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

Percentage Accurate: 94.8% → 97.4%

Time: 11.7s

Alternatives: 25

Speedup: 0.5×

• 36.4% 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: 94.8% 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: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* (- (+ t y) 2.0) b) (- (- x (* z (- y 1.0))) (* a (- t 1.0))))))
   (if (<= t_1 2e+304)
     t_1
     (fma (- b a) t (fma (- y 2.0) b (fma (- 1.0 y) z a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= 2e+304) {
		tmp = t_1;
	} else {
		tmp = fma((b - a), t, fma((y - 2.0), b, fma((1.0 - y), z, a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(t + y) - 2.0) * b) + Float64(Float64(x - Float64(z * Float64(y - 1.0))) - Float64(a * Float64(t - 1.0))))
	tmp = 0.0
	if (t_1 <= 2e+304)
		tmp = t_1;
	else
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, fma(Float64(1.0 - y), z, a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $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, 2e+304], t$95$1, N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + N[(N[(1.0 - y), $MachinePrecision] * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 1.9999999999999999e304

   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 1.9999999999999999e304 < (+.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 73.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.2%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 34.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* (- (+ t y) 2.0) b) (- (- x (* z (- y 1.0))) (* a (- t 1.0))))))
   (if (<= t_1 (- INFINITY))
     (* (- a) t)
     (if (<= t_1 2e+304) (+ z x) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -a * t;
	} else if (t_1 <= 2e+304) {
		tmp = z + x;
	} 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 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -a * t;
	} else if (t_1 <= 2e+304) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -a * t
	elif t_1 <= 2e+304:
		tmp = z + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(t + y) - 2.0) * b) + 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 <= 2e+304)
		tmp = Float64(z + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -a * t;
	elseif (t_1 <= 2e+304)
		tmp = z + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $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, 2e+304], N[(z + x), $MachinePrecision], N[(b * t), $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 50.1

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

   5. Applied rewrites 50.1%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 39.8%

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

   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)) < 1.9999999999999999e304

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 74.5

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 45.6%

       \[\leadsto z + x \]

   if 1.9999999999999999e304 < (+.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 73.1%

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

   3. Taylor expanded in t around inf

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

      1. *-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 54.4

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

   5. Applied rewrites 54.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 39.3%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq -\infty:\\ \;\;\;\;\left(-a\right) \cdot t\\ \mathbf{elif}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 34.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* (- (+ t y) 2.0) b) (- (- x (* z (- y 1.0))) (* a (- t 1.0))))))
   (if (<= t_1 (- INFINITY)) (* b y) (if (<= t_1 2e+304) (+ z x) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = b * y;
	} else if (t_1 <= 2e+304) {
		tmp = z + x;
	} 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 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = b * y;
	} else if (t_1 <= 2e+304) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = b * y
	elif t_1 <= 2e+304:
		tmp = z + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(t + y) - 2.0) * b) + 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 * y);
	elseif (t_1 <= 2e+304)
		tmp = Float64(z + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = b * y;
	elseif (t_1 <= 2e+304)
		tmp = z + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $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 * y), $MachinePrecision], If[LessEqual[t$95$1, 2e+304], N[(z + x), $MachinePrecision], N[(b * t), $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 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 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 29.5%

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

   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)) < 1.9999999999999999e304

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 74.5

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 45.6%

       \[\leadsto z + x \]

   if 1.9999999999999999e304 < (+.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 73.1%

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

   3. Taylor expanded in t around inf

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

      1. *-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 54.4

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

   5. Applied rewrites 54.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 39.3%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq -\infty:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 34.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* (- (+ t y) 2.0) b) (- (- x (* z (- y 1.0))) (* a (- t 1.0))))))
   (if (<= t_1 (- INFINITY)) (* b t) (if (<= t_1 2e+304) (+ z x) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = b * t;
	} else if (t_1 <= 2e+304) {
		tmp = z + x;
	} 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 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = b * t;
	} else if (t_1 <= 2e+304) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = b * t
	elif t_1 <= 2e+304:
		tmp = z + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(t + y) - 2.0) * b) + 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 <= 2e+304)
		tmp = Float64(z + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((t + y) - 2.0) * b) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = b * t;
	elseif (t_1 <= 2e+304)
		tmp = z + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $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, 2e+304], N[(z + x), $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 1.9999999999999999e304 < (+.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 84.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 52.6

