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

Percentage Accurate: 95.3% → 97.8%

Time: 12.1s

Alternatives: 17

Speedup: 0.5×

• 35.3% 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: 95.3% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.5

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

   5. Applied rewrites 71.5%

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

4. Final simplification 99.2%

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

Alternative 2: 45.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 10^{+302}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* b (- (+ t y) 2.0)) (- (- x (* z (- y 1.0))) (* a (- t 1.0))))))
   (if (<= t_1 (- INFINITY))
     (* (- a) t)
     (if (<= t_1 1e+302) (+ (+ a x) z) (* (- 1.0 t) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -a * t;
	} else if (t_1 <= 1e+302) {
		tmp = (a + x) + z;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -a * t;
	} else if (t_1 <= 1e+302) {
		tmp = (a + x) + z;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -a * t
	elif t_1 <= 1e+302:
		tmp = (a + x) + z
	else:
		tmp = (1.0 - t) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(t + y) - 2.0)) + Float64(Float64(x - Float64(z * Float64(y - 1.0))) - Float64(a * Float64(t - 1.0))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(-a) * t);
	elseif (t_1 <= 1e+302)
		tmp = Float64(Float64(a + x) + z);
	else
		tmp = Float64(Float64(1.0 - t) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -a * t;
	elseif (t_1 <= 1e+302)
		tmp = (a + x) + z;
	else
		tmp = (1.0 - t) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[((-a) * t), $MachinePrecision], If[LessEqual[t$95$1, 1e+302], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.4

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

   5. Applied rewrites 69.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 49.5%

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

   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)) < 1.0000000000000001e302

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 60.0%

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

   if 1.0000000000000001e302 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 87.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 32.6

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

   5. Applied rewrites 32.6%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq -\infty:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq 10^{+302}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 44.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ t_2 := \left(-a\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+302}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* b (- (+ t y) 2.0)) (- (- x (* z (- y 1.0))) (* a (- t 1.0)))))
        (t_2 (* (- a) t)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 1e+302) (+ (+ a x) z) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double t_2 = -a * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+302) {
		tmp = (a + x) + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double t_2 = -a * t;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 1e+302) {
		tmp = (a + x) + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)))
	t_2 = -a * t
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 1e+302:
		tmp = (a + x) + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(t + y) - 2.0)) + Float64(Float64(x - Float64(z * Float64(y - 1.0))) - Float64(a * Float64(t - 1.0))))
	t_2 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+302)
		tmp = Float64(Float64(a + x) + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	t_2 = -a * t;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 1e+302)
		tmp = (a + x) + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+302], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -inf.0 or 1.0000000000000001e302 < (+.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 91.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 60.2

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 37.6%

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

   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)) < 1.0000000000000001e302

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 60.0%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq -\infty:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq 10^{+302}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 43.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t\_1 \leq 10^{+305}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* b (- (+ t y) 2.0)) (- (- x (* z (- y 1.0))) (* a (- t 1.0))))))
   (if (<= t_1 (- INFINITY))
     (* b t)
     (if (<= t_1 1e+305) (+ (+ a x) z) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = b * t;
	} else if (t_1 <= 1e+305) {
		tmp = (a + x) + z;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = b * t;
	} else if (t_1 <= 1e+305) {
		tmp = (a + x) + z;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = b * t
	elif t_1 <= 1e+305:
		tmp = (a + x) + z
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(t + y) - 2.0)) + Float64(Float64(x - Float64(z * Float64(y - 1.0))) - Float64(a * Float64(t - 1.0))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(b * t);
	elseif (t_1 <= 1e+305)
		tmp = Float64(Float64(a + x) + z);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = b * t;
	elseif (t_1 <= 1e+305)
		tmp = (a + x) + z;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(b * t), $MachinePrecision], If[LessEqual[t$95$1, 1e+305], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], N[(b * t), $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 or 9.9999999999999994e304 < (+.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 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 45.7

