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

Percentage Accurate: 95.1% → 97.7%

Time: 15.7s

Alternatives: 23

Speedup: 1.1×

• 36.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-+l- N/A

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

   2. associate--l- N/A

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

   3. --lowering--.f64 N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. sub-neg N/A

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

   6. +-lowering-+.f64 N/A

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

   7. metadata-eval N/A

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

   8. *-commutative N/A

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

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

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

   10. accelerator-lowering-fma.f64 N/A

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

   11. sub-neg N/A

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

   12. +-lowering-+.f64 N/A

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

   13. metadata-eval N/A

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

   14. *-lowering-*.f64 N/A

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

   15. neg-lowering-neg.f64 N/A

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

   16. associate--l+ N/A

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

   17. +-lowering-+.f64 N/A

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

   18. sub-neg N/A

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

   19. +-lowering-+.f64 N/A

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

   20. metadata-eval 99.6

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

4. Applied egg-rr 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 83.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+195}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-109}:\\ \;\;\;\;x - \mathsf{fma}\left(y + -1, z, t \cdot \left(a - b\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+195)
   (* b (+ y (+ t -2.0)))
   (if (<= b -2.6e-109)
     (- x (fma (+ y -1.0) z (* t (- a b))))
     (if (<= b 7e+79)
       (fma a (- 1.0 t) (fma z (- 1.0 y) x))
       (+ x (* b (- (+ y t) 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+195) {
		tmp = b * (y + (t + -2.0));
	} else if (b <= -2.6e-109) {
		tmp = x - fma((y + -1.0), z, (t * (a - b)));
	} else if (b <= 7e+79) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = x + (b * ((y + t) - 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+195)
		tmp = Float64(b * Float64(y + Float64(t + -2.0)));
	elseif (b <= -2.6e-109)
		tmp = Float64(x - fma(Float64(y + -1.0), z, Float64(t * Float64(a - b))));
	elseif (b <= 7e+79)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+195], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.6e-109], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(t * N[(a - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+79], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.99999999999999995e195

   1. Initial program 96.0%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.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. +-lowering-+.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. +-lowering-+.f64 N/A

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

      7. metadata-eval 96.0

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

   5. Simplified 96.0%

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

   if -1.99999999999999995e195 < b < -2.5999999999999998e-109

   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. Step-by-step derivation

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. --lowering--.f64 N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub-neg N/A

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

      12. +-lowering-+.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. neg-lowering-neg.f64 N/A

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

      16. associate--l+ N/A

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

      17. +-lowering-+.f64 N/A

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

      18. sub-neg N/A

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

      19. +-lowering-+.f64 N/A

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

      20. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 76.4

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

   7. Simplified 76.4%

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

   if -2.5999999999999998e-109 < b < 6.99999999999999961e79

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

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

      1. 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. accelerator-lowering-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. --lowering--.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. accelerator-lowering-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 92.6%

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

   if 6.99999999999999961e79 < b

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 87.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+195}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-109}:\\ \;\;\;\;x - \mathsf{fma}\left(y + -1, z, t \cdot \left(a - b\right)\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.055:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 y) x)) (t_2 (* b (+ y (+ t -2.0)))))
   (if (<= b -1.2e+54)
     t_2
     (if (<= b 1.9e-274)
       t_1
       (if (<= b 0.055) (fma a (- 1.0 t) x) (if (<= b 1.9e+71) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (1.0 - y), x);
	double t_2 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -1.2e+54) {
		tmp = t_2;
	} else if (b <= 1.9e-274) {
		tmp = t_1;
	} else if (b <= 0.055) {
		tmp = fma(a, (1.0 - t), x);
	} else if (b <= 1.9e+71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(1.0 - y), x)
	t_2 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -1.2e+54)
		tmp = t_2;
	elseif (b <= 1.9e-274)
		tmp = t_1;
	elseif (b <= 0.055)
		tmp = fma(a, Float64(1.0 - t), x);
	elseif (b <= 1.9e+71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+54], t$95$2, If[LessEqual[b, 1.9e-274], t$95$1, If[LessEqual[b, 0.055], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[b, 1.9e+71], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.19999999999999999e54 or 1.9e71 < b

   1. Initial program 95.7%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.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. +-lowering-+.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. +-lowering-+.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 -1.19999999999999999e54 < b < 1.89999999999999992e-274 or 0.0550000000000000003 < b < 1.9e71

   1. Initial program 96.9%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. --lowering--.f64 N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub-neg N/A

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

      12. +-lowering-+.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. neg-lowering-neg.f64 N/A

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

      16. associate--l+ N/A

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

      17. +-lowering-+.f64 N/A

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

      18. sub-neg N/A

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

      19. +-lowering-+.f64 N/A

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

      20. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 86.2

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

   7. Simplified 86.2%

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

   8. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. --lowering--.f64 64.2

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

   10. Simplified 64.2%

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

   if 1.89999999999999992e-274 < b < 0.0550000000000000003

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 74.0

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

   5. Simplified 74.0%

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

   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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 66.6