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

   5. Applied rewrites 52.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 29.8%

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

   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)) < 1.9999999999999999e304

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 74.5

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

   5. Applied rewrites 74.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 45.6%

       \[\leadsto z + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq -\infty:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, x\right)\\ t_2 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-277}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a x)) (t_2 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.5e+112)
     t_2
     (if (<= b -2.5e-71)
       t_1
       (if (<= b 1.35e-277)
         (fma (- 1.0 y) z x)
         (if (<= b 1.15e+52) 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 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.5e+112) {
		tmp = t_2;
	} else if (b <= -2.5e-71) {
		tmp = t_1;
	} else if (b <= 1.35e-277) {
		tmp = fma((1.0 - y), z, x);
	} else if (b <= 1.15e+52) {
		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(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.5e+112)
		tmp = t_2;
	elseif (b <= -2.5e-71)
		tmp = t_1;
	elseif (b <= 1.35e-277)
		tmp = fma(Float64(1.0 - y), z, x);
	elseif (b <= 1.15e+52)
		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[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.5e+112], t$95$2, If[LessEqual[b, -2.5e-71], t$95$1, If[LessEqual[b, 1.35e-277], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[b, 1.15e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4999999999999999e112 or 1.15e52 < b

   1. Initial program 86.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in b around inf

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

      1. *-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. lower-+.f64 73.2

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

   8. Applied rewrites 73.2%

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

   if -1.4999999999999999e112 < b < -2.49999999999999999e-71 or 1.34999999999999988e-277 < b < 1.15e52

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 81.2

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

   8. Applied rewrites 81.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 64.7%

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

   if -2.49999999999999999e-71 < b < 1.34999999999999988e-277

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 77.2%

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

Alternative 6: 89.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.8e+62)
   (fma (- b a) t (fma (- y 2.0) b (fma (- 1.0 y) z a)))
   (if (<= y 3.9e-7)
     (fma (- 1.0 t) a (+ (fma (- t 2.0) b x) z))
     (fma (- 1.0 y) z (fma (- (+ t y) 2.0) b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.8e+62) {
		tmp = fma((b - a), t, fma((y - 2.0), b, fma((1.0 - y), z, a)));
	} else if (y <= 3.9e-7) {
		tmp = fma((1.0 - t), a, (fma((t - 2.0), b, x) + z));
	} else {
		tmp = fma((1.0 - y), z, fma(((t + y) - 2.0), b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.8e+62)
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, fma(Float64(1.0 - y), z, a)));
	elseif (y <= 3.9e-7)
		tmp = fma(Float64(1.0 - t), a, Float64(fma(Float64(t - 2.0), b, x) + z));
	else
		tmp = fma(Float64(1.0 - y), z, fma(Float64(Float64(t + y) - 2.0), b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.8e+62], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + N[(N[(1.0 - y), $MachinePrecision] * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-7], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999968e62

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.8%

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

   if -5.79999999999999968e62 < y < 3.90000000000000025e-7

   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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. metadata-eval N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 98.8%

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

   if 3.90000000000000025e-7 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 87.8

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

   5. Applied rewrites 87.8%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (fma (- (+ t y) 2.0) b x))))
   (if (<= y -1.65e+63)
     t_1
     (if (<= y 3.9e-7) (fma (- 1.0 t) a (+ (fma (- t 2.0) b 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(((t + y) - 2.0), b, x));
	double tmp;
	if (y <= -1.65e+63) {
		tmp = t_1;
	} else if (y <= 3.9e-7) {
		tmp = fma((1.0 - t), a, (fma((t - 2.0), b, 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, fma(Float64(Float64(t + y) - 2.0), b, x))
	tmp = 0.0
	if (y <= -1.65e+63)
		tmp = t_1;
	elseif (y <= 3.9e-7)
		tmp = fma(Float64(1.0 - t), a, Float64(fma(Float64(t - 2.0), b, 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[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+63], t$95$1, If[LessEqual[y, 3.9e-7], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6500000000000001e63 or 3.90000000000000025e-7 < y

   1. Initial program 89.9%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if -1.6500000000000001e63 < y < 3.90000000000000025e-7