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

   5. Applied rewrites 45.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 28.9%

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

   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)) < 9.9999999999999994e304

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 84.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 69.2%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 59.3%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq -\infty:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq 10^{+305}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, x\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-246}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a x)) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -7.5e+40)
     t_2
     (if (<= b -4.5e-185)
       t_1
       (if (<= b -1.2e-246)
         (fma (- 1.0 y) z x)
         (if (<= b 3.1e+84) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, x);
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -7.5e+40) {
		tmp = t_2;
	} else if (b <= -4.5e-185) {
		tmp = t_1;
	} else if (b <= -1.2e-246) {
		tmp = fma((1.0 - y), z, x);
	} else if (b <= 3.1e+84) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, x)
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -7.5e+40)
		tmp = t_2;
	elseif (b <= -4.5e-185)
		tmp = t_1;
	elseif (b <= -1.2e-246)
		tmp = fma(Float64(1.0 - y), z, x);
	elseif (b <= 3.1e+84)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+40], t$95$2, If[LessEqual[b, -4.5e-185], t$95$1, If[LessEqual[b, -1.2e-246], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[b, 3.1e+84], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.4999999999999996e40 or 3.10000000000000003e84 < b

   1. Initial program 94.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 70.3

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

   5. Applied rewrites 70.3%

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

   if -7.4999999999999996e40 < b < -4.5000000000000001e-185 or -1.1999999999999999e-246 < b < 3.10000000000000003e84

   1. Initial program 99.3%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 84.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 79.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 64.3%

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

   if -4.5000000000000001e-185 < b < -1.1999999999999999e-246

   1. Initial program 95.2%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

   5. Applied rewrites 95.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 81.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-185}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-246}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -225000:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a + x\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.05e+32)
     t_1
     (if (<= t -225000.0)
       (* (- 1.0 y) z)
       (if (<= t 3.2e-78)
         (fma (- y 2.0) b (+ a x))
         (if (<= t 4.2e+115) (fma (- 1.0 y) z x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.05e+32) {
		tmp = t_1;
	} else if (t <= -225000.0) {
		tmp = (1.0 - y) * z;
	} else if (t <= 3.2e-78) {
		tmp = fma((y - 2.0), b, (a + x));
	} else if (t <= 4.2e+115) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.05e+32)
		tmp = t_1;
	elseif (t <= -225000.0)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= 3.2e-78)
		tmp = fma(Float64(y - 2.0), b, Float64(a + x));
	elseif (t <= 4.2e+115)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.05e+32], t$95$1, If[LessEqual[t, -225000.0], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 3.2e-78], N[(N[(y - 2.0), $MachinePrecision] * b + N[(a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+115], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05e32 or 4.20000000000000007e115 < t

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if -1.05e32 < t < -225000

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 86.3

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

   5. Applied rewrites 86.3%

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

   if -225000 < t < 3.2e-78

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

      21. +-commutative N/A

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

   5. Applied rewrites 98.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 73.6%

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

   if 3.2e-78 < t < 4.20000000000000007e115

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

   5. Applied rewrites 76.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.7%

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

Alternative 7: 86.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (+ (fma (- y 2.0) b x) a))))
   (if (<= y -3.1e+120)
     t_1
     (if (<= y 7.5e+72) (fma (- t 2.0) b (+ (fma (- 1.0 t) a x) z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, (fma((y - 2.0), b, x) + a));
	double tmp;
	if (y <= -3.1e+120) {
		tmp = t_1;
	} else if (y <= 7.5e+72) {
		tmp = fma((t - 2.0), b, (fma((1.0 - t), a, x) + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, Float64(fma(Float64(y - 2.0), b, x) + a))
	tmp = 0.0
	if (y <= -3.1e+120)
		tmp = t_1;
	elseif (y <= 7.5e+72)
		tmp = fma(Float64(t - 2.0), b, Float64(fma(Float64(1.0 - t), a, x) + z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+120], t$95$1, If[LessEqual[y, 7.5e+72], N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.09999999999999974e120 or 7.50000000000000027e72 < y

   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 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

      21. +-commutative N/A

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

   5. Applied rewrites 85.5%

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

   if -3.09999999999999974e120 < y < 7.50000000000000027e72

   1. Initial program 99.4%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 95.7%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-a\right) \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.4e+27)
   (fma (- 1.0 y) z (fma (- 1.0 t) a x))
   (if (<= t 7.2e+114)
     (fma (- 1.0 y) z (+ (fma (- y 2.0) b x) a))
     (fma t b (* (- a) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.4e+27) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else if (t <= 7.2e+114) {
		tmp = fma((1.0 - y), z, (fma((y - 2.0), b, x) + a));
	} else {
		tmp = fma(t, b, (-a * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.4e+27)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	elseif (t <= 7.2e+114)
		tmp = fma(Float64(1.0 - y), z, Float64(fma(Float64(y - 2.0), b, x) + a));
	else
		tmp = fma(t, b, Float64(Float64(-a) * t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.4e+27], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+114], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(t * b + N[((-a) * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4e27

