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

Percentage Accurate: 95.6% → 97.7%

Time: 16.3s

Alternatives: 21

Speedup: 0.5×

• 36.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. metadata-eval 78.2

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

   5. Simplified 78.2%

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

4. Final simplification 99.2%

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

Alternative 2: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, x\right)\\ t_2 := b \cdot \left(t + \left(y + -2\right)\right)\\ t_3 := \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-91}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- 1.0 t) x))
        (t_2 (* b (+ t (+ y -2.0))))
        (t_3 (fma z (- 1.0 y) x)))
   (if (<= b -6.8e+105)
     t_2
     (if (<= b -1.05e+29)
       t_1
       (if (<= b -1.08e-91)
         t_3
         (if (<= b -6.5e-267)
           t_1
           (if (<= b 1.2) t_3 (if (<= b 1.7e+165) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (1.0 - t), x);
	double t_2 = b * (t + (y + -2.0));
	double t_3 = fma(z, (1.0 - y), x);
	double tmp;
	if (b <= -6.8e+105) {
		tmp = t_2;
	} else if (b <= -1.05e+29) {
		tmp = t_1;
	} else if (b <= -1.08e-91) {
		tmp = t_3;
	} else if (b <= -6.5e-267) {
		tmp = t_1;
	} else if (b <= 1.2) {
		tmp = t_3;
	} else if (b <= 1.7e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(1.0 - t), x)
	t_2 = Float64(b * Float64(t + Float64(y + -2.0)))
	t_3 = fma(z, Float64(1.0 - y), x)
	tmp = 0.0
	if (b <= -6.8e+105)
		tmp = t_2;
	elseif (b <= -1.05e+29)
		tmp = t_1;
	elseif (b <= -1.08e-91)
		tmp = t_3;
	elseif (b <= -6.5e-267)
		tmp = t_1;
	elseif (b <= 1.2)
		tmp = t_3;
	elseif (b <= 1.7e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[b, -6.8e+105], t$95$2, If[LessEqual[b, -1.05e+29], t$95$1, If[LessEqual[b, -1.08e-91], t$95$3, If[LessEqual[b, -6.5e-267], t$95$1, If[LessEqual[b, 1.2], t$95$3, If[LessEqual[b, 1.7e+165], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.7999999999999999e105 or 1.70000000000000005e165 < b

   1. Initial program 92.5%

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

   3. Taylor expanded in b around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. metadata-eval 88.4

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

   5. Simplified 88.4%

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

   if -6.7999999999999999e105 < b < -1.0500000000000001e29 or -1.07999999999999998e-91 < b < -6.4999999999999999e-267 or 1.19999999999999996 < b < 1.70000000000000005e165

   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 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. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 84.5

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

   5. Simplified 84.5%

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

   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 65.5

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

   8. Simplified 65.5%

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

   if -1.0500000000000001e29 < b < -1.07999999999999998e-91 or -6.4999999999999999e-267 < b < 1.19999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

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

      4. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 78.5

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

   5. Simplified 78.5%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

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

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

      3. --lowering--.f64 70.8

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

   8. Simplified 70.8%

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

Alternative 3: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := \mathsf{fma}\left(b, y + -2, a\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-107}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-11}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 y) x))
        (t_2 (* t (- b a)))
        (t_3 (fma b (+ y -2.0) a)))
   (if (<= t -1.7e+65)
     t_2
     (if (<= t -1.05e-47)
       t_1
       (if (<= t -6e-107)
         t_3
         (if (<= t 1.35e-200)
           t_1
           (if (<= t 1.32e-11) t_3 (if (<= t 9.5e+54) 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 = t * (b - a);
	double t_3 = fma(b, (y + -2.0), a);
	double tmp;
	if (t <= -1.7e+65) {
		tmp = t_2;
	} else if (t <= -1.05e-47) {
		tmp = t_1;
	} else if (t <= -6e-107) {
		tmp = t_3;
	} else if (t <= 1.35e-200) {
		tmp = t_1;
	} else if (t <= 1.32e-11) {
		tmp = t_3;
	} else if (t <= 9.5e+54) {
		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(t * Float64(b - a))
	t_3 = fma(b, Float64(y + -2.0), a)
	tmp = 0.0
	if (t <= -1.7e+65)
		tmp = t_2;
	elseif (t <= -1.05e-47)
		tmp = t_1;
	elseif (t <= -6e-107)
		tmp = t_3;
	elseif (t <= 1.35e-200)
		tmp = t_1;
	elseif (t <= 1.32e-11)
		tmp = t_3;
	elseif (t <= 9.5e+54)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(y + -2.0), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[t, -1.7e+65], t$95$2, If[LessEqual[t, -1.05e-47], t$95$1, If[LessEqual[t, -6e-107], t$95$3, If[LessEqual[t, 1.35e-200], t$95$1, If[LessEqual[t, 1.32e-11], t$95$3, If[LessEqual[t, 9.5e+54], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e65 or 9.4999999999999999e54 < t