   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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. metadata-eval N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 98.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+126}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (fma a (- t 1.0) (* z (- y 1.0))))))
   (if (<= z -1.4e+56)
     t_1
     (if (<= z 4.1e+126) (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	double tmp;
	if (z <= -1.4e+56) {
		tmp = t_1;
	} else if (z <= 4.1e+126) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))))
	tmp = 0.0
	if (z <= -1.4e+56)
		tmp = t_1;
	elseif (z <= 4.1e+126)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+56], t$95$1, If[LessEqual[z, 4.1e+126], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000004e56 or 4.1000000000000001e126 < z

   1. Initial program 89.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 91.8%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 86.9

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

   8. Applied rewrites 86.9%

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

   if -1.40000000000000004e56 < z < 4.1000000000000001e126

   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 x around 0

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

   5. Applied rewrites 75.1%

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

   6. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 95.2

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

   8. Applied rewrites 95.2%

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

Alternative 9: 83.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -1.7e+64)
     t_1
     (if (<= y 1.2e+114) (fma (- 1.0 t) a (+ (fma (- t 2.0) b x) z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -1.7e+64) {
		tmp = t_1;
	} else if (y <= 1.2e+114) {
		tmp = fma((1.0 - t), a, (fma((t - 2.0), b, x) + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -1.7e+64)
		tmp = t_1;
	elseif (y <= 1.2e+114)
		tmp = fma(Float64(1.0 - t), a, Float64(fma(Float64(t - 2.0), b, x) + z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.7e+64], t$95$1, If[LessEqual[y, 1.2e+114], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e64 or 1.2e114 < y

   1. Initial program 88.5%

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

   3. Taylor expanded in y around 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 78.2

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

   5. Applied rewrites 78.2%

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

   if -1.7000000000000001e64 < y < 1.2e114

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

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

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. metadata-eval N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 94.0%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+64}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-135}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 0.0021:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)) (t_2 (* (- b z) y)))
   (if (<= y -5.8e+62)
     t_2
     (if (<= y -1.02e-79)
       t_1
       (if (<= y 1.95e-135) (+ z x) (if (<= y 0.0021) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double t_2 = (b - z) * y;
	double tmp;
	if (y <= -5.8e+62) {
		tmp = t_2;
	} else if (y <= -1.02e-79) {
		tmp = t_1;
	} else if (y <= 1.95e-135) {
		tmp = z + x;
	} else if (y <= 0.0021) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (b - a) * t
    t_2 = (b - z) * y
    if (y <= (-5.8d+62)) then
        tmp = t_2
    else if (y <= (-1.02d-79)) then
        tmp = t_1
    else if (y <= 1.95d-135) then
        tmp = z + x
    else if (y <= 0.0021d0) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = (b - z) * y;
	double tmp;
	if (y <= -5.8e+62) {
		tmp = t_2;
	} else if (y <= -1.02e-79) {
		tmp = t_1;
	} else if (y <= 1.95e-135) {
		tmp = z + x;
	} else if (y <= 0.0021) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	t_2 = (b - z) * y
	tmp = 0
	if y <= -5.8e+62:
		tmp = t_2
	elif y <= -1.02e-79:
		tmp = t_1
	elif y <= 1.95e-135:
		tmp = z + x
	elif y <= 0.0021:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	t_2 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -5.8e+62)
		tmp = t_2;
	elseif (y <= -1.02e-79)
		tmp = t_1;
	elseif (y <= 1.95e-135)
		tmp = Float64(z + x);
	elseif (y <= 0.0021)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	t_2 = (b - z) * y;
	tmp = 0.0;
	if (y <= -5.8e+62)
		tmp = t_2;
	elseif (y <= -1.02e-79)
		tmp = t_1;
	elseif (y <= 1.95e-135)
		tmp = z + x;
	elseif (y <= 0.0021)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -5.8e+62], t$95$2, If[LessEqual[y, -1.02e-79], t$95$1, If[LessEqual[y, 1.95e-135], N[(z + x), $MachinePrecision], If[LessEqual[y, 0.0021], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999968e62 or 0.00209999999999999987 < y

   1. Initial program 89.8%

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

   3. Taylor expanded in y around 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 72.5

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

   5. Applied rewrites 72.5%

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

   if -5.79999999999999968e62 < y < -1.02000000000000002e-79 or 1.95000000000000011e-135 < y < 0.00209999999999999987