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

   5. Applied rewrites 78.1%

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

   if -3.4e27 < t < 7.2000000000000001e114

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. metadata-eval N/A

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

      15. +-commutative N/A

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

      16. distribute-neg-in N/A

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

      17. metadata-eval N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

      21. +-commutative N/A

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

   5. Applied rewrites 93.3%

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

   if 7.2000000000000001e114 < t

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.7

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

   5. Applied rewrites 73.7%

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

   7. Applied rewrites 73.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-a\right) \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+126}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -1.5e+170)
     t_1
     (if (<= b 1.25e+126) (fma (- 1.0 y) z (fma (- 1.0 t) a 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 <= -1.5e+170) {
		tmp = t_1;
	} else if (b <= 1.25e+126) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -1.5e+170)
		tmp = t_1;
	elseif (b <= 1.25e+126)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.5e+170], t$95$1, If[LessEqual[b, 1.25e+126], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.49999999999999998e170 or 1.24999999999999994e126 < b

   1. Initial program 94.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 83.2

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

   5. Applied rewrites 83.2%

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

   if -1.49999999999999998e170 < b < 1.24999999999999994e126

   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. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

   5. Applied rewrites 85.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+170}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+126}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-138}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-77}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.2e+79)
   (* b t)
   (if (<= t -1.6e-138)
     (+ a z)
     (if (<= t 2.7e-77) (+ a x) (if (<= t 3.4e+101) (+ z x) (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.2e+79) {
		tmp = b * t;
	} else if (t <= -1.6e-138) {
		tmp = a + z;
	} else if (t <= 2.7e-77) {
		tmp = a + x;
	} else if (t <= 3.4e+101) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.2d+79)) then
        tmp = b * t
    else if (t <= (-1.6d-138)) then
        tmp = a + z
    else if (t <= 2.7d-77) then
        tmp = a + x
    else if (t <= 3.4d+101) then
        tmp = z + x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.2e+79) {
		tmp = b * t;
	} else if (t <= -1.6e-138) {
		tmp = a + z;
	} else if (t <= 2.7e-77) {
		tmp = a + x;
	} else if (t <= 3.4e+101) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.2e+79:
		tmp = b * t
	elif t <= -1.6e-138:
		tmp = a + z
	elif t <= 2.7e-77:
		tmp = a + x
	elif t <= 3.4e+101:
		tmp = z + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.2e+79)
		tmp = Float64(b * t);
	elseif (t <= -1.6e-138)
		tmp = Float64(a + z);
	elseif (t <= 2.7e-77)
		tmp = Float64(a + x);
	elseif (t <= 3.4e+101)
		tmp = Float64(z + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.2e+79)
		tmp = b * t;
	elseif (t <= -1.6e-138)
		tmp = a + z;
	elseif (t <= 2.7e-77)
		tmp = a + x;
	elseif (t <= 3.4e+101)
		tmp = z + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.2e+79], N[(b * t), $MachinePrecision], If[LessEqual[t, -1.6e-138], N[(a + z), $MachinePrecision], If[LessEqual[t, 2.7e-77], N[(a + x), $MachinePrecision], If[LessEqual[t, 3.4e+101], N[(z + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.20000000000000029e79 or 3.40000000000000017e101 < t

   1. Initial program 95.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 35.1

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

   5. Applied rewrites 35.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 35.1%

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

   if -5.20000000000000029e79 < t < -1.60000000000000005e-138

   1. Initial program 97.4%

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

   3. 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 69.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 62.5%

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

   12. Taylor expanded in x around 0

       \[\leadsto a + z \]
   13. Step-by-step derivation

   14. Applied rewrites 57.1%

       \[\leadsto z + a \]

   if -1.60000000000000005e-138 < t < 2.7e-77

   1. Initial program 97.7%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 67.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 56.2%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 56.2%

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

   12. Taylor expanded in z around 0

       \[\leadsto a + x \]
   13. Step-by-step derivation

   14. Applied rewrites 43.1%

       \[\leadsto a + x \]

   if 2.7e-77 < t < 3.40000000000000017e101

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 72.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 61.7%