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

   8. Simplified 66.6%

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

Alternative 4: 94.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \mathsf{fma}\left(y + -1, z, t \cdot \left(a - b\right)\right)\\ \mathbf{if}\;t \leq -1350000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 370000:\\ \;\;\;\;x + \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(b, y + -2, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (fma (+ y -1.0) z (* t (- a b))))))
   (if (<= t -1350000000.0)
     t_1
     (if (<= t 370000.0) (+ x (fma z (- 1.0 y) (fma b (+ y -2.0) a))) 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 (t <= -1350000000.0) {
		tmp = t_1;
	} else if (t <= 370000.0) {
		tmp = x + fma(z, (1.0 - y), fma(b, (y + -2.0), a));
	} 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 (t <= -1350000000.0)
		tmp = t_1;
	elseif (t <= 370000.0)
		tmp = Float64(x + fma(z, Float64(1.0 - y), fma(b, Float64(y + -2.0), a)));
	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[t, -1350000000.0], t$95$1, If[LessEqual[t, 370000.0], N[(x + N[(z * N[(1.0 - y), $MachinePrecision] + N[(b * N[(y + -2.0), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e9 or 3.7e5 < t

   1. Initial program 95.1%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. --lowering--.f64 N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub-neg N/A

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

      12. +-lowering-+.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. neg-lowering-neg.f64 N/A

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

      16. associate--l+ N/A

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

      17. +-lowering-+.f64 N/A

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

      18. sub-neg N/A

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

      19. +-lowering-+.f64 N/A

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

      20. metadata-eval 99.2

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 96.5

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

   7. Simplified 96.5%

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

   if -1.35e9 < t < 3.7e5

   1. Initial program 98.5%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. --lowering--.f64 N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub-neg N/A

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

      12. +-lowering-+.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. neg-lowering-neg.f64 N/A

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

      16. associate--l+ N/A

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

      17. +-lowering-+.f64 N/A

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

      18. sub-neg N/A

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

      19. +-lowering-+.f64 N/A

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

      20. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-lft-out N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      18. sub-neg N/A

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

      19. --lowering--.f64 N/A

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

   7. Simplified 99.1%

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

Alternative 5: 94.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \mathsf{fma}\left(y + -1, z, t \cdot \left(a - b\right)\right)\\ \mathbf{if}\;t \leq -1.45:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 70000:\\ \;\;\;\;x + \mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(z, 1 - y, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (fma (+ y -1.0) z (* t (- a b))))))
   (if (<= t -1.45)
     t_1
     (if (<= t 70000.0) (+ x (fma b (+ y -2.0) (fma z (- 1.0 y) a))) 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 (t <= -1.45) {
		tmp = t_1;
	} else if (t <= 70000.0) {
		tmp = x + fma(b, (y + -2.0), fma(z, (1.0 - y), a));
	} 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 (t <= -1.45)
		tmp = t_1;
	elseif (t <= 70000.0)
		tmp = Float64(x + fma(b, Float64(y + -2.0), fma(z, Float64(1.0 - y), a)));
	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[t, -1.45], t$95$1, If[LessEqual[t, 70000.0], N[(x + N[(b * N[(y + -2.0), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999996 or 7e4 < t

   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. Step-by-step derivation

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. --lowering--.f64 N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub-neg N/A

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

      12. +-lowering-+.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. neg-lowering-neg.f64 N/A

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

      16. associate--l+ N/A

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

      17. +-lowering-+.f64 N/A

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

      18. sub-neg N/A

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

      19. +-lowering-+.f64 N/A

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

      20. metadata-eval 99.2

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 95.8

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

   7. Simplified 95.8%

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

   if -1.44999999999999996 < t < 7e4

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-lowering-+.f64 N/A

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

      3. sub-neg N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. mul-1-neg N/A

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

      16. sub-neg N/A

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

      17. metadata-eval N/A

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

      18. +-commutative N/A

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

      19. distribute-neg-in N/A

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

      20. metadata-eval N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 98.3

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

   5. Simplified 98.3%

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

Alternative 6: 83.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;x + \mathsf{fma}\left(y, b, b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.8e+64)
   (+ x (fma y b (* b (+ t -2.0))))
   (if (<= b 1.6e+80)
     (fma a (- 1.0 t) (fma z (- 1.0 y) x))
     (+ x (* b (- (+ y t) 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.8e+64) {
		tmp = x + fma(y, b, (b * (t + -2.0)));
	} else if (b <= 1.6e+80) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = x + (b * ((y + t) - 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.8e+64)
		tmp = Float64(x + fma(y, b, Float64(b * Float64(t + -2.0))));
	elseif (b <= 1.6e+80)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.8e+64], N[(x + N[(y * b + N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+80], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.79999999999999986e64