   1. Initial program 97.0%

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

   3. Taylor expanded in 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 48.6

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

   5. Applied rewrites 48.6%

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

   if -1.02000000000000002e-79 < y < 1.95000000000000011e-135

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 69.6

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

   5. Applied rewrites 69.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 69.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 51.8%

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

Alternative 11: 82.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \mathbf{if}\;b \leq -33000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+155}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b a) t (fma (- y 2.0) b a))))
   (if (<= b -33000000000000.0)
     t_1
     (if (<= b 7.2e+155) (- x (fma a (- t 1.0) (* z (- y 1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - a), t, fma((y - 2.0), b, a));
	double tmp;
	if (b <= -33000000000000.0) {
		tmp = t_1;
	} else if (b <= 7.2e+155) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, a))
	tmp = 0.0
	if (b <= -33000000000000.0)
		tmp = t_1;
	elseif (b <= 7.2e+155)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	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 + N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -33000000000000.0], t$95$1, If[LessEqual[b, 7.2e+155], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.3e13 or 7.20000000000000015e155 < b

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 91.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(b - a, t, a + b \cdot \left(y - 2\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 86.0%

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

   if -3.3e13 < b < 7.20000000000000015e155

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 89.6

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

   8. Applied rewrites 89.6%

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

Alternative 12: 65.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.85 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-98}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2.85e+107)
     t_1
     (if (<= t -7e-98)
       (fma (- 1.0 y) z x)
       (if (<= t 3.2e+39) (fma (- y 2.0) b (+ a 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 <= -2.85e+107) {
		tmp = t_1;
	} else if (t <= -7e-98) {
		tmp = fma((1.0 - y), z, x);
	} else if (t <= 3.2e+39) {
		tmp = fma((y - 2.0), b, (a + 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 <= -2.85e+107)
		tmp = t_1;
	elseif (t <= -7e-98)
		tmp = fma(Float64(1.0 - y), z, x);
	elseif (t <= 3.2e+39)
		tmp = fma(Float64(y - 2.0), b, Float64(a + 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, -2.85e+107], t$95$1, If[LessEqual[t, -7e-98], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[t, 3.2e+39], N[(N[(y - 2.0), $MachinePrecision] * b + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.84999999999999986e107 or 3.19999999999999993e39 < t

   1. Initial program 87.5%

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

   3. Taylor expanded in t around inf

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

      1. *-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 66.2

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

   5. Applied rewrites 66.2%

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

   if -2.84999999999999986e107 < t < -7.0000000000000004e-98

   1. Initial program 97.8%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 70.9%

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

   if -7.0000000000000004e-98 < t < 3.19999999999999993e39

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 74.9%

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

   6. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 74.9

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

   8. Applied rewrites 74.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 74.5%

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

Alternative 13: 73.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 75000000:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(-2, b, z\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3.5e+63)
     t_1
     (if (<= y 75000000.0) (fma (- b a) t (+ (fma -2.0 b z) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.5e+63) {
		tmp = t_1;
	} else if (y <= 75000000.0) {
		tmp = fma((b - a), t, (fma(-2.0, b, z) + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -3.5e+63)
		tmp = t_1;
	elseif (y <= 75000000.0)
		tmp = fma(Float64(b - a), t, Float64(fma(-2.0, b, z) + a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.5e+63], t$95$1, If[LessEqual[y, 75000000.0], N[(N[(b - a), $MachinePrecision] * t + N[(N[(-2.0 * b + z), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.50000000000000029e63 or 7.5e7 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 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 73.2

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

   5. Applied rewrites 73.2%

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

   if -3.50000000000000029e63 < y < 7.5e7

   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 x around 0

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

   5. Applied rewrites 77.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(b - a, t, a + \left(z + -2 \cdot b\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 76.7%

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

Alternative 14: 62.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, \left(1 - t\right) \cdot a\right)\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (* (- 1.0 t) a))))
   (if (<= a -1.1e+166)
     t_1
     (if (<= a 1.65e+57) (+ (fma (- t 2.0) b z) x) 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, ((1.0 - t) * a));
	double tmp;
	if (a <= -1.1e+166) {
		tmp = t_1;
	} else if (a <= 1.65e+57) {
		tmp = fma((t - 2.0), b, z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, Float64(Float64(1.0 - t) * a))
	tmp = 0.0
	if (a <= -1.1e+166)
		tmp = t_1;
	elseif (a <= 1.65e+57)
		tmp = Float64(fma(Float64(t - 2.0), b, z) + x);
	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[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.1e+166], t$95$1, If[LessEqual[a, 1.65e+57], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1e166 or 1.6500000000000001e57 < a