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

   9. Taylor expanded in a around 0

      \[\leadsto x + z \]
   10. Step-by-step derivation

   11. Applied rewrites 49.0%

       \[\leadsto z + x \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-138}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-77}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-201}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2e+33)
     t_1
     (if (<= t 6e-201)
       (+ (+ a x) z)
       (if (<= t 4.2e+115) (fma (- 1.0 y) z x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -2e+33) {
		tmp = t_1;
	} else if (t <= 6e-201) {
		tmp = (a + x) + z;
	} else if (t <= 4.2e+115) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -2e+33)
		tmp = t_1;
	elseif (t <= 6e-201)
		tmp = Float64(Float64(a + x) + z);
	elseif (t <= 4.2e+115)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2e+33], t$95$1, If[LessEqual[t, 6e-201], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t, 4.2e+115], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9999999999999999e33 or 4.20000000000000007e115 < t

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.4

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

   5. Applied rewrites 74.4%

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

   if -1.9999999999999999e33 < t < 6.00000000000000004e-201

   1. Initial program 96.8%

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

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 75.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 64.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 63.8%

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

   if 6.00000000000000004e-201 < t < 4.20000000000000007e115

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

   5. Applied rewrites 69.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 56.2%

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

Alternative 12: 70.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -4.4e+94) t_1 (if (<= b 5.6e+88) (fma (- 1.0 t) a (+ z x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -4.4e+94) {
		tmp = t_1;
	} else if (b <= 5.6e+88) {
		tmp = fma((1.0 - t), a, (z + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -4.4e+94)
		tmp = t_1;
	elseif (b <= 5.6e+88)
		tmp = fma(Float64(1.0 - t), a, Float64(z + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e+94], t$95$1, If[LessEqual[b, 5.6e+88], N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.40000000000000024e94 or 5.59999999999999977e88 < b

   1. Initial program 94.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 74.1

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

   5. Applied rewrites 74.1%

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

   if -4.40000000000000024e94 < b < 5.59999999999999977e88

   1. Initial program 98.3%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 74.4%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+94}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+53}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2e+33) t_1 (if (<= t 1.6e+53) (+ (+ a x) z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -2e+33) {
		tmp = t_1;
	} else if (t <= 1.6e+53) {
		tmp = (a + x) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-2d+33)) then
        tmp = t_1
    else if (t <= 1.6d+53) then
        tmp = (a + x) + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -2e+33) {
		tmp = t_1;
	} else if (t <= 1.6e+53) {
		tmp = (a + x) + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -2e+33:
		tmp = t_1
	elif t <= 1.6e+53:
		tmp = (a + x) + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -2e+33)
		tmp = t_1;
	elseif (t <= 1.6e+53)
		tmp = Float64(Float64(a + x) + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -2e+33)
		tmp = t_1;
	elseif (t <= 1.6e+53)
		tmp = (a + x) + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2e+33], t$95$1, If[LessEqual[t, 1.6e+53], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999999e33 or 1.6e53 < t

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.2

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

   5. Applied rewrites 69.2%

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

   if -1.9999999999999999e33 < t < 1.6e53

   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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 70.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 58.8%

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

Alternative 14: 43.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+38}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+81}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.5e+38) (* (- y) z) (if (<= y 2.5e+81) (+ (+ a x) z) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.5e+38) {
		tmp = -y * z;
	} else if (y <= 2.5e+81) {
		tmp = (a + x) + z;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.5d+38)) then
        tmp = -y * z
    else if (y <= 2.5d+81) then
        tmp = (a + x) + z
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.5e+38) {
		tmp = -y * z;
	} else if (y <= 2.5e+81) {
		tmp = (a + x) + z;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.5e+38:
		tmp = -y * z
	elif y <= 2.5e+81:
		tmp = (a + x) + z
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.5e+38)
		tmp = Float64(Float64(-y) * z);
	elseif (y <= 2.5e+81)
		tmp = Float64(Float64(a + x) + z);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.5e+38)
		tmp = -y * z;
	elseif (y <= 2.5e+81)
		tmp = (a + x) + z;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.5e+38], N[((-y) * z), $MachinePrecision], If[LessEqual[y, 2.5e+81], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e38

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. metadata-eval N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 50.1

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

   5. Applied rewrites 50.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 50.1%

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

   if -6.5e38 < y < 2.4999999999999999e81

   1. Initial program 99.4%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 96.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 74.2%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 54.1%

