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

Percentage Accurate: 95.7% → 97.8%

Time: 14.0s

Alternatives: 24

Speedup: 0.5×

• 36.9% 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: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

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

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 (* (+ y t) b))))

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 = (y + t) * b;
	}
	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 = (y + t) * b;
	}
	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 = (y + t) * b
	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(Float64(y + t) * b);
	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 = (y + t) * b;
	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[(N[(y + t), $MachinePrecision] * b), $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 z around 0

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

   5. Simplified 50.0%

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

   6. Taylor expanded in b around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. +-lowering-+.f64 66.7

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

   8. Simplified 66.7%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 66.7%

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

4. Final simplification 98.4%

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

Alternative 2: 54.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \mathsf{fma}\left(t, b, z\right)\\ t_2 := \mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-233}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (fma t b z))) (t_2 (fma a (- 1.0 t) x)))
   (if (<= a -2.6e+95)
     t_2
     (if (<= a -1.25e-67)
       t_1
       (if (<= a -1e-233) (* (+ y t) b) (if (<= a 1.6e+101) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + fma(t, b, z);
	double t_2 = fma(a, (1.0 - t), x);
	double tmp;
	if (a <= -2.6e+95) {
		tmp = t_2;
	} else if (a <= -1.25e-67) {
		tmp = t_1;
	} else if (a <= -1e-233) {
		tmp = (y + t) * b;
	} else if (a <= 1.6e+101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + fma(t, b, z))
	t_2 = fma(a, Float64(1.0 - t), x)
	tmp = 0.0
	if (a <= -2.6e+95)
		tmp = t_2;
	elseif (a <= -1.25e-67)
		tmp = t_1;
	elseif (a <= -1e-233)
		tmp = Float64(Float64(y + t) * b);
	elseif (a <= 1.6e+101)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * b + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.6e+95], t$95$2, If[LessEqual[a, -1.25e-67], t$95$1, If[LessEqual[a, -1e-233], N[(N[(y + t), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 1.6e+101], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5999999999999999e95 or 1.60000000000000003e101 < a

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 85.2%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. *-rgt-identity N/A

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. distribute-lft-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. --lowering--.f64 70.1

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

   8. Simplified 70.1%

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

   if -2.5999999999999999e95 < a < -1.25e-67 or -9.99999999999999958e-234 < a < 1.60000000000000003e101

   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 y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 74.8

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 64.6%

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

   9. Taylor expanded in a around 0

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

       1. +-commutative N/A

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

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

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. accelerator-lowering-fma.f64 60.8

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

   11. Simplified 60.8%

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

   if -1.25e-67 < a < -9.99999999999999958e-234

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 87.8%

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

   6. Taylor expanded in b around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. +-lowering-+.f64 75.8

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

   8. Simplified 75.8%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 67.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-67}:\\ \;\;\;\;x + \mathsf{fma}\left(t, b, z\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-233}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+101}:\\ \;\;\;\;x + \mathsf{fma}\left(t, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \mathsf{fma}\left(t, b, z\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-230}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (fma t b z))))
   (if (<= a -2.8e+95)
     (- a (* t a))
     (if (<= a -3.4e-66)
       t_1
       (if (<= a -1.85e-230)
         (* (+ y t) b)
         (if (<= a 1.95e+173) t_1 (fma (- t) a a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + fma(t, b, z);
	double tmp;
	if (a <= -2.8e+95) {
		tmp = a - (t * a);
	} else if (a <= -3.4e-66) {
		tmp = t_1;
	} else if (a <= -1.85e-230) {
		tmp = (y + t) * b;
	} else if (a <= 1.95e+173) {
		tmp = t_1;
	} else {
		tmp = fma(-t, a, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + fma(t, b, z))
	tmp = 0.0
	if (a <= -2.8e+95)
		tmp = Float64(a - Float64(t * a));
	elseif (a <= -3.4e-66)
		tmp = t_1;
	elseif (a <= -1.85e-230)
		tmp = Float64(Float64(y + t) * b);
	elseif (a <= 1.95e+173)
		tmp = t_1;
	else
		tmp = fma(Float64(-t), a, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * b + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+95], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.4e-66], t$95$1, If[LessEqual[a, -1.85e-230], N[(N[(y + t), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 1.95e+173], t$95$1, N[((-t) * a + a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7999999999999998e95

   1. Initial program 95.5%

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

   3. Taylor expanded in a around 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. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. neg-mul-1 N/A

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

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

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

      7. *-commutative N/A

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

      8. unsub-neg N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      9. --lowering--.f64 N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      10. *-commutative N/A

          \[\leadsto a - \color{blue}{t \cdot a} \]

      11. *-lowering-*.f64 66.7

          \[\leadsto a - \color{blue}{t \cdot a} \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{a - t \cdot a} \]

   if -2.7999999999999998e95 < a < -3.39999999999999997e-66 or -1.84999999999999991e-230 < a < 1.9499999999999999e173

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 74.4

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

   5. Simplified 74.4%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 65.1%

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

   9. Taylor expanded in a around 0

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

       1. +-commutative N/A

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

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

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. accelerator-lowering-fma.f64 59.7

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

   11. Simplified 59.7%

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

   if -3.39999999999999997e-66 < a < -1.84999999999999991e-230

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 87.8%

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

   6. Taylor expanded in b around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. +-lowering-+.f64 75.8

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

   8. Simplified 75.8%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 67.8%

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

   if 1.9499999999999999e173 < 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. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. neg-mul-1 N/A