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 82.7%

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

   if -1.1e166 < a < 1.6500000000000001e57

   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 a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 90.8

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

   5. Applied rewrites 90.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 66.4%

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

Alternative 15: 61.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, \left(1 - t\right) \cdot a\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y) z (* (- 1.0 t) a))))
   (if (<= a -4.2e+166)
     t_1
     (if (<= a 2.4e+67) (+ (fma (- t 2.0) b z) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-y, z, ((1.0 - t) * a));
	double tmp;
	if (a <= -4.2e+166) {
		tmp = t_1;
	} else if (a <= 2.4e+67) {
		tmp = fma((t - 2.0), b, z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-y), z, Float64(Float64(1.0 - t) * a))
	tmp = 0.0
	if (a <= -4.2e+166)
		tmp = t_1;
	elseif (a <= 2.4e+67)
		tmp = Float64(fma(Float64(t - 2.0), b, z) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+166], t$95$1, If[LessEqual[a, 2.4e+67], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.2000000000000001e166 or 2.40000000000000002e67 < a

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 84.2%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot y, z, \left(1 - t\right) \cdot a\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 82.0%

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

   if -4.2000000000000001e166 < a < 2.40000000000000002e67

   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 a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 91.0

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

   5. Applied rewrites 91.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 66.1%

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

Alternative 16: 57.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-236}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;y \leq 125000:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -1.55e+64)
     t_1
     (if (<= y 2.65e-236)
       (fma (- 1.0 t) a x)
       (if (<= y 125000.0) (+ (fma -2.0 b z) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -1.55e+64) {
		tmp = t_1;
	} else if (y <= 2.65e-236) {
		tmp = fma((1.0 - t), a, x);
	} else if (y <= 125000.0) {
		tmp = fma(-2.0, b, z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -1.55e+64)
		tmp = t_1;
	elseif (y <= 2.65e-236)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (y <= 125000.0)
		tmp = Float64(fma(-2.0, b, 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 - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.55e+64], t$95$1, If[LessEqual[y, 2.65e-236], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[y, 125000.0], N[(N[(-2.0 * b + z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e64 or 125000 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 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 73.2

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

   5. Applied rewrites 73.2%

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

   if -1.55e64 < y < 2.6500000000000001e-236

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 77.8%

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

   6. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 81.6

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

   8. Applied rewrites 81.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 61.3%

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

   if 2.6500000000000001e-236 < y < 125000

   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 a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 76.8

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

   5. Applied rewrites 76.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 76.8%

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

   9. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(-2, b, z\right) + x \]
   10. Step-by-step derivation

   11. Applied rewrites 61.3%

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

Alternative 17: 45.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -12.5:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+70}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -2.8e+107)
     t_1
     (if (<= t -12.5) (* (- 1.0 y) z) (if (<= t 1.6e+70) (+ 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 <= -2.8e+107) {
		tmp = t_1;
	} else if (t <= -12.5) {
		tmp = (1.0 - y) * z;
	} else if (t <= 1.6e+70) {
		tmp = z + x;
	} 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 <= (-2.8d+107)) then
        tmp = t_1
    else if (t <= (-12.5d0)) then
        tmp = (1.0d0 - y) * z
    else if (t <= 1.6d+70) then
        tmp = z + x
    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 <= -2.8e+107) {
		tmp = t_1;
	} else if (t <= -12.5) {
		tmp = (1.0 - y) * z;
	} else if (t <= 1.6e+70) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -2.8e+107:
		tmp = t_1
	elif t <= -12.5:
		tmp = (1.0 - y) * z
	elif t <= 1.6e+70:
		tmp = 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 <= -2.8e+107)
		tmp = t_1;
	elseif (t <= -12.5)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= 1.6e+70)
		tmp = Float64(z + x);
	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 <= -2.8e+107)
		tmp = t_1;
	elseif (t <= -12.5)
		tmp = (1.0 - y) * z;
	elseif (t <= 1.6e+70)
		tmp = z + x;
	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, -2.8e+107], t$95$1, If[LessEqual[t, -12.5], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 1.6e+70], N[(z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999985e107 or 1.6000000000000001e70 < t

