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

Percentage Accurate: 95.4% → 98.1%

Time: 14.6s

Alternatives: 21

Speedup: 1.2×

• 36.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.4% 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: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 57.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 72.1%

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

4. Final simplification 98.5%

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

Alternative 2: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-188}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(-z, y, z\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (fma z (- 1.0 y) x))) (t_2 (* t (- b a))))
   (if (<= t -8.6e+100)
     t_2
     (if (<= t -1.75e-291)
       t_1
       (if (<= t 3.8e-188)
         (fma b (+ y -2.0) (fma (- z) y z))
         (if (<= t 1.35e-99)
           (fma b (+ y -2.0) (+ x a))
           (if (<= t 1.25e+69) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + fma(z, (1.0 - y), x);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8.6e+100) {
		tmp = t_2;
	} else if (t <= -1.75e-291) {
		tmp = t_1;
	} else if (t <= 3.8e-188) {
		tmp = fma(b, (y + -2.0), fma(-z, y, z));
	} else if (t <= 1.35e-99) {
		tmp = fma(b, (y + -2.0), (x + a));
	} else if (t <= 1.25e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + fma(z, Float64(1.0 - y), x))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.6e+100)
		tmp = t_2;
	elseif (t <= -1.75e-291)
		tmp = t_1;
	elseif (t <= 3.8e-188)
		tmp = fma(b, Float64(y + -2.0), fma(Float64(-z), y, z));
	elseif (t <= 1.35e-99)
		tmp = fma(b, Float64(y + -2.0), Float64(x + a));
	elseif (t <= 1.25e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+100], t$95$2, If[LessEqual[t, -1.75e-291], t$95$1, If[LessEqual[t, 3.8e-188], N[(b * N[(y + -2.0), $MachinePrecision] + N[((-z) * y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-99], N[(b * N[(y + -2.0), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+69], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.59999999999999986e100 or 1.25000000000000009e69 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if -8.59999999999999986e100 < t < -1.74999999999999998e-291 or 1.35e-99 < t < 1.25000000000000009e69

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 77.0%

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

   if -1.74999999999999998e-291 < t < 3.8e-188

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(b, y + -2, z \cdot \left(1 - y\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 80.2%

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

   10. Applied rewrites 80.3%

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

   if 3.8e-188 < t < 1.35e-99

   1. Initial program 83.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 87.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-291}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-188}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(-z, y, z\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+69}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-188}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, z - y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (fma z (- 1.0 y) x))) (t_2 (* t (- b a))))
   (if (<= t -8.6e+100)
     t_2
     (if (<= t -1.75e-291)
       t_1
       (if (<= t 3.8e-188)
         (fma b (+ y -2.0) (- z (* y z)))
         (if (<= t 1.35e-99)
           (fma b (+ y -2.0) (+ x a))
           (if (<= t 1.25e+69) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + fma(z, (1.0 - y), x);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8.6e+100) {
		tmp = t_2;
	} else if (t <= -1.75e-291) {
		tmp = t_1;
	} else if (t <= 3.8e-188) {
		tmp = fma(b, (y + -2.0), (z - (y * z)));
	} else if (t <= 1.35e-99) {
		tmp = fma(b, (y + -2.0), (x + a));
	} else if (t <= 1.25e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + fma(z, Float64(1.0 - y), x))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.6e+100)
		tmp = t_2;
	elseif (t <= -1.75e-291)
		tmp = t_1;
	elseif (t <= 3.8e-188)
		tmp = fma(b, Float64(y + -2.0), Float64(z - Float64(y * z)));
	elseif (t <= 1.35e-99)
		tmp = fma(b, Float64(y + -2.0), Float64(x + a));
	elseif (t <= 1.25e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+100], t$95$2, If[LessEqual[t, -1.75e-291], t$95$1, If[LessEqual[t, 3.8e-188], N[(b * N[(y + -2.0), $MachinePrecision] + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-99], N[(b * N[(y + -2.0), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+69], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.59999999999999986e100 or 1.25000000000000009e69 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if -8.59999999999999986e100 < t < -1.74999999999999998e-291 or 1.35e-99 < t < 1.25000000000000009e69

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 77.0%

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

   if -1.74999999999999998e-291 < t < 3.8e-188

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(b, y + -2, z \cdot \left(1 - y\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 80.2%

