. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, x\right)\right) \]

   16. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), x\right)\right) \]

   17. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), x\right)\right) \]

   18. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), x\right)\right) \]

   19. distribute-neg-in N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, x\right)\right) \]

   20. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), x\right)\right) \]

   21. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

   22. lower--.f64 78.8

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

5. Simplified 78.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]

6. Taylor expanded in b around 0

   \[\leadsto \color{blue}{x + a \cdot \left(1 - t\right)} \]
7. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + x} \]

   2. sub-neg N/A

      \[\leadsto a \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)} + x \]

   3. mul-1-neg N/A

      \[\leadsto a \cdot \left(1 + \color{blue}{-1 \cdot t}\right) + x \]

   4. +-commutative N/A

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot t + 1\right)} + x \]

   5. mul-1-neg N/A

      \[\leadsto a \cdot \left(\color{blue}{\left(\mathsf{neg}\left(t\right)\right)} + 1\right) + x \]

   6. metadata-eval N/A

      \[\leadsto a \cdot \left(\left(\mathsf{neg}\left(t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right) + x \]

   7. distribute-neg-in N/A

      \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t + -1\right)\right)\right)} + x \]

   8. metadata-eval N/A

      \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) + x \]

   9. sub-neg N/A

      \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right)}\right)\right) + x \]

   10. mul-1-neg N/A

       \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + x \]

   11. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x\right)} \]

   12. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x\right) \]

   14. distribute-lft-in N/A

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, x\right) \]

   15. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, x\right) \]

   16. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, x\right) \]

   17. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x\right) \]

   18. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

   19. lower--.f64 41.8

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

8. Simplified 41.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]

9. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a + x} \]
10. Step-by-step derivation

    1. +-commutative N/A

       \[\leadsto \color{blue}{x + a} \]

    2. lower-+.f64 22.3

       \[\leadsto \color{blue}{x + a} \]

11. Simplified 22.3%

    \[\leadsto \color{blue}{x + a} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024207 
(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)))