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 80.9

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

   5. Simplified 80.9%

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

   if -1.7e65 < t < -1.05e-47 or -5.9999999999999994e-107 < t < 1.3500000000000001e-200 or 1.32e-11 < t < 9.4999999999999999e54

   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 a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

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

      4. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 82.4

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

   5. Simplified 82.4%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

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

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

      3. --lowering--.f64 64.0

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

   8. Simplified 64.0%

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

   if -1.05e-47 < t < -5.9999999999999994e-107 or 1.3500000000000001e-200 < t < 1.32e-11

   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. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 77.7

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

   5. Simplified 77.7%

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

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

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

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

      7. sub-neg N/A

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

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

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

      9. metadata-eval 77.6

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

   8. Simplified 77.6%

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

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

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

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

       3. sub-neg N/A

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

       4. metadata-eval N/A

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

       5. +-lowering-+.f64 64.5

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

   11. Simplified 64.5%

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

Alternative 4: 50.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-230}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 78:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* t (- b a))))
   (if (<= t -4.2e+40)
     t_2
     (if (<= t -6.5e-230)
       (fma y b x)
       (if (<= t -4.4e-259)
         t_1
         (if (<= t 78.0) (+ x a) (if (<= t 1.82e+53) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.2e+40) {
		tmp = t_2;
	} else if (t <= -6.5e-230) {
		tmp = fma(y, b, x);
	} else if (t <= -4.4e-259) {
		tmp = t_1;
	} else if (t <= 78.0) {
		tmp = x + a;
	} else if (t <= 1.82e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.2e+40)
		tmp = t_2;
	elseif (t <= -6.5e-230)
		tmp = fma(y, b, x);
	elseif (t <= -4.4e-259)
		tmp = t_1;
	elseif (t <= 78.0)
		tmp = Float64(x + a);
	elseif (t <= 1.82e+53)
		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]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+40], t$95$2, If[LessEqual[t, -6.5e-230], N[(y * b + x), $MachinePrecision], If[LessEqual[t, -4.4e-259], t$95$1, If[LessEqual[t, 78.0], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.82e+53], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.2000000000000002e40 or 1.81999999999999999e53 < t

   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 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 77.9

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

   5. Simplified 77.9%

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

   if -4.2000000000000002e40 < t < -6.5000000000000004e-230

   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 x around inf

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

   5. Simplified 58.1%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 48.4%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 48.4

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

   10. Applied egg-rr 48.4%

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

   if -6.5000000000000004e-230 < t < -4.40000000000000019e-259 or 78 < t < 1.81999999999999999e53

   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 z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. neg-mul-1 N/A

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

      5. metadata-eval N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. distribute-neg-in N/A

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

      16. metadata-eval N/A

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

      17. sub-neg N/A

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

      18. --lowering--.f64 66.2

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

   5. Simplified 66.2%

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

   if -4.40000000000000019e-259 < t < 78

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. 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. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 72.1