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

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

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

      7. *-commutative N/A

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

      8. unsub-neg N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      9. --lowering--.f64 N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      10. *-commutative N/A

          \[\leadsto a - \color{blue}{t \cdot a} \]

      11. *-lowering-*.f64 72.7

          \[\leadsto a - \color{blue}{t \cdot a} \]

   5. Simplified 72.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. neg-lowering-neg.f64 72.7

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

   7. Applied egg-rr 72.7%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-66}:\\ \;\;\;\;x + \mathsf{fma}\left(t, b, z\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-230}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+173}:\\ \;\;\;\;x + \mathsf{fma}\left(t, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, b - a, a + \mathsf{fma}\left(b, y + -2, x\right)\right)\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma t (- b a) (+ a (fma b (+ y -2.0) x)))))
   (if (<= b -3.6e-5)
     t_1
     (if (<= b 3.2e+63) (fma a (- 1.0 t) (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(t, (b - a), (a + fma(b, (y + -2.0), x)));
	double tmp;
	if (b <= -3.6e-5) {
		tmp = t_1;
	} else if (b <= 3.2e+63) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(t, Float64(b - a), Float64(a + fma(b, Float64(y + -2.0), x)))
	tmp = 0.0
	if (b <= -3.6e-5)
		tmp = t_1;
	elseif (b <= 3.2e+63)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision] + N[(a + N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e-5], t$95$1, If[LessEqual[b, 3.2e+63], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.60000000000000009e-5 or 3.20000000000000011e63 < b

   1. Initial program 91.3%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 86.8%

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

   if -3.60000000000000009e-5 < b < 3.20000000000000011e63

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

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

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

   5. Simplified 92.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(t, b - a, a + \mathsf{fma}\left(b, y + -2, x\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b - a, a + \mathsf{fma}\left(b, y + -2, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.65e+127)
     t_1
     (if (<= b 3.7e+95) (fma a (- 1.0 t) (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.65e+127) {
		tmp = t_1;
	} else if (b <= 3.7e+95) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} 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 <= -1.65e+127)
		tmp = t_1;
	elseif (b <= 3.7e+95)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+127], t$95$1, If[LessEqual[b, 3.7e+95], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.64999999999999988e127 or 3.7000000000000001e95 < b

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 88.6%

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

   if -1.64999999999999988e127 < b < 3.7000000000000001e95

   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 b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

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

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

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

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

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

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

   5. Simplified 89.8%

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

Alternative 6: 75.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+95}:\\ \;\;\;\;x + \mathsf{fma}\left(b, t, \mathsf{fma}\left(a, 1 - t, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3.9e+127)
     t_1
     (if (<= b 1.45e+95) (+ x (fma b t (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 <= -3.9e+127) {
		tmp = t_1;
	} else if (b <= 1.45e+95) {
		tmp = x + fma(b, t, 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 <= -3.9e+127)
		tmp = t_1;
	elseif (b <= 1.45e+95)
		tmp = Float64(x + fma(b, t, 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, -3.9e+127], t$95$1, If[LessEqual[b, 1.45e+95], N[(x + N[(b * t + N[(a * N[(1.0 - t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.89999999999999981e127 or 1.45000000000000007e95 < b

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 88.6%

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

   if -3.89999999999999981e127 < b < 1.45000000000000007e95

   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 y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 78.2

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

   5. Simplified 78.2%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 77.0%

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

Alternative 7: 62.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, b - a, x\right)\\ \mathbf{if}\;t \leq -1450000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 3.4:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma t (- b a) x)))
   (if (<= t -1450000000000.0)
     t_1
     (if (<= t 7e-46)
       (fma b (+ y -2.0) x)
       (if (<= t 3.4) (+ z (+ x a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(t, (b - a), x);
	double tmp;
	if (t <= -1450000000000.0) {
		tmp = t_1;
	} else if (t <= 7e-46) {
		tmp = fma(b, (y + -2.0), x);
	} else if (t <= 3.4) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(t, Float64(b - a), x)
	tmp = 0.0
	if (t <= -1450000000000.0)
		tmp = t_1;
	elseif (t <= 7e-46)
		tmp = fma(b, Float64(y + -2.0), x);
	elseif (t <= 3.4)
		tmp = Float64(z + 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] + x), $MachinePrecision]}, If[LessEqual[t, -1450000000000.0], t$95$1, If[LessEqual[t, 7e-46], N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 3.4], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e12 or 3.39999999999999991 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 78.0%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 80.3%

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

   if -1.45e12 < t < 7.0000000000000004e-46

   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 58.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 57.7

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

   8. Simplified 57.7%

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

   if 7.0000000000000004e-46 < t < 3.39999999999999991

   1. Initial program 89.8%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 80.3

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

   5. Simplified 80.3%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 80.9%

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

   9. Taylor expanded in t around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-lowering-+.f64 67.1

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

   11. Simplified 67.1%

       \[\leadsto \color{blue}{z + \left(a + x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1450000000000:\\ \;\;\;\;\mathsf{fma}\left(t, b - a, x\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 3.4:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b - a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6.3 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+86}:\\ \;\;\;\;x + \mathsf{fma}\left(t, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -6.3e+41)
     t_1
     (if (<= t 1.05e-45)
       (fma b (+ y -2.0) x)
       (if (<= t 1.75e+86) (+ x (fma t b z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6.3e+41) {
		tmp = t_1;
	} else if (t <= 1.05e-45) {
		tmp = fma(b, (y + -2.0), x);
	} else if (t <= 1.75e+86) {
		tmp = x + fma(t, b, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6.3e+41)
		tmp = t_1;
	elseif (t <= 1.05e-45)
		tmp = fma(b, Float64(y + -2.0), x);
	elseif (t <= 1.75e+86)
		tmp = Float64(x + fma(t, b, z));
	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, -6.3e+41], t$95$1, If[LessEqual[t, 1.05e-45], N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.75e+86], N[(x + N[(t * b + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2999999999999999e41 or 1.75000000000000009e86 < t