   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 x around inf

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

   5. Simplified 80.4%

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-+r+ N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. +-lowering-+.f64 80.5

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

   7. Applied egg-rr 80.5%

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

   if -5.79999999999999986e64 < b < 1.59999999999999995e80

   1. Initial program 97.6%

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

   3. Taylor expanded in 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. accelerator-lowering-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. --lowering--.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. accelerator-lowering-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 88.2%

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

   if 1.59999999999999995e80 < b

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 87.8%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+64}:\\ \;\;\;\;x + \mathsf{fma}\left(y, b, b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-34}:\\ \;\;\;\;a + \mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.1e+39)
     t_1
     (if (<= t 5.8e-34)
       (+ a (fma b (+ y -2.0) x))
       (if (<= t 3.6e+50) (fma z (- 1.0 y) 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 <= -4.1e+39) {
		tmp = t_1;
	} else if (t <= 5.8e-34) {
		tmp = a + fma(b, (y + -2.0), x);
	} else if (t <= 3.6e+50) {
		tmp = fma(z, (1.0 - y), 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 <= -4.1e+39)
		tmp = t_1;
	elseif (t <= 5.8e-34)
		tmp = Float64(a + fma(b, Float64(y + -2.0), x));
	elseif (t <= 3.6e+50)
		tmp = fma(z, Float64(1.0 - y), 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, -4.1e+39], t$95$1, If[LessEqual[t, 5.8e-34], N[(a + N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+50], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.10000000000000004e39 or 3.59999999999999986e50 < t

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 75.1

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

   5. Simplified 75.1%

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

   if -4.10000000000000004e39 < t < 5.8000000000000004e-34

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 70.1

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

   5. Simplified 70.1%

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

   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. +-lowering-+.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. accelerator-lowering-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. metadata-eval N/A

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

      6. +-lowering-+.f64 68.1

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

   8. Simplified 68.1%

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

   if 5.8000000000000004e-34 < t < 3.59999999999999986e50

   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. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. --lowering--.f64 N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub-neg N/A

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

      12. +-lowering-+.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. neg-lowering-neg.f64 N/A

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

      16. associate--l+ N/A

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

      17. +-lowering-+.f64 N/A

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

      18. sub-neg N/A

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

      19. +-lowering-+.f64 N/A

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

      20. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 90.1

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

   7. Simplified 90.1%

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

   8. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. --lowering--.f64 71.8

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

   10. Simplified 71.8%

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

Alternative 8: 57.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-47}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.9e+16)
     t_1
     (if (<= t -8e-47)
       (fma b (+ y -2.0) x)
       (if (<= t 1.35e+51) (fma z (- 1.0 y) 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 <= -2.9e+16) {
		tmp = t_1;
	} else if (t <= -8e-47) {
		tmp = fma(b, (y + -2.0), x);
	} else if (t <= 1.35e+51) {
		tmp = fma(z, (1.0 - y), 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 <= -2.9e+16)
		tmp = t_1;
	elseif (t <= -8e-47)
		tmp = fma(b, Float64(y + -2.0), x);
	elseif (t <= 1.35e+51)
		tmp = fma(z, Float64(1.0 - y), 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, -2.9e+16], t$95$1, If[LessEqual[t, -8e-47], N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.35e+51], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9e16 or 1.34999999999999996e51 < t

   1. Initial program 94.7%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 74.5

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

   5. Simplified 74.5%

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

   if -2.9e16 < t < -7.9999999999999998e-47

   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 x around inf

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 68.8

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

   8. Simplified 68.8%

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

   if -7.9999999999999998e-47 < t < 1.34999999999999996e51

   1. Initial program 99.2%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. --lowering--.f64 N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub-neg N/A

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

      12. +-lowering-+.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. neg-lowering-neg.f64 N/A

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

      16. associate--l+ N/A

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

      17. +-lowering-+.f64 N/A

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

      18. sub-neg N/A

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

      19. +-lowering-+.f64 N/A

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

      20. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 58.2

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

   7. Simplified 58.2%

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

   8. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. --lowering--.f64 56.1

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

   10. Simplified 56.1%

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

Alternative 9: 54.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-180}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 32000000000000:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -7.6e+22)
     t_1
     (if (<= t 5.6e-180)
       (fma b (+ y -2.0) x)
       (if (<= t 32000000000000.0) (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 = t * (b - a);
	double tmp;
	if (t <= -7.6e+22) {
		tmp = t_1;
	} else if (t <= 5.6e-180) {
		tmp = fma(b, (y + -2.0), x);
	} else if (t <= 32000000000000.0) {
		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(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.6e+22)
		tmp = t_1;
	elseif (t <= 5.6e-180)
		tmp = fma(b, Float64(y + -2.0), x);
	elseif (t <= 32000000000000.0)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e+22], t$95$1, If[LessEqual[t, 5.6e-180], N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 32000000000000.0], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.6000000000000008e22 or 3.2e13 < t