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

   5. Simplified 72.1%

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

   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 48.4

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

   8. Simplified 48.4%

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

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

       2. +-lowering-+.f64 47.4

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

   11. Simplified 47.4%

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

Alternative 5: 87.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, x\right)\\ t_2 := t + \left(y + -2\right)\\ \mathbf{if}\;b \leq -8.6 \cdot 10^{+37}:\\ \;\;\;\;\mathsf{fma}\left(b, t\_2, t\_1\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, t\_2, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- 1.0 t) x)) (t_2 (+ t (+ y -2.0))))
   (if (<= b -8.6e+37)
     (fma b t_2 t_1)
     (if (<= b 3.5e+86)
       (fma z (- 1.0 y) t_1)
       (fma b t_2 (fma z (- 1.0 y) x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (1.0 - t), x);
	double t_2 = t + (y + -2.0);
	double tmp;
	if (b <= -8.6e+37) {
		tmp = fma(b, t_2, t_1);
	} else if (b <= 3.5e+86) {
		tmp = fma(z, (1.0 - y), t_1);
	} else {
		tmp = fma(b, t_2, fma(z, (1.0 - y), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(1.0 - t), x)
	t_2 = Float64(t + Float64(y + -2.0))
	tmp = 0.0
	if (b <= -8.6e+37)
		tmp = fma(b, t_2, t_1);
	elseif (b <= 3.5e+86)
		tmp = fma(z, Float64(1.0 - y), t_1);
	else
		tmp = fma(b, t_2, fma(z, Float64(1.0 - y), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.6e+37], N[(b * t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 3.5e+86], N[(z * N[(1.0 - y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(b * t$95$2 + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.5999999999999994e37

   1. Initial program 96.2%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 95.4

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

   5. Simplified 95.4%

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

   if -8.5999999999999994e37 < b < 3.50000000000000019e86

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

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

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

      20. mul-1-neg N/A

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

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

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

   5. Simplified 89.7%

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

   if 3.50000000000000019e86 < b

   1. Initial program 90.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

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

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

      4. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 84.1

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

   5. Simplified 84.1%

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

Alternative 6: 87.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, x\right)\\ t_2 := \mathsf{fma}\left(b, t + \left(y + -2\right), t\_1\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- 1.0 t) x)) (t_2 (fma b (+ t (+ y -2.0)) t_1)))
   (if (<= b -2.8e+40) t_2 (if (<= b 5e+116) (fma z (- 1.0 y) t_1) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (1.0 - t), x);
	double t_2 = fma(b, (t + (y + -2.0)), t_1);
	double tmp;
	if (b <= -2.8e+40) {
		tmp = t_2;
	} else if (b <= 5e+116) {
		tmp = fma(z, (1.0 - y), t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(1.0 - t), x)
	t_2 = fma(b, Float64(t + Float64(y + -2.0)), t_1)
	tmp = 0.0
	if (b <= -2.8e+40)
		tmp = t_2;
	elseif (b <= 5e+116)
		tmp = fma(z, Float64(1.0 - y), t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[b, -2.8e+40], t$95$2, If[LessEqual[b, 5e+116], N[(z * N[(1.0 - y), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.8000000000000001e40 or 5.00000000000000025e116 < b

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. 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. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 90.0

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

   5. Simplified 90.0%

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

   if -2.8000000000000001e40 < b < 5.00000000000000025e116

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

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

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

      20. mul-1-neg N/A

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

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

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

   5. Simplified 89.0%

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

Alternative 7: 38.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(0 - a\right)\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-238}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+25}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+251}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- 0.0 a))))
   (if (<= t -1.08e+138)
     t_1
     (if (<= t -7.4e-238)
       (fma y b x)
       (if (<= t 6.4e+25) (+ x a) (if (<= t 2.15e+251) t_1 (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (0.0 - a);
	double tmp;
	if (t <= -1.08e+138) {
		tmp = t_1;
	} else if (t <= -7.4e-238) {
		tmp = fma(y, b, x);
	} else if (t <= 6.4e+25) {
		tmp = x + a;
	} else if (t <= 2.15e+251) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(0.0 - a))
	tmp = 0.0
	if (t <= -1.08e+138)
		tmp = t_1;
	elseif (t <= -7.4e-238)
		tmp = fma(y, b, x);
	elseif (t <= 6.4e+25)
		tmp = Float64(x + a);
	elseif (t <= 2.15e+251)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(0.0 - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.08e+138], t$95$1, If[LessEqual[t, -7.4e-238], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 6.4e+25], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.15e+251], t$95$1, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.08000000000000007e138 or 6.3999999999999999e25 < t < 2.15e251

   1. Initial program 93.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 79.6

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

   5. Simplified 79.6%

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

   6. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto t \cdot \color{blue}{\left(0 - a\right)} \]

      3. --lowering--.f64 52.5

         \[\leadsto t \cdot \color{blue}{\left(0 - a\right)} \]

   8. Simplified 52.5%

      \[\leadsto t \cdot \color{blue}{\left(0 - a\right)} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 52.5

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

   10. Applied egg-rr 52.5%

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

   if -1.08000000000000007e138 < t < -7.40000000000000048e-238

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 54.5%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 41.8%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 41.8