   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 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 81.6

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

   5. Simplified 81.6%

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

   if -6.2999999999999999e41 < t < 1.04999999999999998e-45

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 58.2%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 57.1

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

   8. Simplified 57.1%

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

   if 1.04999999999999998e-45 < t < 1.75000000000000009e86

   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 y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 81.1

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 81.3%

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

   9. Taylor expanded in a around 0

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

       1. +-commutative N/A

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

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

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. accelerator-lowering-fma.f64 53.3

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

   11. Simplified 53.3%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+86}:\\ \;\;\;\;x + \mathsf{fma}\left(t, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+96}:\\ \;\;\;\;z + \mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.65e+127)
     t_1
     (if (<= b 1.85e+96) (+ z (fma a (- 1.0 t) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.65e+127) {
		tmp = t_1;
	} else if (b <= 1.85e+96) {
		tmp = z + fma(a, (1.0 - t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.65e+127)
		tmp = t_1;
	elseif (b <= 1.85e+96)
		tmp = Float64(z + fma(a, Float64(1.0 - t), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+127], t$95$1, If[LessEqual[b, 1.85e+96], N[(z + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.64999999999999988e127 or 1.84999999999999996e96 < b

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 88.6%

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

   if -1.64999999999999988e127 < b < 1.84999999999999996e96

   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 y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 78.2

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

   5. Simplified 78.2%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

      5. +-commutative N/A

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

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

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

      7. --lowering--.f64 71.9

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

   8. Simplified 71.9%

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

Alternative 10: 70.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1150000000000:\\ \;\;\;\;\mathsf{fma}\left(t, b - a, x\right)\\ \mathbf{elif}\;t \leq 0.000205:\\ \;\;\;\;x + \mathsf{fma}\left(b, y + -2, a\right)\\ \mathbf{else}:\\ \;\;\;\;a + \mathsf{fma}\left(t, b - a, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1150000000000.0)
   (fma t (- b a) x)
   (if (<= t 0.000205) (+ x (fma b (+ y -2.0) a)) (+ a (fma t (- b a) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1150000000000.0) {
		tmp = fma(t, (b - a), x);
	} else if (t <= 0.000205) {
		tmp = x + fma(b, (y + -2.0), a);
	} else {
		tmp = a + fma(t, (b - a), z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1150000000000.0)
		tmp = fma(t, Float64(b - a), x);
	elseif (t <= 0.000205)
		tmp = Float64(x + fma(b, Float64(y + -2.0), a));
	else
		tmp = Float64(a + fma(t, Float64(b - a), z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1150000000000.0], N[(t * N[(b - a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 0.000205], N[(x + N[(b * N[(y + -2.0), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(a + N[(t * N[(b - a), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e12

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 80.1%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 83.9%

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

   if -1.15e12 < t < 2.05e-4

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 74.3%

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

   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. metadata-eval N/A

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

      9. +-lowering-+.f64 72.5

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

   8. Simplified 72.5%

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

   if 2.05e-4 < 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 y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 85.5

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 85.5%

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

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. distribute-lft-out-- N/A

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

       3. *-rgt-identity N/A

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

       4. unsub-neg N/A

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

       5. mul-1-neg N/A

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

       6. +-commutative N/A

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

       7. associate-+r+ N/A

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

       8. associate-*r* N/A

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

       9. distribute-rgt-in N/A

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

       10. associate-+l+ N/A

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

       11. +-commutative N/A

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

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

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

       13. +-commutative N/A

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

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

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

       15. mul-1-neg N/A

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

       16. unsub-neg N/A

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

       17. --lowering--.f64 81.4

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

   11. Simplified 81.4%

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

Alternative 11: 61.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1100000000000:\\ \;\;\;\;\mathsf{fma}\left(t, b - a, x\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;a + \mathsf{fma}\left(t, b - a, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1100000000000.0)
   (fma t (- b a) x)
   (if (<= t 1.05e-45) (fma b (+ y -2.0) x) (+ a (fma t (- b a) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1100000000000.0) {
		tmp = fma(t, (b - a), x);
	} else if (t <= 1.05e-45) {
		tmp = fma(b, (y + -2.0), x);
	} else {
		tmp = a + fma(t, (b - a), z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1100000000000.0)
		tmp = fma(t, Float64(b - a), x);
	elseif (t <= 1.05e-45)
		tmp = fma(b, Float64(y + -2.0), x);
	else
		tmp = Float64(a + fma(t, Float64(b - a), z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1100000000000.0], N[(t * N[(b - a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.05e-45], N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision], N[(a + N[(t * N[(b - a), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e12

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 80.1%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 83.9%

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

   if -1.1e12 < t < 1.04999999999999998e-45

   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 58.0%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 57.7