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 72.5

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

   5. Simplified 72.5%

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

   if -7.6000000000000008e22 < t < 5.59999999999999994e-180

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.8%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 52.8

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

   8. Simplified 52.8%

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

   if 5.59999999999999994e-180 < t < 3.2e13

   1. Initial program 97.5%

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

   3. Taylor expanded in 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 68.9

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

   5. Simplified 68.9%

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

   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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 51.7

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

   8. Simplified 51.7%

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

Alternative 10: 71.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(t, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b y (fma a (- 1.0 t) x))))
   (if (<= a -5.2e+75)
     t_1
     (if (<= a 5.4e+57) (fma z (- 1.0 y) (fma t b x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, y, fma(a, (1.0 - t), x));
	double tmp;
	if (a <= -5.2e+75) {
		tmp = t_1;
	} else if (a <= 5.4e+57) {
		tmp = fma(z, (1.0 - y), fma(t, b, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(b, y, fma(a, Float64(1.0 - t), x))
	tmp = 0.0
	if (a <= -5.2e+75)
		tmp = t_1;
	elseif (a <= 5.4e+57)
		tmp = fma(z, Float64(1.0 - y), fma(t, b, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * y + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+75], t$95$1, If[LessEqual[a, 5.4e+57], N[(z * N[(1.0 - y), $MachinePrecision] + N[(t * b + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.1999999999999997e75 or 5.3999999999999997e57 < a

   1. Initial program 93.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 92.1

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

   5. Simplified 92.1%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 80.3%

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

   if -5.1999999999999997e75 < a < 5.3999999999999997e57

   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. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. --lowering--.f64 N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub-neg N/A

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

      12. +-lowering-+.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. neg-lowering-neg.f64 N/A

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

      16. associate--l+ N/A

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

      17. +-lowering-+.f64 N/A

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

      18. sub-neg N/A

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

      19. +-lowering-+.f64 N/A

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

      20. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 82.0

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

   7. Simplified 82.0%

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

   8. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

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

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. sub-neg N/A

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

      19. --lowering--.f64 N/A

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

      20. +-commutative N/A

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

      21. *-commutative N/A

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

      22. accelerator-lowering-fma.f64 79.2

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

   10. Simplified 79.2%

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

Alternative 11: 50.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1250000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1250000000.0)
     t_1
     (if (<= t 7.6e-280) (* y (- b z)) (if (<= t 7.8e+15) (+ x a) 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 <= -1250000000.0) {
		tmp = t_1;
	} else if (t <= 7.6e-280) {
		tmp = y * (b - z);
	} else if (t <= 7.8e+15) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-1250000000.0d0)) then
        tmp = t_1
    else if (t <= 7.6d-280) then
        tmp = y * (b - z)
    else if (t <= 7.8d+15) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1250000000.0) {
		tmp = t_1;
	} else if (t <= 7.6e-280) {
		tmp = y * (b - z);
	} else if (t <= 7.8e+15) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1250000000.0:
		tmp = t_1
	elif t <= 7.6e-280:
		tmp = y * (b - z)
	elif t <= 7.8e+15:
		tmp = x + a
	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 <= -1250000000.0)
		tmp = t_1;
	elseif (t <= 7.6e-280)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 7.8e+15)
		tmp = Float64(x + a);
	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 <= -1250000000.0)
		tmp = t_1;
	elseif (t <= 7.6e-280)
		tmp = y * (b - z);
	elseif (t <= 7.8e+15)
		tmp = x + a;
	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, -1250000000.0], t$95$1, If[LessEqual[t, 7.6e-280], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+15], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25e9 or 7.8e15 < t

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 72.0

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

   5. Simplified 72.0%

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

   if -1.25e9 < t < 7.6000000000000003e-280

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 45.8

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

   5. Simplified 45.8%

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

   if 7.6000000000000003e-280 < t < 7.8e15

   1. Initial program 98.4%

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

   3. Taylor expanded in 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 72.6

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

   5. Simplified 72.6%

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

   6. Taylor expanded in 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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 52.3