   1. Initial program 86.5%

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

   3. Taylor expanded in t around inf

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

      1. *-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 69.0

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

   5. Applied rewrites 69.0%

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

   if -2.79999999999999985e107 < t < -12.5

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf

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

      1. *-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. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 58.7

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

   5. Applied rewrites 58.7%

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

   if -12.5 < t < 1.6000000000000001e70

   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 a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 79.2

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 51.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 39.6%

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

Alternative 18: 41.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.76 \cdot 10^{+22}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+96}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -1.7e+100)
     t_1
     (if (<= a 1.76e+22) (+ z x) (if (<= a 4.6e+96) (* (- 1.0 y) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -1.7e+100) {
		tmp = t_1;
	} else if (a <= 1.76e+22) {
		tmp = z + x;
	} else if (a <= 4.6e+96) {
		tmp = (1.0 - y) * 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 = (1.0d0 - t) * a
    if (a <= (-1.7d+100)) then
        tmp = t_1
    else if (a <= 1.76d+22) then
        tmp = z + x
    else if (a <= 4.6d+96) then
        tmp = (1.0d0 - y) * 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 = (1.0 - t) * a;
	double tmp;
	if (a <= -1.7e+100) {
		tmp = t_1;
	} else if (a <= 1.76e+22) {
		tmp = z + x;
	} else if (a <= 4.6e+96) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - t) * a
	tmp = 0
	if a <= -1.7e+100:
		tmp = t_1
	elif a <= 1.76e+22:
		tmp = z + x
	elif a <= 4.6e+96:
		tmp = (1.0 - y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -1.7e+100)
		tmp = t_1;
	elseif (a <= 1.76e+22)
		tmp = Float64(z + x);
	elseif (a <= 4.6e+96)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - t) * a;
	tmp = 0.0;
	if (a <= -1.7e+100)
		tmp = t_1;
	elseif (a <= 1.76e+22)
		tmp = z + x;
	elseif (a <= 4.6e+96)
		tmp = (1.0 - y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -1.7e+100], t$95$1, If[LessEqual[a, 1.76e+22], N[(z + x), $MachinePrecision], If[LessEqual[a, 4.6e+96], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.69999999999999997e100 or 4.6000000000000003e96 < a

   1. Initial program 89.9%

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

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-lft-in N/A

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

      14. metadata-eval N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 62.3

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

   5. Applied rewrites 62.3%

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

   if -1.69999999999999997e100 < a < 1.76e22

   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 a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 94.0

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

   5. Applied rewrites 94.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 68.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 45.2%

       \[\leadsto z + x \]

   if 1.76e22 < a < 4.6000000000000003e96

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

      1. *-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. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 46.7

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

   5. Applied rewrites 46.7%

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

Alternative 19: 37.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot y\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+38}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+15}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- z) y)))
   (if (<= y -1.8e+218)
     t_1
     (if (<= y -6.8e+38) (* b y) (if (<= y 1.1e+15) (+ z x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * y;
	double tmp;
	if (y <= -1.8e+218) {
		tmp = t_1;
	} else if (y <= -6.8e+38) {
		tmp = b * y;
	} else if (y <= 1.1e+15) {
		tmp = z + x;
	} 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 = -z * y
    if (y <= (-1.8d+218)) then
        tmp = t_1
    else if (y <= (-6.8d+38)) then
        tmp = b * y
    else if (y <= 1.1d+15) then
        tmp = z + x
    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 = -z * y;
	double tmp;
	if (y <= -1.8e+218) {
		tmp = t_1;
	} else if (y <= -6.8e+38) {
		tmp = b * y;
	} else if (y <= 1.1e+15) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -z * y
	tmp = 0
	if y <= -1.8e+218:
		tmp = t_1
	elif y <= -6.8e+38:
		tmp = b * y
	elif y <= 1.1e+15:
		tmp = z + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-z) * y)
	tmp = 0.0
	if (y <= -1.8e+218)
		tmp = t_1;
	elseif (y <= -6.8e+38)
		tmp = Float64(b * y);
	elseif (y <= 1.1e+15)
		tmp = Float64(z + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -z * y;
	tmp = 0.0;
	if (y <= -1.8e+218)
		tmp = t_1;
	elseif (y <= -6.8e+38)
		tmp = b * y;
	elseif (y <= 1.1e+15)
		tmp = z + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * y), $MachinePrecision]}, If[LessEqual[y, -1.8e+218], t$95$1, If[LessEqual[y, -6.8e+38], N[(b * y), $MachinePrecision], If[LessEqual[y, 1.1e+15], N[(z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999995e218 or 1.1e15 < y