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

   8. Simplified 57.7%

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

   if 1.04999999999999998e-45 < t

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 84.2

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

   5. Simplified 84.2%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 84.3%

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

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

       2. distribute-lft-out-- N/A

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

       3. *-rgt-identity N/A

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

       4. unsub-neg N/A

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

       5. mul-1-neg N/A

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

       6. +-commutative N/A

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

       7. associate-+r+ N/A

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

       8. associate-*r* N/A

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

       9. distribute-rgt-in N/A

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

       10. associate-+l+ N/A

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

       11. +-commutative N/A

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

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

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

       13. +-commutative N/A

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

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

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

       15. mul-1-neg N/A

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

       16. unsub-neg N/A

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

       17. --lowering--.f64 79.4

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

   11. Simplified 79.4%

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

Alternative 12: 60.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + \left(y + -2\right)\right)\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t (+ y -2.0)))))
   (if (<= b -1.85e+127) t_1 (if (<= b 5.8e+94) (fma a (- 1.0 t) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + (y + -2.0));
	double tmp;
	if (b <= -1.85e+127) {
		tmp = t_1;
	} else if (b <= 5.8e+94) {
		tmp = fma(a, (1.0 - t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + Float64(y + -2.0)))
	tmp = 0.0
	if (b <= -1.85e+127)
		tmp = t_1;
	elseif (b <= 5.8e+94)
		tmp = fma(a, Float64(1.0 - t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.85e+127], t$95$1, If[LessEqual[b, 5.8e+94], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8499999999999999e127 or 5.7999999999999997e94 < b

   1. Initial program 91.4%

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

   3. Taylor expanded in b around inf

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

      1. *-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 82.8

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

   5. Simplified 82.8%

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

   if -1.8499999999999999e127 < b < 5.7999999999999997e94

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 65.6%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. *-rgt-identity N/A

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. distribute-lft-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. --lowering--.f64 56.9

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

   8. Simplified 56.9%

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

Alternative 13: 54.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, t + -2, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.65e+127)
   (* (+ y t) b)
   (if (<= b 1.4e+95) (fma a (- 1.0 t) x) (fma b (+ t -2.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.65e+127) {
		tmp = (y + t) * b;
	} else if (b <= 1.4e+95) {
		tmp = fma(a, (1.0 - t), x);
	} else {
		tmp = fma(b, (t + -2.0), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.65e+127)
		tmp = Float64(Float64(y + t) * b);
	elseif (b <= 1.4e+95)
		tmp = fma(a, Float64(1.0 - t), x);
	else
		tmp = fma(b, Float64(t + -2.0), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.65e+127], N[(N[(y + t), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 1.4e+95], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], N[(b * N[(t + -2.0), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.64999999999999988e127

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 92.7%

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

   6. Taylor expanded in b around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. +-lowering-+.f64 82.6

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

   8. Simplified 82.6%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 73.0%

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

   if -1.64999999999999988e127 < b < 1.3999999999999999e95

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 65.6%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. *-rgt-identity N/A

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. distribute-lft-in N/A

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

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

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. --lowering--.f64 56.9

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

   8. Simplified 56.9%

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

   if 1.3999999999999999e95 < b

   1. Initial program 90.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 66.4

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

   8. Simplified 66.4%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, t + -2, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1550:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -9e+35) t_1 (if (<= t 1550.0) (+ z (+ 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 <= -9e+35) {
		tmp = t_1;
	} else if (t <= 1550.0) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-9d+35)) then
        tmp = t_1
    else if (t <= 1550.0d0) then
        tmp = z + (x + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -9e+35) {
		tmp = t_1;
	} else if (t <= 1550.0) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -9e+35:
		tmp = t_1
	elif t <= 1550.0:
		tmp = z + (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 <= -9e+35)
		tmp = t_1;
	elseif (t <= 1550.0)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -9e+35)
		tmp = t_1;
	elseif (t <= 1550.0)
		tmp = z + (x + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+35], t$95$1, If[LessEqual[t, 1550.0], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.9999999999999993e35 or 1550 < t

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf

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

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

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

      2. --lowering--.f64 75.0

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

   5. Simplified 75.0%

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

   if -8.9999999999999993e35 < t < 1550

   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 y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 64.5

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

   5. Simplified 64.5%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 51.3%

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

   9. Taylor expanded in t around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-lowering-+.f64 48.0

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

   11. Simplified 48.0%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1550:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + t\right) \cdot b\\ \mathbf{if}\;b \leq -8 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y t) b)))
   (if (<= b -8e-5) t_1 (if (<= b 2.05e+71) (+ z (+ x a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * b;
	double tmp;
	if (b <= -8e-5) {
		tmp = t_1;
	} else if (b <= 2.05e+71) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y + t) * b
    if (b <= (-8d-5)) then
        tmp = t_1
    else if (b <= 2.05d+71) then
        tmp = z + (x + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + t) * b;
	double tmp;
	if (b <= -8e-5) {
		tmp = t_1;
	} else if (b <= 2.05e+71) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + t) * b
	tmp = 0
	if b <= -8e-5:
		tmp = t_1
	elif b <= 2.05e+71:
		tmp = z + (x + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + t) * b)
	tmp = 0.0
	if (b <= -8e-5)
		tmp = t_1;
	elseif (b <= 2.05e+71)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + t) * b;
	tmp = 0.0;
	if (b <= -8e-5)
		tmp = t_1;
	elseif (b <= 2.05e+71)
		tmp = z + (x + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + t), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -8e-5], t$95$1, If[LessEqual[b, 2.05e+71], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.00000000000000065e-5 or 2.0500000000000001e71 < b