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

   8. Simplified 52.3%

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

   9. Taylor expanded in t around 0

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

       1. +-lowering-+.f64 49.9

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

   11. Simplified 49.9%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1250000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -40000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -40000000.0)
     t_1
     (if (<= t 6.4e-279) (* b (+ y -2.0)) (if (<= t 9.5e+15) (+ x a) 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 <= -40000000.0) {
		tmp = t_1;
	} else if (t <= 6.4e-279) {
		tmp = b * (y + -2.0);
	} else if (t <= 9.5e+15) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-40000000.0d0)) then
        tmp = t_1
    else if (t <= 6.4d-279) then
        tmp = b * (y + (-2.0d0))
    else if (t <= 9.5d+15) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -40000000.0) {
		tmp = t_1;
	} else if (t <= 6.4e-279) {
		tmp = b * (y + -2.0);
	} else if (t <= 9.5e+15) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -40000000.0:
		tmp = t_1
	elif t <= 6.4e-279:
		tmp = b * (y + -2.0)
	elif t <= 9.5e+15:
		tmp = x + a
	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 <= -40000000.0)
		tmp = t_1;
	elseif (t <= 6.4e-279)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (t <= 9.5e+15)
		tmp = Float64(x + a);
	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 <= -40000000.0)
		tmp = t_1;
	elseif (t <= 6.4e-279)
		tmp = b * (y + -2.0);
	elseif (t <= 9.5e+15)
		tmp = x + a;
	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, -40000000.0], t$95$1, If[LessEqual[t, 6.4e-279], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+15], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4e7 or 9.5e15 < t

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 72.0

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

   5. Simplified 72.0%

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

   if -4e7 < t < 6.3999999999999997e-279

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 49.3%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 49.3

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

   8. Simplified 49.3%

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

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.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. metadata-eval N/A

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

       4. +-lowering-+.f64 38.1

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

   11. Simplified 38.1%

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

   if 6.3999999999999997e-279 < t < 9.5e15

   1. Initial program 98.4%

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

   3. Taylor expanded in 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 72.6

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

   5. Simplified 72.6%

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

   6. Taylor expanded in 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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 52.3

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

   8. Simplified 52.3%

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

   9. Taylor expanded in t around 0

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

       1. +-lowering-+.f64 49.9

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

   11. Simplified 49.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -40000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-279}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.4e-17)
   (fma t b x)
   (if (<= t 1.4e-277) (* b (+ y -2.0)) (if (<= t 1.0) (+ x a) (fma t b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.4e-17) {
		tmp = fma(t, b, x);
	} else if (t <= 1.4e-277) {
		tmp = b * (y + -2.0);
	} else if (t <= 1.0) {
		tmp = x + a;
	} else {
		tmp = fma(t, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.4e-17)
		tmp = fma(t, b, x);
	elseif (t <= 1.4e-277)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (t <= 1.0)
		tmp = Float64(x + a);
	else
		tmp = fma(t, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.4e-17], N[(t * b + x), $MachinePrecision], If[LessEqual[t, 1.4e-277], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.0], N[(x + a), $MachinePrecision], N[(t * b + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4000000000000002e-17 or 1 < t

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 53.7%

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-+r+ N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. +-lowering-+.f64 53.7

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

   7. Applied egg-rr 53.7%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 53.7%

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

   11. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. accelerator-lowering-fma.f64 50.1

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

   13. Simplified 50.1%

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

   if -5.4000000000000002e-17 < t < 1.39999999999999988e-277

   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 x around inf

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

   5. Simplified 49.1%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 49.1

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

   8. Simplified 49.1%

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

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.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. metadata-eval N/A

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

       4. +-lowering-+.f64 38.8

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

   11. Simplified 38.8%

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

   if 1.39999999999999988e-277 < t < 1

   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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 73.3

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

   5. Simplified 73.3%

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

   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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 52.0

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

   8. Simplified 52.0%

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

   9. Taylor expanded in t around 0

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

       1. +-lowering-+.f64 51.3

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

   11. Simplified 51.3%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-252}:\\ \;\;\;\;\mathsf{fma}\left(b, -2, x\right)\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5e+24)
   (fma t b x)
   (if (<= t 1.25e-252) (fma b -2.0 x) (if (<= t 1.0) (+ x a) (fma t b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e+24) {
		tmp = fma(t, b, x);
	} else if (t <= 1.25e-252) {
		tmp = fma(b, -2.0, x);
	} else if (t <= 1.0) {
		tmp = x + a;
	} else {
		tmp = fma(t, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5e+24)
		tmp = fma(t, b, x);
	elseif (t <= 1.25e-252)
		tmp = fma(b, -2.0, x);
	elseif (t <= 1.0)
		tmp = Float64(x + a);
	else
		tmp = fma(t, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5e+24], N[(t * b + x), $MachinePrecision], If[LessEqual[t, 1.25e-252], N[(b * -2.0 + x), $MachinePrecision], If[LessEqual[t, 1.0], N[(x + a), $MachinePrecision], N[(t * b + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.00000000000000045e24 or 1 < t

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 53.8%

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-+r+ N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. +-lowering-+.f64 53.9

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

   7. Applied egg-rr 53.9%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 53.9%

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

   11. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. accelerator-lowering-fma.f64 50.8

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

   13. Simplified 50.8%

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

   if -5.00000000000000045e24 < t < 1.25000000000000002e-252

   1. Initial program 98.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 49.5%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 49.5