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

   10. Applied egg-rr 41.8%

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

   if -7.40000000000000048e-238 < t < 6.3999999999999999e25

   1. Initial program 98.9%

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

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 69.8

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

   5. Simplified 69.8%

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

   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 44.3

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

   8. Simplified 44.3%

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

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

       2. +-lowering-+.f64 43.5

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

   11. Simplified 43.5%

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

   if 2.15e251 < t

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 92.3

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

   5. Simplified 92.3%

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

   6. Taylor expanded in b around inf

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

   8. Simplified 84.0%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \left(0 - a\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-238}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+25}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+251}:\\ \;\;\;\;t \cdot \left(0 - a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.38 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.16 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x + a\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+149}:\\ \;\;\;\;x + \mathsf{fma}\left(a, 1 - t, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.38e+57)
     t_1
     (if (<= b -1.16e-91)
       (fma z (- 1.0 y) (+ x a))
       (if (<= b 5.2e+149) (+ x (fma a (- 1.0 t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.38e+57) {
		tmp = t_1;
	} else if (b <= -1.16e-91) {
		tmp = fma(z, (1.0 - y), (x + a));
	} else if (b <= 5.2e+149) {
		tmp = x + fma(a, (1.0 - t), z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.38e+57)
		tmp = t_1;
	elseif (b <= -1.16e-91)
		tmp = fma(z, Float64(1.0 - y), Float64(x + a));
	elseif (b <= 5.2e+149)
		tmp = Float64(x + fma(a, Float64(1.0 - t), z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.38e+57], t$95$1, If[LessEqual[b, -1.16e-91], N[(z * N[(1.0 - y), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+149], N[(x + N[(a * N[(1.0 - t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.38e57 or 5.19999999999999957e149 < b

   1. Initial program 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 86.6%

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

   if -1.38e57 < b < -1.15999999999999994e-91

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

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

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

      20. mul-1-neg N/A

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

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

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

   5. Simplified 86.2%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 76.9

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

   8. Simplified 76.9%

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

   if -1.15999999999999994e-91 < b < 5.19999999999999957e149

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

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

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

      20. mul-1-neg N/A

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

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

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

   5. Simplified 87.7%

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

   6. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

      4. --lowering--.f64 71.9

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

   8. Simplified 71.9%

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

Alternative 9: 83.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+59}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+165}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + \left(y + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e+59)
   (+ x (* (- (+ y t) 2.0) b))
   (if (<= b 4.1e+165)
     (fma z (- 1.0 y) (fma a (- 1.0 t) x))
     (* b (+ t (+ y -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e+59) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (b <= 4.1e+165) {
		tmp = fma(z, (1.0 - y), fma(a, (1.0 - t), x));
	} else {
		tmp = b * (t + (y + -2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1e+59)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (b <= 4.1e+165)
		tmp = fma(z, Float64(1.0 - y), fma(a, Float64(1.0 - t), x));
	else
		tmp = Float64(b * Float64(t + Float64(y + -2.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1e+59], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e+165], N[(z * N[(1.0 - y), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e59

   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 x around inf

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

   5. Simplified 89.1%

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

   if -1.1e59 < b < 4.1000000000000003e165

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

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

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

      20. mul-1-neg N/A

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

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

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

   5. Simplified 86.6%

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

   if 4.1000000000000003e165 < b

   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 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. associate--l+ N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. metadata-eval 88.3

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

   5. Simplified 88.3%

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

Alternative 10: 51.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-240}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+21}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.26e+36)
     t_1
     (if (<= t -1.7e-240) (fma y b x) (if (<= t 2.9e+21) (+ 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 <= -1.26e+36) {
		tmp = t_1;
	} else if (t <= -1.7e-240) {
		tmp = fma(y, b, x);
	} else if (t <= 2.9e+21) {
		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 <= -1.26e+36)
		tmp = t_1;
	elseif (t <= -1.7e-240)
		tmp = fma(y, b, x);
	elseif (t <= 2.9e+21)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+36], t$95$1, If[LessEqual[t, -1.7e-240], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 2.9e+21], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25999999999999994e36 or 2.9e21 < t

   1. Initial program 93.9%

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

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

   5. Simplified 73.7%

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

   if -1.25999999999999994e36 < t < -1.69999999999999995e-240

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 46.4%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 46.4