   1. Initial program 88.2%

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

   3. Taylor expanded in y around 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 76.8

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

   5. Applied rewrites 76.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 57.0%

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

   if -1.79999999999999995e218 < y < -6.79999999999999992e38

   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 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 57.4

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 42.5%

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

   if -6.79999999999999992e38 < y < 1.1e15

   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 a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 69.3

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

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 68.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 42.6%

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

Alternative 20: 67.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 176000:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3.2e+63)
     t_1
     (if (<= y 176000.0) (+ (fma (- t 2.0) b z) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.2e+63) {
		tmp = t_1;
	} else if (y <= 176000.0) {
		tmp = fma((t - 2.0), b, z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -3.2e+63)
		tmp = t_1;
	elseif (y <= 176000.0)
		tmp = Float64(fma(Float64(t - 2.0), b, 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 - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.2e+63], t$95$1, If[LessEqual[y, 176000.0], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000011e63 or 176000 < y

   1. Initial program 89.7%

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

   3. Taylor expanded in y around 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 73.2

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

   5. Applied rewrites 73.2%

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

   if -3.20000000000000011e63 < y < 176000

   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 a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 68.0

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

   5. Applied rewrites 68.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 67.5%

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

Alternative 21: 55.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+105}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z x)))
   (if (<= z -1.4e+56) t_1 (if (<= z 2.95e+105) (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 = fma((1.0 - y), z, x);
	double tmp;
	if (z <= -1.4e+56) {
		tmp = t_1;
	} else if (z <= 2.95e+105) {
		tmp = fma((1.0 - t), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, x)
	tmp = 0.0
	if (z <= -1.4e+56)
		tmp = t_1;
	elseif (z <= 2.95e+105)
		tmp = 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[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[z, -1.4e+56], t$95$1, If[LessEqual[z, 2.95e+105], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000004e56 or 2.94999999999999983e105 < z

   1. Initial program 88.8%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 85.2

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

   5. Applied rewrites 85.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 72.9%

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

   if -1.40000000000000004e56 < z < 2.94999999999999983e105

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 74.6%

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

   6. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 95.1

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

   8. Applied rewrites 95.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 60.1%

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

Alternative 22: 53.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+107}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -1.05e+92) t_1 (if (<= z 5.7e+107) (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 = (1.0 - y) * z;
	double tmp;
	if (z <= -1.05e+92) {
		tmp = t_1;
	} else if (z <= 5.7e+107) {
		tmp = fma((1.0 - t), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -1.05e+92)
		tmp = t_1;
	elseif (z <= 5.7e+107)
		tmp = 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[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.05e+92], t$95$1, If[LessEqual[z, 5.7e+107], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999993e92 or 5.69999999999999972e107 < z

   1. Initial program 88.7%

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

   3. Taylor expanded in z around 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. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if -1.04999999999999993e92 < z < 5.69999999999999972e107

   1. Initial program 97.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 74.9%

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

   6. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 93.0

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

   8. Applied rewrites 93.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 59.9%

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

Alternative 23: 40.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+98}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -1.7e+100) t_1 (if (<= a 6e+98) (+ z x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -1.7e+100) {
		tmp = t_1;
	} else if (a <= 6e+98) {
		tmp = z + x;
	} 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 = (1.0d0 - t) * a
    if (a <= (-1.7d+100)) then
        tmp = t_1
    else if (a <= 6d+98) then
        tmp = z + x
    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 = (1.0 - t) * a;
	double tmp;
	if (a <= -1.7e+100) {
		tmp = t_1;
	} else if (a <= 6e+98) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - t) * a
	tmp = 0
	if a <= -1.7e+100:
		tmp = t_1
	elif a <= 6e+98:
		tmp = z + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -1.7e+100)
		tmp = t_1;
	elseif (a <= 6e+98)
		tmp = Float64(z + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - t) * a;
	tmp = 0.0;
	if (a <= -1.7e+100)
		tmp = t_1;
	elseif (a <= 6e+98)
		tmp = z + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -1.7e+100], t$95$1, If[LessEqual[a, 6e+98], N[(z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999997e100 or 6.0000000000000003e98 < a