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

   8. Simplified 49.5%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

          \[\leadsto \color{blue}{-2 \cdot b + x} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{b \cdot -2} + x \]

       3. accelerator-lowering-fma.f64 33.4

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

   11. Simplified 33.4%

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

   if 1.25000000000000002e-252 < t < 1

   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 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 75.6

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

   5. Simplified 75.6%

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

   6. Taylor expanded in 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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 53.8

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

   8. Simplified 53.8%

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

   9. Taylor expanded in t around 0

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

       1. +-lowering-+.f64 53.0

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

   11. Simplified 53.0%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-252}:\\ \;\;\;\;\mathsf{fma}\left(b, -2, x\right)\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \mathsf{fma}\left(t, b - a, z\right)\\ \mathbf{if}\;t \leq -1400000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-31}:\\ \;\;\;\;a + \mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (fma t (- b a) z))))
   (if (<= t -1400000000.0)
     t_1
     (if (<= t 2e-31) (+ 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 = x + fma(t, (b - a), z);
	double tmp;
	if (t <= -1400000000.0) {
		tmp = t_1;
	} else if (t <= 2e-31) {
		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(x + fma(t, Float64(b - a), z))
	tmp = 0.0
	if (t <= -1400000000.0)
		tmp = t_1;
	elseif (t <= 2e-31)
		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[(x + N[(t * N[(b - a), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1400000000.0], t$95$1, If[LessEqual[t, 2e-31], 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 < -1.4e9 or 2e-31 < t

   1. Initial program 95.3%

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

      1. associate-+l- N/A

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

      2. associate--l- N/A

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

      3. --lowering--.f64 N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. *-commutative N/A

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

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

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. sub-neg N/A

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

      12. +-lowering-+.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-lowering-*.f64 N/A

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

      15. neg-lowering-neg.f64 N/A

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

      16. associate--l+ N/A

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

      17. +-lowering-+.f64 N/A

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

      18. sub-neg N/A

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

      19. +-lowering-+.f64 N/A

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

      20. metadata-eval 99.2

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 95.9

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

   7. Simplified 95.9%

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

   8. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

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

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

      6. mul-1-neg N/A

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

      7. mul-1-neg N/A

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

      8. remove-double-neg N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. neg-sub0 N/A

          \[\leadsto x + \mathsf{fma}\left(t, \color{blue}{0 - \left(a - b\right)}, z\right) \]

      12. associate-+l- N/A

          \[\leadsto x + \mathsf{fma}\left(t, \color{blue}{\left(0 - a\right) + b}, z\right) \]

      13. neg-sub0 N/A

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

      14. mul-1-neg N/A

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

      15. +-commutative N/A

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

      16. mul-1-neg N/A

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

      17. sub-neg N/A

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

      18. --lowering--.f64 90.8

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

   10. Simplified 90.8%

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

   if -1.4e9 < t < 2e-31

   1. Initial program 98.4%

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

   3. Taylor expanded in 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 68.9

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

   5. Simplified 68.9%

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

   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. +-lowering-+.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. accelerator-lowering-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. metadata-eval N/A

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

      6. +-lowering-+.f64 68.3

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

   8. Simplified 68.3%

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

Alternative 16: 33.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(b, -2, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+17}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.8e+102)
   (* t b)
   (if (<= t 7e-253) (fma b -2.0 x) (if (<= t 4.8e+17) (+ x a) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+102) {
		tmp = t * b;
	} else if (t <= 7e-253) {
		tmp = fma(b, -2.0, x);
	} else if (t <= 4.8e+17) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.8e+102)
		tmp = Float64(t * b);
	elseif (t <= 7e-253)
		tmp = fma(b, -2.0, x);
	elseif (t <= 4.8e+17)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.8e+102], N[(t * b), $MachinePrecision], If[LessEqual[t, 7e-253], N[(b * -2.0 + x), $MachinePrecision], If[LessEqual[t, 4.8e+17], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999989e102 or 4.8e17 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 53.7%

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

   6. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 41.3

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

   8. Simplified 41.3%

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

   if -4.79999999999999989e102 < t < 7.00000000000000045e-253

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 51.3%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 48.1

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

   8. Simplified 48.1%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

          \[\leadsto \color{blue}{-2 \cdot b + x} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{b \cdot -2} + x \]

       3. accelerator-lowering-fma.f64 32.9

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

   11. Simplified 32.9%

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

   if 7.00000000000000045e-253 < t < 4.8e17

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 74.7

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

   5. Simplified 74.7%

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

   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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 54.0