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

   10. Applied egg-rr 46.4%

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

   if -1.69999999999999995e-240 < t < 2.9e21

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. +-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. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 70.5

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

   5. Simplified 70.5%

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

   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 44.8

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

   8. Simplified 44.8%

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

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

       2. +-lowering-+.f64 44.0

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

   11. Simplified 44.0%

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

Alternative 11: 67.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -8.2e+58) t_1 (if (<= t 6.1e+53) (fma z (- 1.0 y) (+ 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 <= -8.2e+58) {
		tmp = t_1;
	} else if (t <= 6.1e+53) {
		tmp = fma(z, (1.0 - y), (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 <= -8.2e+58)
		tmp = t_1;
	elseif (t <= 6.1e+53)
		tmp = fma(z, Float64(1.0 - y), Float64(x + a));
	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, -8.2e+58], t$95$1, If[LessEqual[t, 6.1e+53], N[(z * N[(1.0 - y), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.2e58 or 6.1000000000000002e53 < t

   1. Initial program 92.9%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 80.9

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

   5. Simplified 80.9%

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

   if -8.2e58 < t < 6.1000000000000002e53

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

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

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

      20. mul-1-neg N/A

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

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

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

   5. Simplified 73.9%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 71.2

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

   8. Simplified 71.2%

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

Alternative 12: 67.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.68 \cdot 10^{+165}:\\ \;\;\;\;x + \mathsf{fma}\left(a, 1 - t, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -2.4e+107)
     t_1
     (if (<= b 1.68e+165) (+ x (fma a (- 1.0 t) z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -2.4e+107) {
		tmp = t_1;
	} else if (b <= 1.68e+165) {
		tmp = x + fma(a, (1.0 - t), z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -2.4e+107)
		tmp = t_1;
	elseif (b <= 1.68e+165)
		tmp = Float64(x + fma(a, Float64(1.0 - t), z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+107], t$95$1, If[LessEqual[b, 1.68e+165], N[(x + N[(a * N[(1.0 - t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4000000000000001e107 or 1.67999999999999992e165 < b

   1. Initial program 92.5%

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

   3. Taylor expanded in b around inf

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

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

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

      2. associate--l+ N/A

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

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

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

      4. sub-neg N/A

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

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

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

      6. metadata-eval 88.4

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

   5. Simplified 88.4%

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

   if -2.4000000000000001e107 < b < 1.67999999999999992e165

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. mul-1-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

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

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

      20. mul-1-neg N/A

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

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

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

   5. Simplified 86.0%

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

   6. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

      4. --lowering--.f64 67.7

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

   8. Simplified 67.7%

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

Alternative 13: 37.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+62}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.3e+118)
   (* t b)
   (if (<= t -4.2e-239) (fma y b x) (if (<= t 6.2e+62) (+ x a) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.3e+118) {
		tmp = t * b;
	} else if (t <= -4.2e-239) {
		tmp = fma(y, b, x);
	} else if (t <= 6.2e+62) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.3e+118)
		tmp = Float64(t * b);
	elseif (t <= -4.2e-239)
		tmp = fma(y, b, x);
	elseif (t <= 6.2e+62)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.3e+118], N[(t * b), $MachinePrecision], If[LessEqual[t, -4.2e-239], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 6.2e+62], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3e118 or 6.20000000000000029e62 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 86.7

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

   5. Simplified 86.7%

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

   6. Taylor expanded in b around inf

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

   8. Simplified 46.7%

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

   if -3.3e118 < t < -4.2000000000000004e-239

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 53.2%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 42.2%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 42.3

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

   10. Applied egg-rr 42.3%

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

   if -4.2000000000000004e-239 < t < 6.20000000000000029e62

   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 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. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 69.9

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

   5. Simplified 69.9%

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

   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 45.1

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

   8. Simplified 45.1%

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

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

       2. +-lowering-+.f64 41.3

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

   11. Simplified 41.3%

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

Alternative 14: 58.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.7e+49) t_1 (if (<= y 3.7e+26) (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 = y * (b - z);
	double tmp;
	if (y <= -1.7e+49) {
		tmp = t_1;
	} else if (y <= 3.7e+26) {
		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(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.7e+49)
		tmp = t_1;
	elseif (y <= 3.7e+26)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+49], t$95$1, If[LessEqual[y, 3.7e+26], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e49 or 3.69999999999999988e26 < y