   1. Initial program 89.8%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-lft-in N/A

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

      14. metadata-eval N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 63.0

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

   5. Applied rewrites 63.0%

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

   if -1.69999999999999997e100 < a < 6.0000000000000003e98

   1. Initial program 97.0%

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

   3. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot y + -1 \cdot -1}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot y + \color{blue}{1}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. lower-+.f64 92.5

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 92.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{\left(z + b \cdot \left(t - 2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 65.6%

      \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \color{blue}{x} \]

   9. Taylor expanded in b around 0

      \[\leadsto x + z \]
   10. Step-by-step derivation

   11. Applied rewrites 42.3%

       \[\leadsto z + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 30.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+73}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+99}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.7e+73) (+ z x) (if (<= x 1.15e+99) (+ a z) (+ z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.7e+73) {
		tmp = z + x;
	} else if (x <= 1.15e+99) {
		tmp = a + z;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.7d+73)) then
        tmp = z + x
    else if (x <= 1.15d+99) then
        tmp = a + z
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.7e+73) {
		tmp = z + x;
	} else if (x <= 1.15e+99) {
		tmp = a + z;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.7e+73:
		tmp = z + x
	elif x <= 1.15e+99:
		tmp = a + z
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.7e+73)
		tmp = Float64(z + x);
	elseif (x <= 1.15e+99)
		tmp = Float64(a + z);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.7e+73)
		tmp = z + x;
	elseif (x <= 1.15e+99)
		tmp = a + z;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.7e+73], N[(z + x), $MachinePrecision], If[LessEqual[x, 1.15e+99], N[(a + z), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6999999999999999e73 or 1.1500000000000001e99 < x

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y - 1\right) \cdot z}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} \cdot z + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(y - 1\right), z, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(y + \color{blue}{-1}\right), z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot y + -1 \cdot -1}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot y + \color{blue}{1}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. lower-+.f64 80.7

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{\left(z + b \cdot \left(t - 2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 55.7%

      \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \color{blue}{x} \]

   9. Taylor expanded in b around 0

      \[\leadsto x + z \]
   10. Step-by-step derivation

   11. Applied rewrites 47.6%

       \[\leadsto z + x \]

   if -2.6999999999999999e73 < x < 1.1500000000000001e99

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + z \cdot \left(1 - y\right)\right)} \]

   8. Applied rewrites 64.9%

      \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, \left(1 - t\right) \cdot a\right) \]

   9. Taylor expanded in y around 0

      \[\leadsto z + a \cdot \color{blue}{\left(1 - t\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 48.5%

       \[\leadsto \mathsf{fma}\left(1 - t, a, z\right) \]

   12. Taylor expanded in t around 0

       \[\leadsto a + z \]
   13. Step-by-step derivation

   14. Applied rewrites 32.2%

       \[\leadsto a + z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 24.6% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ z + x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ z x))

C

double code(double x, double y, double z, double t, double a, double b) {
	return z + 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 = z + x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return z + x;
}

Python

def code(x, y, z, t, a, b):
	return z + x

Julia

function code(x, y, z, t, a, b)
	return Float64(z + x)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = z + x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + x), $MachinePrecision]

Derivation

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 a around 0

   \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
4. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   3. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y - 1\right) \cdot z}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   4. distribute-lft-neg-in N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   5. mul-1-neg N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} \cdot z + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   6. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(y - 1\right), z, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   7. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(-1 \cdot \left(y + \color{blue}{-1}\right), z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   9. distribute-lft-in N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot y + -1 \cdot -1}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(-1 \cdot y + \color{blue}{1}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   12. neg-mul-1 N/A

       \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   13. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   14. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

   17. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

   18. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

   19. lower-+.f64 74.4

       \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

5. Applied rewrites 74.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

6. Taylor expanded in y around 0

   \[\leadsto x + \color{blue}{\left(z + b \cdot \left(t - 2\right)\right)} \]
7. Step-by-step derivation

8. Applied rewrites 51.0%

   \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \color{blue}{x} \]

9. Taylor expanded in b around 0

   \[\leadsto x + z \]
10. Step-by-step derivation

11. Applied rewrites 30.5%

    \[\leadsto z + x \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024294 
(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)))