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

   8. Simplified 54.0%

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

   9. Taylor expanded in t around 0

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

       1. +-lowering-+.f64 51.4

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

   11. Simplified 51.4%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-253}:\\ \;\;\;\;\mathsf{fma}\left(b, -2, x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+17}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + t\right)\\ \mathbf{if}\;b \leq -1.32 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y t))))
   (if (<= b -1.32e+162) t_1 (if (<= b 9.2e+185) (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);
	double tmp;
	if (b <= -1.32e+162) {
		tmp = t_1;
	} else if (b <= 9.2e+185) {
		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 + t))
	tmp = 0.0
	if (b <= -1.32e+162)
		tmp = t_1;
	elseif (b <= 9.2e+185)
		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 + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.32e+162], t$95$1, If[LessEqual[b, 9.2e+185], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.31999999999999999e162 or 9.2000000000000005e185 < 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 x around inf

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

   5. Simplified 95.1%

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-+r+ N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. +-lowering-+.f64 95.1

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

   7. Applied egg-rr 95.1%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 74.0%

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

   11. Taylor expanded in x around 0

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

       1. distribute-lft-in N/A

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

       2. *-lowering-*.f64 N/A

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

       3. +-lowering-+.f64 74.1

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

   13. Simplified 74.1%

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

   if -1.31999999999999999e162 < b < 9.2000000000000005e185

   1. Initial program 97.5%

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

   3. Taylor expanded in 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 71.7

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

   5. Simplified 71.7%

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

   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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 55.2

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

   8. Simplified 55.2%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+162}:\\ \;\;\;\;b \cdot \left(y + t\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;a \leq -4.3 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= a -4.3e+154) t_1 (if (<= a 1.6e+194) (fma t b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (a <= -4.3e+154) {
		tmp = t_1;
	} else if (a <= 1.6e+194) {
		tmp = fma(t, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (a <= -4.3e+154)
		tmp = t_1;
	elseif (a <= 1.6e+194)
		tmp = fma(t, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[a, -4.3e+154], t$95$1, If[LessEqual[a, 1.6e+194], N[(t * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.2999999999999998e154 or 1.60000000000000011e194 < a

   1. Initial program 89.1%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-in N/A

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

      5. neg-mul-1 N/A

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

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

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

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

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

      8. mul-1-neg N/A

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

      9. *-lft-identity N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. mul-1-neg N/A

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

      12. neg-lowering-neg.f64 78.9

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

   5. Simplified 78.9%

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

   6. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-lowering-neg.f64 49.2

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

   8. Simplified 49.2%

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

   if -4.2999999999999998e154 < a < 1.60000000000000011e194

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 61.1%

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. associate-+r+ N/A

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

      4. *-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

      8. +-lowering-+.f64 61.1

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

   7. Applied egg-rr 61.1%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 52.3%

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

   11. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. accelerator-lowering-fma.f64 43.2

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

   13. Simplified 43.2%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+194}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+144}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4e+144) (* t b) (if (<= t 3.4e+15) (+ x a) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+144) {
		tmp = t * b;
	} else if (t <= 3.4e+15) {
		tmp = x + a;
	} 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 <= (-4d+144)) then
        tmp = t * b
    else if (t <= 3.4d+15) then
        tmp = x + a
    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 <= -4e+144) {
		tmp = t * b;
	} else if (t <= 3.4e+15) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4e+144:
		tmp = t * b
	elif t <= 3.4e+15:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4e+144)
		tmp = Float64(t * b);
	elseif (t <= 3.4e+15)
		tmp = Float64(x + a);
	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 <= -4e+144)
		tmp = t * b;
	elseif (t <= 3.4e+15)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4e+144], N[(t * b), $MachinePrecision], If[LessEqual[t, 3.4e+15], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.00000000000000009e144 or 3.4e15 < t

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 55.4%

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

   6. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 43.1

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

   8. Simplified 43.1%

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

   if -4.00000000000000009e144 < t < 3.4e15

   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 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 70.9

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

   5. Simplified 70.9%

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

   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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 42.9

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

   8. Simplified 42.9%

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

   9. Taylor expanded in t around 0

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

       1. +-lowering-+.f64 35.8

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

   11. Simplified 35.8%

       \[\leadsto \color{blue}{a + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+144}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+15}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+204}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+146}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.1e+204) (* b -2.0) (if (<= b 2.2e+146) (+ x a) (* b -2.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e+204) {
		tmp = b * -2.0;
	} else if (b <= 2.2e+146) {
		tmp = x + a;
	} else {
		tmp = b * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.1d+204)) then
        tmp = b * (-2.0d0)
    else if (b <= 2.2d+146) then
        tmp = x + a
    else
        tmp = b * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e+204) {
		tmp = b * -2.0;
	} else if (b <= 2.2e+146) {
		tmp = x + a;
	} else {
		tmp = b * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.1e+204:
		tmp = b * -2.0
	elif b <= 2.2e+146:
		tmp = x + a
	else:
		tmp = b * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.1e+204)
		tmp = Float64(b * -2.0);
	elseif (b <= 2.2e+146)
		tmp = Float64(x + a);
	else
		tmp = Float64(b * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.1e+204)
		tmp = b * -2.0;
	elseif (b <= 2.2e+146)
		tmp = x + a;
	else
		tmp = b * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.1e+204], N[(b * -2.0), $MachinePrecision], If[LessEqual[b, 2.2e+146], N[(x + a), $MachinePrecision], N[(b * -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1e204 or 2.1999999999999998e146 < 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 x around inf