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

   if 2.4999999999999999e81 < y

   1. Initial program 92.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 48.7

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

   5. Applied rewrites 48.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 43.7%

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

Alternative 15: 31.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+150}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+78}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -5.7e+150) (+ a z) (if (<= a 7.5e+78) (+ z x) (+ a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -5.7e+150) {
		tmp = a + z;
	} else if (a <= 7.5e+78) {
		tmp = z + x;
	} else {
		tmp = a + 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 (a <= (-5.7d+150)) then
        tmp = a + z
    else if (a <= 7.5d+78) then
        tmp = z + x
    else
        tmp = a + 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 (a <= -5.7e+150) {
		tmp = a + z;
	} else if (a <= 7.5e+78) {
		tmp = z + x;
	} else {
		tmp = a + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -5.7e+150:
		tmp = a + z
	elif a <= 7.5e+78:
		tmp = z + x
	else:
		tmp = a + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -5.7e+150)
		tmp = Float64(a + z);
	elseif (a <= 7.5e+78)
		tmp = Float64(z + x);
	else
		tmp = Float64(a + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -5.7e+150)
		tmp = a + z;
	elseif (a <= 7.5e+78)
		tmp = z + x;
	else
		tmp = a + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -5.7e+150], N[(a + z), $MachinePrecision], If[LessEqual[a, 7.5e+78], N[(z + x), $MachinePrecision], N[(a + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.7000000000000002e150

   1. Initial program 93.8%

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

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 88.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 85.0%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 49.2%

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

   12. Taylor expanded in x around 0

       \[\leadsto a + z \]
   13. Step-by-step derivation

   14. Applied rewrites 48.6%

       \[\leadsto z + a \]

   if -5.7000000000000002e150 < a < 7.49999999999999934e78

   1. Initial program 98.3%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 49.4%

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

   9. Taylor expanded in a around 0

      \[\leadsto x + z \]
   10. Step-by-step derivation

   11. Applied rewrites 37.3%

       \[\leadsto z + x \]

   if 7.49999999999999934e78 < a

   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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 81.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 77.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 46.7%

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

   12. Taylor expanded in z around 0

       \[\leadsto a + x \]
   13. Step-by-step derivation

   14. Applied rewrites 44.6%

       \[\leadsto a + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+150}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+78}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a + x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+185}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+88}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.8e+185) (+ a z) (if (<= z 2.7e+88) (+ a x) (+ a z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.8e+185) {
		tmp = a + z;
	} else if (z <= 2.7e+88) {
		tmp = a + x;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.8d+185)) then
        tmp = a + z
    else if (z <= 2.7d+88) then
        tmp = a + x
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.8e+185) {
		tmp = a + z;
	} else if (z <= 2.7e+88) {
		tmp = a + x;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.8e+185:
		tmp = a + z
	elif z <= 2.7e+88:
		tmp = a + x
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.8e+185)
		tmp = Float64(a + z);
	elseif (z <= 2.7e+88)
		tmp = Float64(a + x);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.8e+185)
		tmp = a + z;
	elseif (z <= 2.7e+88)
		tmp = a + x;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.8e+185], N[(a + z), $MachinePrecision], If[LessEqual[z, 2.7e+88], N[(a + x), $MachinePrecision], N[(a + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999998e185 or 2.70000000000000016e88 < z

   1. Initial program 94.9%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 60.3%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 50.5%

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

   12. Taylor expanded in x around 0

       \[\leadsto a + z \]
   13. Step-by-step derivation

   14. Applied rewrites 43.3%

       \[\leadsto z + a \]

   if -3.7999999999999998e185 < z < 2.70000000000000016e88

   1. Initial program 98.3%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. sub-neg N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower-+.f64 N/A

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

   5. Applied rewrites 78.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 58.4%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 37.9%

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

   12. Taylor expanded in z around 0

       \[\leadsto a + x \]
   13. Step-by-step derivation

   14. Applied rewrites 36.1%

       \[\leadsto a + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+185}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+88}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.3% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ a + x \end{array} \]

FPCore

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

C

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

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 + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + x), $MachinePrecision]

Derivation

1. Initial program 97.3%

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

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

   2. associate--l+ N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. lower--.f64 N/A

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

   6. +-commutative N/A

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

   7. associate--r+ N/A

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

   8. sub-neg N/A

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

   9. mul-1-neg N/A

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

   10. remove-double-neg N/A

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

   11. lower-+.f64 N/A

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

5. Applied rewrites 76.7%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 59.0%

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

9. Taylor expanded in t around 0

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

11. Applied rewrites 41.7%

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

12. Taylor expanded in z around 0

    \[\leadsto a + x \]
13. Step-by-step derivation

14. Applied rewrites 29.2%

    \[\leadsto a + x \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024249 
(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)))