   1. Initial program 91.3%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 86.8%

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

   6. Taylor expanded in b around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. +-lowering-+.f64 75.6

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

   8. Simplified 75.6%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 63.1%

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

   if -8.00000000000000065e-5 < b < 2.0500000000000001e71

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 79.7

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

   5. Simplified 79.7%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 78.3%

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

   9. Taylor expanded in t around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-lowering-+.f64 50.3

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

   11. Simplified 50.3%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{-5}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+71}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+90}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.9e+109)
   (* b (+ y -2.0))
   (if (<= b 1.95e+90) (+ z (+ x a)) (* b (+ t -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+109) {
		tmp = b * (y + -2.0);
	} else if (b <= 1.95e+90) {
		tmp = z + (x + a);
	} else {
		tmp = b * (t + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.9d+109)) then
        tmp = b * (y + (-2.0d0))
    else if (b <= 1.95d+90) then
        tmp = z + (x + a)
    else
        tmp = b * (t + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+109) {
		tmp = b * (y + -2.0);
	} else if (b <= 1.95e+90) {
		tmp = z + (x + a);
	} else {
		tmp = b * (t + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.9e+109:
		tmp = b * (y + -2.0)
	elif b <= 1.95e+90:
		tmp = z + (x + a)
	else:
		tmp = b * (t + -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.9e+109)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (b <= 1.95e+90)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = Float64(b * Float64(t + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.9e+109)
		tmp = b * (y + -2.0);
	elseif (b <= 1.95e+90)
		tmp = z + (x + a);
	else
		tmp = b * (t + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.9e+109], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e+90], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.9e109

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 93.3%

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

   6. Taylor expanded in b around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. +-lowering-+.f64 81.9

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

   8. Simplified 81.9%

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

   9. Taylor expanded in t around 0

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

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

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

       2. sub-neg N/A

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

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

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

       4. metadata-eval 50.4

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

   11. Simplified 50.4%

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

   if -2.9e109 < b < 1.9500000000000001e90

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 77.4

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

   5. Simplified 77.4%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 76.2%

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

   9. Taylor expanded in t around 0

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

       1. associate-+r+ N/A

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

       2. +-commutative N/A

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

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

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

       4. +-lowering-+.f64 47.4

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

   11. Simplified 47.4%

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

   if 1.9500000000000001e90 < b

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

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

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

      3. sub-neg N/A

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

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

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

      5. sub-neg N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

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

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 75.4

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

   5. Simplified 75.4%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 - t, z\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]

      2. sub-neg N/A

         \[\leadsto b \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)} \]

      3. metadata-eval N/A

         \[\leadsto b \cdot \left(t + \color{blue}{-2}\right) \]

      4. +-lowering-+.f64 60.8

         \[\leadsto b \cdot \color{blue}{\left(t + -2\right)} \]

   8. Simplified 60.8%

      \[\leadsto \color{blue}{b \cdot \left(t + -2\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+90}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+74}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t -2.0))))
   (if (<= b -6e+108) t_1 (if (<= b 4.6e+74) (+ z (+ x a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + -2.0);
	double tmp;
	if (b <= -6e+108) {
		tmp = t_1;
	} else if (b <= 4.6e+74) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t + (-2.0d0))
    if (b <= (-6d+108)) then
        tmp = t_1
    else if (b <= 4.6d+74) then
        tmp = z + (x + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + -2.0);
	double tmp;
	if (b <= -6e+108) {
		tmp = t_1;
	} else if (b <= 4.6e+74) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + -2.0)
	tmp = 0
	if b <= -6e+108:
		tmp = t_1
	elif b <= 4.6e+74:
		tmp = z + (x + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + -2.0))
	tmp = 0.0
	if (b <= -6e+108)
		tmp = t_1;
	elseif (b <= 4.6e+74)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + -2.0);
	tmp = 0.0;
	if (b <= -6e+108)
		tmp = t_1;
	elseif (b <= 4.6e+74)
		tmp = z + (x + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+108], t$95$1, If[LessEqual[b, 4.6e+74], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.99999999999999968e108 or 4.5999999999999997e74 < b

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)\right)} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(b, t - 2, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + \color{blue}{-2}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{neg}\left(\color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)}\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \color{blue}{z}\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), z\right)}\right) \]

      15. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, z\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), z\right)\right) \]

      17. distribute-lft-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, z\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, z\right)\right) \]

      19. +-commutative N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, z\right)\right) \]

      20. neg-mul-1 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, z\right)\right) \]

      21. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

      22. --lowering--.f64 69.7

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

   5. Simplified 69.7%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 - t, z\right)\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]

      2. sub-neg N/A

         \[\leadsto b \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)} \]

      3. metadata-eval N/A

         \[\leadsto b \cdot \left(t + \color{blue}{-2}\right) \]

      4. +-lowering-+.f64 54.6

         \[\leadsto b \cdot \color{blue}{\left(t + -2\right)} \]

   8. Simplified 54.6%

      \[\leadsto \color{blue}{b \cdot \left(t + -2\right)} \]

   if -5.99999999999999968e108 < b < 4.5999999999999997e74

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)\right)} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(b, t - 2, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + \color{blue}{-2}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{neg}\left(\color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)}\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \color{blue}{z}\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), z\right)}\right) \]

      15. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, z\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), z\right)\right) \]

      17. distribute-lft-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, z\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, z\right)\right) \]

      19. +-commutative N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, z\right)\right) \]

      20. neg-mul-1 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, z\right)\right) \]

      21. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

      22. --lowering--.f64 77.4

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 - t, z\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t}, \mathsf{fma}\left(a, 1 - t, z\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 76.2%

      \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t}, \mathsf{fma}\left(a, 1 - t, z\right)\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(x + z\right)} \]
   10. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \color{blue}{\left(a + x\right) + z} \]

       2. +-commutative N/A

          \[\leadsto \color{blue}{z + \left(a + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \color{blue}{z + \left(a + x\right)} \]