   1. Initial program 93.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 67.9

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

   5. Simplified 67.9%

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

   if -1.7e49 < y < 3.69999999999999988e26

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0

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

      1. +-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. associate--l+ N/A

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

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

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

      6. sub-neg N/A

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

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

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

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

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

      12. mul-1-neg N/A

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

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

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-neg-in N/A

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

      19. metadata-eval N/A

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

      20. sub-neg N/A

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

      21. --lowering--.f64 80.1

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

   5. Simplified 80.1%

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

   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 54.1

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

   8. Simplified 54.1%

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

Alternative 15: 45.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.35e+44) t_1 (if (<= a 3.6e+137) (fma y b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.35e+44) {
		tmp = t_1;
	} else if (a <= 3.6e+137) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.35e+44)
		tmp = t_1;
	elseif (a <= 3.6e+137)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+44], t$95$1, If[LessEqual[a, 3.6e+137], N[(y * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.35e44 or 3.6e137 < a

   1. Initial program 94.1%

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

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 61.2

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

   5. Simplified 61.2%

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

   if -1.35e44 < a < 3.6e137

   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 x around inf

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

   5. Simplified 64.7%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 37.2%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 37.2

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

   10. Applied egg-rr 37.2%

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

Alternative 16: 20.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-76}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+186}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.25e+21) x (if (<= x 3.9e-76) a (if (<= x 7.5e+186) z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.25e+21) {
		tmp = x;
	} else if (x <= 3.9e-76) {
		tmp = a;
	} else if (x <= 7.5e+186) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.25d+21)) then
        tmp = x
    else if (x <= 3.9d-76) then
        tmp = a
    else if (x <= 7.5d+186) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.25e+21) {
		tmp = x;
	} else if (x <= 3.9e-76) {
		tmp = a;
	} else if (x <= 7.5e+186) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.25e+21:
		tmp = x
	elif x <= 3.9e-76:
		tmp = a
	elif x <= 7.5e+186:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.25e+21)
		tmp = x;
	elseif (x <= 3.9e-76)
		tmp = a;
	elseif (x <= 7.5e+186)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.25e+21)
		tmp = x;
	elseif (x <= 3.9e-76)
		tmp = a;
	elseif (x <= 7.5e+186)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.25e+21], x, If[LessEqual[x, 3.9e-76], a, If[LessEqual[x, 7.5e+186], z, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e21 or 7.4999999999999998e186 < x

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 39.3%

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

   if -2.25e21 < x < 3.90000000000000025e-76

   1. Initial program 96.2%

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

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

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

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

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 39.1

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

   5. Simplified 39.1%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a} \]
   7. Step-by-step derivation

   8. Simplified 19.6%

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

   if 3.90000000000000025e-76 < x < 7.4999999999999998e186

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)} \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{-1 \cdot y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot y + 1\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)} \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y - 1\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(y - 1\right)\right)} \]

      11. mul-1-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} \]

      12. sub-neg N/A

          \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(-1 + y\right)}\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto z \cdot \color{blue}{\left(\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right)} \]

      16. metadata-eval N/A

          \[\leadsto z \cdot \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} \]

      18. --lowering--.f64 42.5

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 21.8%

      \[\leadsto \color{blue}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 35.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.7 \cdot 10^{+21}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+63}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.7e+21) (* t b) (if (<= t 2.35e+63) (+ x a) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.7e+21) {
		tmp = t * b;
	} else if (t <= 2.35e+63) {
		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 <= (-8.7d+21)) then
        tmp = t * b
    else if (t <= 2.35d+63) 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 <= -8.7e+21) {
		tmp = t * b;
	} else if (t <= 2.35e+63) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8.7e+21:
		tmp = t * b
	elif t <= 2.35e+63:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.7e+21)
		tmp = Float64(t * b);
	elseif (t <= 2.35e+63)
		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 <= -8.7e+21)
		tmp = t * b;
	elseif (t <= 2.35e+63)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.7e+21], N[(t * b), $MachinePrecision], If[LessEqual[t, 2.35e+63], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.7e21 or 2.3500000000000001e63 < t

   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 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 78.6

         \[\leadsto t \cdot \color{blue}{\left(b - a\right)} \]

   5. Simplified 78.6%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto t \cdot \color{blue}{b} \]
   7. Step-by-step derivation