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

   5. Simplified 94.5%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 60.8

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

   8. Simplified 60.8%

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

   9. Taylor expanded in b around inf

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

       1. *-lowering-*.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. metadata-eval N/A

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

       4. +-lowering-+.f64 58.9

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

   11. Simplified 58.9%

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

   12. Taylor expanded in y around 0

       \[\leadsto \color{blue}{-2 \cdot b} \]
   13. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \color{blue}{b \cdot -2} \]

       2. *-lowering-*.f64 29.4

          \[\leadsto \color{blue}{b \cdot -2} \]

   14. Simplified 29.4%

       \[\leadsto \color{blue}{b \cdot -2} \]

   if -2.1e204 < b < 2.1999999999999998e146

   1. Initial program 98.0%

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

   3. Taylor expanded in 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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 71.8

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

   5. Simplified 71.8%

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

   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. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 53.2

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

   8. Simplified 53.2%

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

   9. Taylor expanded in t around 0

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

       1. +-lowering-+.f64 32.7

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

   11. Simplified 32.7%

       \[\leadsto \color{blue}{a + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+204}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+146}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+140}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+192}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.5e+140) a (if (<= a 1.12e+192) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.5e+140) {
		tmp = a;
	} else if (a <= 1.12e+192) {
		tmp = x;
	} else {
		tmp = 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 <= (-6.5d+140)) then
        tmp = a
    else if (a <= 1.12d+192) then
        tmp = x
    else
        tmp = 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 <= -6.5e+140) {
		tmp = a;
	} else if (a <= 1.12e+192) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.5e+140:
		tmp = a
	elif a <= 1.12e+192:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.5e+140)
		tmp = a;
	elseif (a <= 1.12e+192)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.5e+140)
		tmp = a;
	elseif (a <= 1.12e+192)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.5e+140], a, If[LessEqual[a, 1.12e+192], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -6.4999999999999999e140 or 1.12e192 < a

   1. Initial program 89.6%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-in N/A

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

      5. neg-mul-1 N/A

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

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

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

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

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

      8. mul-1-neg N/A

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

      9. *-lft-identity N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. mul-1-neg N/A

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

      12. neg-lowering-neg.f64 76.8

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

   5. Simplified 76.8%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a} \]
   7. Step-by-step derivation

   8. Simplified 30.4%

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

   if -6.4999999999999999e140 < a < 1.12e192

   1. Initial program 99.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 22.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 25.5% 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 96.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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. accelerator-lowering-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. --lowering--.f64 77.1

       \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

5. Simplified 77.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]

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. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]

   3. --lowering--.f64 44.2

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

8. Simplified 44.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]

9. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a + x} \]
10. Step-by-step derivation

    1. +-lowering-+.f64 27.1

       \[\leadsto \color{blue}{a + x} \]

11. Simplified 27.1%

    \[\leadsto \color{blue}{a + x} \]

12. Final simplification 27.1%

    \[\leadsto x + a \]
13. Add Preprocessing

Alternative 23: 11.1% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return 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 = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 96.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
4. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto a \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)} \]

   2. neg-mul-1 N/A

      \[\leadsto a \cdot \left(1 + \color{blue}{-1 \cdot t}\right) \]

   3. +-commutative N/A

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot t + 1\right)} \]

   4. distribute-rgt-in N/A

      \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot a + 1 \cdot a} \]

   5. neg-mul-1 N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot a + 1 \cdot a \]

   6. distribute-lft-neg-in N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(t \cdot a\right)\right)} + 1 \cdot a \]

   7. distribute-rgt-neg-in N/A

      \[\leadsto \color{blue}{t \cdot \left(\mathsf{neg}\left(a\right)\right)} + 1 \cdot a \]

   8. mul-1-neg N/A

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot a\right)} + 1 \cdot a \]

   9. *-lft-identity N/A

      \[\leadsto t \cdot \left(-1 \cdot a\right) + \color{blue}{a} \]

   10. accelerator-lowering-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(t, -1 \cdot a, a\right)} \]

   11. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(t, \color{blue}{\mathsf{neg}\left(a\right)}, a\right) \]

   12. neg-lowering-neg.f64 28.6

       \[\leadsto \mathsf{fma}\left(t, \color{blue}{-a}, a\right) \]

5. Simplified 28.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(t, -a, a\right)} \]

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a} \]
7. Step-by-step derivation

8. Simplified 11.4%

   \[\leadsto \color{blue}{a} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024204 
(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)))