       4. +-lowering-+.f64 47.4

          \[\leadsto z + \color{blue}{\left(a + x\right)} \]

   11. Simplified 47.4%

       \[\leadsto \color{blue}{z + \left(a + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+74}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 20.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-308}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+134}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1e+62) x (if (<= x -6.2e-308) z (if (<= x 1.3e+134) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1e+62) {
		tmp = x;
	} else if (x <= -6.2e-308) {
		tmp = z;
	} else if (x <= 1.3e+134) {
		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 <= (-1d+62)) then
        tmp = x
    else if (x <= (-6.2d-308)) then
        tmp = z
    else if (x <= 1.3d+134) 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 <= -1e+62) {
		tmp = x;
	} else if (x <= -6.2e-308) {
		tmp = z;
	} else if (x <= 1.3e+134) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1e+62:
		tmp = x
	elif x <= -6.2e-308:
		tmp = z
	elif x <= 1.3e+134:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1e+62)
		tmp = x;
	elseif (x <= -6.2e-308)
		tmp = z;
	elseif (x <= 1.3e+134)
		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 <= -1e+62)
		tmp = x;
	elseif (x <= -6.2e-308)
		tmp = z;
	elseif (x <= 1.3e+134)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1e+62], x, If[LessEqual[x, -6.2e-308], z, If[LessEqual[x, 1.3e+134], a, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.00000000000000004e62 or 1.3000000000000001e134 < x

   1. Initial program 94.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 35.7%

      \[\leadsto \color{blue}{x} \]

   if -1.00000000000000004e62 < x < -6.19999999999999983e-308

   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 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. distribute-rgt-in N/A

         \[\leadsto \color{blue}{1 \cdot z + \left(-1 \cdot y\right) \cdot z} \]

      4. associate-*r* N/A

         \[\leadsto 1 \cdot z + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]

      5. *-lft-identity N/A

         \[\leadsto \color{blue}{z} + -1 \cdot \left(y \cdot z\right) \]

      6. mul-1-neg N/A

         \[\leadsto z + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)} \]

      7. unsub-neg N/A

         \[\leadsto \color{blue}{z - y \cdot z} \]

      8. --lowering--.f64 N/A

         \[\leadsto \color{blue}{z - y \cdot z} \]

      9. *-lowering-*.f64 37.9

         \[\leadsto z - \color{blue}{y \cdot z} \]

   5. Simplified 37.9%

      \[\leadsto \color{blue}{z - y \cdot z} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 20.1%

      \[\leadsto \color{blue}{z} \]

   if -6.19999999999999983e-308 < x < 1.3000000000000001e134

   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. distribute-rgt-in N/A

         \[\leadsto \color{blue}{1 \cdot a + \left(-1 \cdot t\right) \cdot a} \]

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{a} + \left(-1 \cdot t\right) \cdot a \]

      5. neg-mul-1 N/A

         \[\leadsto a + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot a \]

      6. distribute-lft-neg-in N/A

         \[\leadsto a + \color{blue}{\left(\mathsf{neg}\left(t \cdot a\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto a + \left(\mathsf{neg}\left(\color{blue}{a \cdot t}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      9. --lowering--.f64 N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      10. *-commutative N/A

          \[\leadsto a - \color{blue}{t \cdot a} \]

      11. *-lowering-*.f64 35.3

          \[\leadsto a - \color{blue}{t \cdot a} \]

   5. Simplified 35.3%

      \[\leadsto \color{blue}{a - t \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a} \]
   7. Step-by-step derivation

   8. Simplified 16.2%

      \[\leadsto \color{blue}{a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 46.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.66 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+32}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.66e+49) (fma t b x) (if (<= t 9e+32) (+ z (+ x a)) (fma t b x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.66e+49) {
		tmp = fma(t, b, x);
	} else if (t <= 9e+32) {
		tmp = z + (x + a);
	} else {
		tmp = fma(t, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.66e+49)
		tmp = fma(t, b, x);
	elseif (t <= 9e+32)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = fma(t, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.66e+49], N[(t * b + x), $MachinePrecision], If[LessEqual[t, 9e+32], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], N[(t * b + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65999999999999999e49 or 9.0000000000000007e32 < t

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]

   5. Simplified 78.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, b - a, \mathsf{fma}\left(b, y + -2, x\right) + a\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(t, b - a, \color{blue}{x}\right) \]
   7. Step-by-step derivation

   8. Simplified 82.6%

      \[\leadsto \mathsf{fma}\left(t, b - a, \color{blue}{x}\right) \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(t, \color{blue}{b}, x\right) \]
   10. Step-by-step derivation

   11. Simplified 52.2%

       \[\leadsto \mathsf{fma}\left(t, \color{blue}{b}, x\right) \]

   if -1.65999999999999999e49 < t < 9.0000000000000007e32

   1. Initial program 96.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)\right)} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(b, t - 2, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + \color{blue}{-2}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{neg}\left(\color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)}\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \color{blue}{z}\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), z\right)}\right) \]

      15. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, z\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), z\right)\right) \]

      17. distribute-lft-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, z\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, z\right)\right) \]

      19. +-commutative N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, z\right)\right) \]

      20. neg-mul-1 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, z\right)\right) \]

      21. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

      22. --lowering--.f64 65.6

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

   5. Simplified 65.6%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 - t, z\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t}, \mathsf{fma}\left(a, 1 - t, z\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 53.2%

      \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t}, \mathsf{fma}\left(a, 1 - t, z\right)\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(x + z\right)} \]
   10. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \color{blue}{\left(a + x\right) + z} \]