   8. Simplified 42.0%

      \[\leadsto t \cdot \color{blue}{b} \]

   if -8.7e21 < t < 2.3500000000000001e63

   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. associate--l+ N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(y - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(y - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{\left(y + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{\left(y + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, t + \left(y + \color{blue}{-2}\right), x - a \cdot \left(t - 1\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x}\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + x\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + x\right) \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x\right)}\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, x\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), x\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), x\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), x\right)\right) \]

      18. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, x\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), x\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

      21. --lowering--.f64 70.7

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

   5. Simplified 70.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]

   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 43.1

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

   8. Simplified 43.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{x + a} \]

       2. +-lowering-+.f64 40.3

          \[\leadsto \color{blue}{x + a} \]

   11. Simplified 40.3%

       \[\leadsto \color{blue}{x + a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 31.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+208}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.45e+47) (* y b) (if (<= y 3.5e+208) (+ x a) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.45e+47) {
		tmp = y * b;
	} else if (y <= 3.5e+208) {
		tmp = x + a;
	} else {
		tmp = y * 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 (y <= (-1.45d+47)) then
        tmp = y * b
    else if (y <= 3.5d+208) then
        tmp = x + a
    else
        tmp = y * 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 (y <= -1.45e+47) {
		tmp = y * b;
	} else if (y <= 3.5e+208) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.45e+47:
		tmp = y * b
	elif y <= 3.5e+208:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.45e+47)
		tmp = Float64(y * b);
	elseif (y <= 3.5e+208)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.45e+47)
		tmp = y * b;
	elseif (y <= 3.5e+208)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.45e+47], N[(y * b), $MachinePrecision], If[LessEqual[y, 3.5e+208], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4499999999999999e47 or 3.50000000000000016e208 < y

   1. Initial program 90.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. associate--l+ N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(y - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(y - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{\left(y + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{\left(y + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, t + \left(y + \color{blue}{-2}\right), x - a \cdot \left(t - 1\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x}\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + x\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + x\right) \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x\right)}\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, x\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), x\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), x\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), x\right)\right) \]

      18. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, x\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), x\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

      21. --lowering--.f64 67.6

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

   5. Simplified 67.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{b \cdot y} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 41.0

         \[\leadsto \color{blue}{b \cdot y} \]

   8. Simplified 41.0%

      \[\leadsto \color{blue}{b \cdot y} \]

   if -1.4499999999999999e47 < y < 3.50000000000000016e208

   1. Initial program 98.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. associate--l+ N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(y - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(y - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{\left(y + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{\left(y + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, t + \left(y + \color{blue}{-2}\right), x - a \cdot \left(t - 1\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x}\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + x\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + x\right) \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x\right)}\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, x\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), x\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), x\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), x\right)\right) \]

      18. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, x\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), x\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

      21. --lowering--.f64 78.7

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

   5. Simplified 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]

   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 51.2

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

   8. Simplified 51.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{x + a} \]

       2. +-lowering-+.f64 36.0

          \[\leadsto \color{blue}{x + a} \]

   11. Simplified 36.0%

       \[\leadsto \color{blue}{x + a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+208}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+185}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+182}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.3e+185) z (if (<= z 9.8e+182) (+ x a) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e+185) {
		tmp = z;
	} else if (z <= 9.8e+182) {
		tmp = x + a;
	} else {
		tmp = z;
	}
	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 (z <= (-2.3d+185)) then
        tmp = z
    else if (z <= 9.8d+182) then
        tmp = x + a
    else
        tmp = z
    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 (z <= -2.3e+185) {
		tmp = z;
	} else if (z <= 9.8e+182) {
		tmp = x + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.3e+185:
		tmp = z
	elif z <= 9.8e+182:
		tmp = x + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.3e+185)
		tmp = z;
	elseif (z <= 9.8e+182)
		tmp = Float64(x + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.3e+185)
		tmp = z;
	elseif (z <= 9.8e+182)
		tmp = x + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.3e+185], z, If[LessEqual[z, 9.8e+182], N[(x + a), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e185 or 9.7999999999999999e182 < z

   1. Initial program 92.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)} \]

      2. neg-mul-1 N/A

         \[\leadsto z \cdot \left(1 + \color{blue}{-1 \cdot y}\right) \]

      3. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot y + 1\right)} \]

      4. neg-mul-1 N/A

         \[\leadsto z \cdot \left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} + 1\right) \]