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

   if 3.8e-188 < t < 1.35e-99

   1. Initial program 83.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 87.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-291}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-188}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, z - y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+69}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-177}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-124}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* y (- b z)))) (t_2 (* t (- b a))))
   (if (<= t -1.4e+94)
     t_2
     (if (<= t -7.5e-109)
       t_1
       (if (<= t 2e-177)
         (fma z (- 1.0 y) x)
         (if (<= t 1.52e-124)
           (* b (+ y (+ t -2.0)))
           (if (<= t 5.6e+67) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (y * (b - z));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.4e+94) {
		tmp = t_2;
	} else if (t <= -7.5e-109) {
		tmp = t_1;
	} else if (t <= 2e-177) {
		tmp = fma(z, (1.0 - y), x);
	} else if (t <= 1.52e-124) {
		tmp = b * (y + (t + -2.0));
	} else if (t <= 5.6e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(y * Float64(b - z)))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.4e+94)
		tmp = t_2;
	elseif (t <= -7.5e-109)
		tmp = t_1;
	elseif (t <= 2e-177)
		tmp = fma(z, Float64(1.0 - y), x);
	elseif (t <= 1.52e-124)
		tmp = Float64(b * Float64(y + Float64(t + -2.0)));
	elseif (t <= 5.6e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+94], t$95$2, If[LessEqual[t, -7.5e-109], t$95$1, If[LessEqual[t, 2e-177], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 1.52e-124], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+67], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.39999999999999999e94 or 5.5999999999999995e67 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 73.4

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

   5. Applied rewrites 73.4%

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

   if -1.39999999999999999e94 < t < -7.49999999999999982e-109 or 1.52e-124 < t < 5.5999999999999995e67

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 67.3%

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

   if -7.49999999999999982e-109 < t < 1.9999999999999999e-177

   1. Initial program 94.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.0%

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

   if 1.9999999999999999e-177 < t < 1.52e-124

   1. Initial program 90.9%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 77.0

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

   5. Applied rewrites 77.0%

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

Alternative 5: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (fma z (- 1.0 y) x))) (t_2 (* t (- b a))))
   (if (<= t -8.6e+100)
     t_2
     (if (<= t 1e-179)
       t_1
       (if (<= t 1.35e-99)
         (fma b (+ y -2.0) (+ x a))
         (if (<= t 1.25e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + fma(z, (1.0 - y), x);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -8.6e+100) {
		tmp = t_2;
	} else if (t <= 1e-179) {
		tmp = t_1;
	} else if (t <= 1.35e-99) {
		tmp = fma(b, (y + -2.0), (x + a));
	} else if (t <= 1.25e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + fma(z, Float64(1.0 - y), x))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.6e+100)
		tmp = t_2;
	elseif (t <= 1e-179)
		tmp = t_1;
	elseif (t <= 1.35e-99)
		tmp = fma(b, Float64(y + -2.0), Float64(x + a));
	elseif (t <= 1.25e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+100], t$95$2, If[LessEqual[t, 1e-179], t$95$1, If[LessEqual[t, 1.35e-99], N[(b * N[(y + -2.0), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.59999999999999986e100 or 1.25000000000000009e69 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if -8.59999999999999986e100 < t < 1e-179 or 1.35e-99 < t < 1.25000000000000009e69

   1. Initial program 96.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 96.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 74.2%

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

   if 1e-179 < t < 1.35e-99

   1. Initial program 81.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 91.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 10^{-179}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-99}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+69}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, a + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 y) x)))
   (if (<= t -8.6e+100)
     (* t (- b a))
     (if (<= t 2.65e+79) (fma b (+ y -2.0) (+ a t_1)) (fma a (- 1.0 t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (1.0 - y), x);
	double tmp;
	if (t <= -8.6e+100) {
		tmp = t * (b - a);
	} else if (t <= 2.65e+79) {
		tmp = fma(b, (y + -2.0), (a + t_1));
	} else {
		tmp = fma(a, (1.0 - t), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(1.0 - y), x)
	tmp = 0.0
	if (t <= -8.6e+100)
		tmp = Float64(t * Float64(b - a));
	elseif (t <= 2.65e+79)
		tmp = fma(b, Float64(y + -2.0), Float64(a + t_1));
	else
		tmp = fma(a, Float64(1.0 - t), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -8.6e+100], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+79], N[(b * N[(y + -2.0), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.59999999999999986e100

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 78.4

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

   5. Applied rewrites 78.4%

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

   if -8.59999999999999986e100 < t < 2.64999999999999989e79

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 94.0%

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

   if 2.64999999999999989e79 < t

   1. Initial program 93.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 73.3%

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

Alternative 7: 82.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+79}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, \mathsf{fma}\left(b, y + -2, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.6e+100)
   (* t (- b a))
   (if (<= t 2.65e+79)
     (+ a (fma z (- 1.0 y) (fma b (+ y -2.0) x)))
     (fma a (- 1.0 t) (fma z (- 1.0 y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.6e+100) {
		tmp = t * (b - a);
	} else if (t <= 2.65e+79) {
		tmp = a + fma(z, (1.0 - y), fma(b, (y + -2.0), x));
	} else {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.6e+100)
		tmp = Float64(t * Float64(b - a));
	elseif (t <= 2.65e+79)
		tmp = Float64(a + fma(z, Float64(1.0 - y), fma(b, Float64(y + -2.0), x)));
	else
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.6e+100], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+79], N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.59999999999999986e100