       2. +-commutative N/A

          \[\leadsto \color{blue}{z + \left(a + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \color{blue}{z + \left(a + x\right)} \]

       4. +-lowering-+.f64 46.6

          \[\leadsto z + \color{blue}{\left(a + x\right)} \]

   11. Simplified 46.6%

       \[\leadsto \color{blue}{z + \left(a + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.66 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+32}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 42.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.66 \cdot 10^{+49}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+99}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.66e+49) (* t b) (if (<= t 2.1e+99) (+ z (+ x a)) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.66e+49) {
		tmp = t * b;
	} else if (t <= 2.1e+99) {
		tmp = z + (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 <= (-1.66d+49)) then
        tmp = t * b
    else if (t <= 2.1d+99) then
        tmp = z + (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 <= -1.66e+49) {
		tmp = t * b;
	} else if (t <= 2.1e+99) {
		tmp = z + (x + a);
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.66e+49:
		tmp = t * b
	elif t <= 2.1e+99:
		tmp = z + (x + a)
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.66e+49)
		tmp = Float64(t * b);
	elseif (t <= 2.1e+99)
		tmp = Float64(z + 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 <= -1.66e+49)
		tmp = t * b;
	elseif (t <= 2.1e+99)
		tmp = z + (x + a);
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.66e+49], N[(t * b), $MachinePrecision], If[LessEqual[t, 2.1e+99], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65999999999999999e49 or 2.1000000000000001e99 < t

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

   5. Simplified 54.0%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 50.4

         \[\leadsto \color{blue}{b \cdot t} \]

   8. Simplified 50.4%

      \[\leadsto \color{blue}{b \cdot t} \]

   if -1.65999999999999999e49 < t < 2.1000000000000001e99

   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 y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)\right)} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(b, t - 2, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + \color{blue}{-2}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{neg}\left(\color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)}\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \color{blue}{z}\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), z\right)}\right) \]

      15. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, z\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), z\right)\right) \]

      17. distribute-lft-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, z\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, z\right)\right) \]

      19. +-commutative N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, z\right)\right) \]

      20. neg-mul-1 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, z\right)\right) \]

      21. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

      22. --lowering--.f64 66.9

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

   5. Simplified 66.9%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 - t, z\right)\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t}, \mathsf{fma}\left(a, 1 - t, z\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 55.6%

      \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t}, \mathsf{fma}\left(a, 1 - t, z\right)\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a + \left(x + z\right)} \]
   10. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \color{blue}{\left(a + x\right) + z} \]

       2. +-commutative N/A

          \[\leadsto \color{blue}{z + \left(a + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \color{blue}{z + \left(a + x\right)} \]

       4. +-lowering-+.f64 45.6

          \[\leadsto z + \color{blue}{\left(a + x\right)} \]

   11. Simplified 45.6%

       \[\leadsto \color{blue}{z + \left(a + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.66 \cdot 10^{+49}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+99}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+39}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+100}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.02e+39) (* t b) (if (<= t 1.55e+100) (+ x z) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.02e+39) {
		tmp = t * b;
	} else if (t <= 1.55e+100) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.02d+39)) then
        tmp = t * b
    else if (t <= 1.55d+100) then
        tmp = x + z
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.02e+39) {
		tmp = t * b;
	} else if (t <= 1.55e+100) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.02e+39:
		tmp = t * b
	elif t <= 1.55e+100:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.02e+39)
		tmp = Float64(t * b);
	elseif (t <= 1.55e+100)
		tmp = Float64(x + z);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.02e+39)
		tmp = t * b;
	elseif (t <= 1.55e+100)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.02e+39], N[(t * b), $MachinePrecision], If[LessEqual[t, 1.55e+100], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02e39 or 1.55000000000000003e100 < 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 x around inf

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

   5. Simplified 52.9%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{b \cdot t} \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 49.4

         \[\leadsto \color{blue}{b \cdot t} \]

   8. Simplified 49.4%

      \[\leadsto \color{blue}{b \cdot t} \]

   if -1.02e39 < t < 1.55000000000000003e100

   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 y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)\right)} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(b, t - 2, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + \color{blue}{-2}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{neg}\left(\color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)}\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \color{blue}{z}\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), z\right)}\right) \]

      15. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, z\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), z\right)\right) \]

      17. distribute-lft-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, z\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, z\right)\right) \]

      19. +-commutative N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, z\right)\right) \]

      20. neg-mul-1 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, z\right)\right) \]

      21. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

      22. --lowering--.f64 66.5

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

   5. Simplified 66.5%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 - t, z\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 32.6%

      \[\leadsto x + \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+39}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+100}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+92}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+173}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.8e+92) a (if (<= a 1.95e+173) (+ x z) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.8e+92) {
		tmp = a;
	} else if (a <= 1.95e+173) {
		tmp = x + z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.8d+92)) then
        tmp = a
    else if (a <= 1.95d+173) then
        tmp = x + z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.8e+92) {
		tmp = a;
	} else if (a <= 1.95e+173) {
		tmp = x + z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.8e+92:
		tmp = a
	elif a <= 1.95e+173:
		tmp = x + z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.8e+92)
		tmp = a;
	elseif (a <= 1.95e+173)
		tmp = Float64(x + z);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.8e+92)
		tmp = a;
	elseif (a <= 1.95e+173)
		tmp = x + z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.8e+92], a, If[LessEqual[a, 1.95e+173], N[(x + z), $MachinePrecision], a]]