      5. metadata-eval N/A

         \[\leadsto z \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)}\right) \]

      6. distribute-neg-in N/A

         \[\leadsto z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y + -1\right)\right)\right)} \]

      7. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y - 1\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(y - 1\right)\right)} \]

      11. mul-1-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} \]

      12. sub-neg N/A

          \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(-1 + y\right)}\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto z \cdot \color{blue}{\left(\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right)} \]

      16. metadata-eval N/A

          \[\leadsto z \cdot \left(\color{blue}{1} + \left(\mathsf{neg}\left(y\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} \]

      18. --lowering--.f64 66.6

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} \]

   5. Simplified 66.6%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 32.5%

      \[\leadsto \color{blue}{z} \]

   if -2.3000000000000001e185 < z < 9.7999999999999999e182

   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. associate--l+ N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(y - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{t + \left(y - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{\left(y + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, t + \color{blue}{\left(y + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, t + \left(y + \color{blue}{-2}\right), x - a \cdot \left(t - 1\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x}\right) \]

      11. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + x\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + x\right) \]

      13. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x\right)}\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, x\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), x\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), x\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), x\right)\right) \]

      18. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, x\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), x\right)\right) \]

      20. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

      21. --lowering--.f64 85.8

          \[\leadsto \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

   5. Simplified 85.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]

   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 51.3

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

   8. Simplified 51.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, x\right)} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{x + a} \]

       2. +-lowering-+.f64 34.5

          \[\leadsto \color{blue}{x + a} \]

   11. Simplified 34.5%

       \[\leadsto \color{blue}{x + a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 21.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.22 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+15}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.22e+21) x (if (<= x 7e+15) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.22e+21) {
		tmp = x;
	} else if (x <= 7e+15) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.22d+21)) then
        tmp = x
    else if (x <= 7d+15) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.22e+21) {
		tmp = x;
	} else if (x <= 7e+15) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.22e+21:
		tmp = x
	elif x <= 7e+15:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.22e+21)
		tmp = x;
	elseif (x <= 7e+15)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.22e+21)
		tmp = x;
	elseif (x <= 7e+15)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.22e+21], x, If[LessEqual[x, 7e+15], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.22e21 or 7e15 < x

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 30.8%

      \[\leadsto \color{blue}{x} \]

   if -2.22e21 < x < 7e15

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right) \]

      5. distribute-lft-in N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t + -1\right)\right)} \]

      6. metadata-eval N/A

         \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

      7. sub-neg N/A

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t - 1\right)\right)} \]

      9. mul-1-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} \]

      10. sub-neg N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right)\right) \]

      13. distribute-neg-in N/A

          \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right)} \]

      14. metadata-eval N/A

          \[\leadsto a \cdot \left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto a \cdot \color{blue}{\left(1 - t\right)} \]

      16. --lowering--.f64 36.2

          \[\leadsto a \cdot \color{blue}{\left(1 - t\right)} \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a} \]
   7. Step-by-step derivation

   8. Simplified 18.9%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 11.3% 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 96.5%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around 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. metadata-eval N/A

      \[\leadsto a \cdot \left(-1 \cdot t + \color{blue}{-1 \cdot -1}\right) \]

   5. distribute-lft-in N/A

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t + -1\right)\right)} \]

   6. metadata-eval N/A

      \[\leadsto a \cdot \left(-1 \cdot \left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) \]

   7. sub-neg N/A

      \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t - 1\right)}\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t - 1\right)\right)} \]

   9. mul-1-neg N/A

      \[\leadsto a \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} \]

   10. sub-neg N/A

       \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto a \cdot \left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right)\right) \]

   12. +-commutative N/A

       \[\leadsto a \cdot \left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right)\right) \]

   13. distribute-neg-in N/A

       \[\leadsto a \cdot \color{blue}{\left(\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right)} \]

   14. metadata-eval N/A

       \[\leadsto a \cdot \left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right)\right) \]

   15. sub-neg N/A

       \[\leadsto a \cdot \color{blue}{\left(1 - t\right)} \]

   16. --lowering--.f64 30.1

       \[\leadsto a \cdot \color{blue}{\left(1 - t\right)} \]

5. Simplified 30.1%

   \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a} \]
7. Step-by-step derivation

8. Simplified 13.7%

   \[\leadsto \color{blue}{a} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024196 
(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)))