Derivation

1. Split input into 2 regimes

2. if a < -2.80000000000000001e92 or 1.9499999999999999e173 < a

   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 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. distribute-rgt-in N/A

         \[\leadsto \color{blue}{1 \cdot a + \left(-1 \cdot t\right) \cdot a} \]

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{a} + \left(-1 \cdot t\right) \cdot a \]

      5. neg-mul-1 N/A

         \[\leadsto a + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot a \]

      6. distribute-lft-neg-in N/A

         \[\leadsto a + \color{blue}{\left(\mathsf{neg}\left(t \cdot a\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto a + \left(\mathsf{neg}\left(\color{blue}{a \cdot t}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      9. --lowering--.f64 N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      10. *-commutative N/A

          \[\leadsto a - \color{blue}{t \cdot a} \]

      11. *-lowering-*.f64 68.4

          \[\leadsto a - \color{blue}{t \cdot a} \]

   5. Simplified 68.4%

      \[\leadsto \color{blue}{a - t \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a} \]
   7. Step-by-step derivation

   8. Simplified 28.1%

      \[\leadsto \color{blue}{a} \]

   if -2.80000000000000001e92 < a < 1.9499999999999999e173

   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 y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)\right)} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(b, t - 2, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(b, \color{blue}{t + \left(\mathsf{neg}\left(2\right)\right)}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + \color{blue}{-2}, \mathsf{neg}\left(\left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{neg}\left(\color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)}\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(\mathsf{neg}\left(-1 \cdot z\right)\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, a \cdot \left(-1 \cdot \left(t - 1\right)\right) + \color{blue}{z}\right) \]

      14. accelerator-lowering-fma.f64 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), z\right)}\right) \]

      15. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, z\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), z\right)\right) \]

      17. distribute-lft-in N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, z\right)\right) \]

      18. metadata-eval N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, z\right)\right) \]

      19. +-commutative N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, z\right)\right) \]

      20. neg-mul-1 N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, z\right)\right) \]

      21. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

      22. --lowering--.f64 70.0

          \[\leadsto x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, \color{blue}{1 - t}, z\right)\right) \]

   5. Simplified 70.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(b, t + -2, \mathsf{fma}\left(a, 1 - t, z\right)\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 31.0%

      \[\leadsto x + \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 20.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+95}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+173}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.9e+95) a (if (<= a 1.95e+173) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.9e+95) {
		tmp = a;
	} else if (a <= 1.95e+173) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.9d+95)) then
        tmp = a
    else if (a <= 1.95d+173) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.9e+95) {
		tmp = a;
	} else if (a <= 1.95e+173) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.9e+95:
		tmp = a
	elif a <= 1.95e+173:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.9e+95)
		tmp = a;
	elseif (a <= 1.95e+173)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.9e+95)
		tmp = a;
	elseif (a <= 1.95e+173)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.9e+95], a, If[LessEqual[a, 1.95e+173], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e95 or 1.9499999999999999e173 < a

   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 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. distribute-rgt-in N/A

         \[\leadsto \color{blue}{1 \cdot a + \left(-1 \cdot t\right) \cdot a} \]

      4. *-lft-identity N/A

         \[\leadsto \color{blue}{a} + \left(-1 \cdot t\right) \cdot a \]

      5. neg-mul-1 N/A

         \[\leadsto a + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot a \]

      6. distribute-lft-neg-in N/A

         \[\leadsto a + \color{blue}{\left(\mathsf{neg}\left(t \cdot a\right)\right)} \]

      7. *-commutative N/A

         \[\leadsto a + \left(\mathsf{neg}\left(\color{blue}{a \cdot t}\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      9. --lowering--.f64 N/A

         \[\leadsto \color{blue}{a - a \cdot t} \]

      10. *-commutative N/A

          \[\leadsto a - \color{blue}{t \cdot a} \]

      11. *-lowering-*.f64 68.4

          \[\leadsto a - \color{blue}{t \cdot a} \]

   5. Simplified 68.4%

      \[\leadsto \color{blue}{a - t \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a} \]
   7. Step-by-step derivation

   8. Simplified 28.1%

      \[\leadsto \color{blue}{a} \]

   if -1.9e95 < a < 1.9499999999999999e173

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 18.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 11.1% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 95.3%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. 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. distribute-rgt-in N/A

      \[\leadsto \color{blue}{1 \cdot a + \left(-1 \cdot t\right) \cdot a} \]

   4. *-lft-identity N/A

      \[\leadsto \color{blue}{a} + \left(-1 \cdot t\right) \cdot a \]

   5. neg-mul-1 N/A

      \[\leadsto a + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)} \cdot a \]

   6. distribute-lft-neg-in N/A

      \[\leadsto a + \color{blue}{\left(\mathsf{neg}\left(t \cdot a\right)\right)} \]

   7. *-commutative N/A

      \[\leadsto a + \left(\mathsf{neg}\left(\color{blue}{a \cdot t}\right)\right) \]

   8. unsub-neg N/A

      \[\leadsto \color{blue}{a - a \cdot t} \]

   9. --lowering--.f64 N/A

      \[\leadsto \color{blue}{a - a \cdot t} \]

   10. *-commutative N/A

       \[\leadsto a - \color{blue}{t \cdot a} \]

   11. *-lowering-*.f64 27.9

       \[\leadsto a - \color{blue}{t \cdot a} \]

5. Simplified 27.9%

   \[\leadsto \color{blue}{a - t \cdot a} \]

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a} \]
7. Step-by-step derivation

8. Simplified 10.8%

   \[\leadsto \color{blue}{a} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024199 
(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)))