   1. Initial program 94.4%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 78.4

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

   5. Applied rewrites 78.4%

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

   if -8.59999999999999986e100 < t < 2.64999999999999989e79

   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 x around 0

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

   5. Applied rewrites 96.8%

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

   6. Taylor expanded in t around 0

      \[\leadsto a + \mathsf{fma}\left(z, 1 - y, x + b \cdot \left(y - 2\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 92.8%

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

   if 2.64999999999999989e79 < t

   1. Initial program 93.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 73.3%

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

Alternative 8: 56.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-177}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -8.6e+100)
     t_1
     (if (<= t 2e-177)
       (fma z (- 1.0 y) x)
       (if (<= t 8.2e-109)
         (* b (+ y -2.0))
         (if (<= t 5.6e+67) (* y (- b z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -8.6e+100) {
		tmp = t_1;
	} else if (t <= 2e-177) {
		tmp = fma(z, (1.0 - y), x);
	} else if (t <= 8.2e-109) {
		tmp = b * (y + -2.0);
	} else if (t <= 5.6e+67) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -8.6e+100)
		tmp = t_1;
	elseif (t <= 2e-177)
		tmp = fma(z, Float64(1.0 - y), x);
	elseif (t <= 8.2e-109)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (t <= 5.6e+67)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+100], t$95$1, If[LessEqual[t, 2e-177], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 8.2e-109], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+67], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.59999999999999986e100 or 5.5999999999999995e67 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 74.1

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

   5. Applied rewrites 74.1%

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

   if -8.59999999999999986e100 < t < 1.9999999999999999e-177

   1. Initial program 96.3%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 59.2%

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

   if 1.9999999999999999e-177 < t < 8.2000000000000004e-109

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.3%

      \[\leadsto b \cdot \left(y + -2\right) \]

   if 8.2000000000000004e-109 < t < 5.5999999999999995e67

   1. Initial program 93.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 56.5

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

   5. Applied rewrites 56.5%

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

Alternative 9: 49.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{-179}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.6e+84)
     t_1
     (if (<= t 1e-179)
       (- z (* y z))
       (if (<= t 8.2e-109)
         (* b (+ y -2.0))
         (if (<= t 5.6e+67) (* y (- b z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.6e+84) {
		tmp = t_1;
	} else if (t <= 1e-179) {
		tmp = z - (y * z);
	} else if (t <= 8.2e-109) {
		tmp = b * (y + -2.0);
	} else if (t <= 5.6e+67) {
		tmp = y * (b - 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 = t * (b - a)
    if (t <= (-3.6d+84)) then
        tmp = t_1
    else if (t <= 1d-179) then
        tmp = z - (y * z)
    else if (t <= 8.2d-109) then
        tmp = b * (y + (-2.0d0))
    else if (t <= 5.6d+67) then
        tmp = y * (b - 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 = t * (b - a);
	double tmp;
	if (t <= -3.6e+84) {
		tmp = t_1;
	} else if (t <= 1e-179) {
		tmp = z - (y * z);
	} else if (t <= 8.2e-109) {
		tmp = b * (y + -2.0);
	} else if (t <= 5.6e+67) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -3.6e+84:
		tmp = t_1
	elif t <= 1e-179:
		tmp = z - (y * z)
	elif t <= 8.2e-109:
		tmp = b * (y + -2.0)
	elif t <= 5.6e+67:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.6e+84)
		tmp = t_1;
	elseif (t <= 1e-179)
		tmp = Float64(z - Float64(y * z));
	elseif (t <= 8.2e-109)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (t <= 5.6e+67)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.6e+84)
		tmp = t_1;
	elseif (t <= 1e-179)
		tmp = z - (y * z);
	elseif (t <= 8.2e-109)
		tmp = b * (y + -2.0);
	elseif (t <= 5.6e+67)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+84], t$95$1, If[LessEqual[t, 1e-179], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-109], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+67], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.5999999999999999e84 or 5.5999999999999995e67 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   if -3.5999999999999999e84 < t < 1e-179

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

         \[\leadsto \color{blue}{z - y \cdot z} \]

      8. lower--.f64 N/A

         \[\leadsto \color{blue}{z - y \cdot z} \]

      9. lower-*.f64 43.2

         \[\leadsto z - \color{blue}{y \cdot z} \]

   5. Applied rewrites 43.2%

      \[\leadsto \color{blue}{z - y \cdot z} \]

   if 1e-179 < t < 8.2000000000000004e-109

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.3%

      \[\leadsto b \cdot \left(y + -2\right) \]

   if 8.2000000000000004e-109 < t < 5.5999999999999995e67

   1. Initial program 93.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 56.5

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

   5. Applied rewrites 56.5%

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

Alternative 10: 82.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -2.4e+97)
     t_1
     (if (<= b 5.2e+120) (fma a (- 1.0 t) (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -2.4e+97) {
		tmp = t_1;
	} else if (b <= 5.2e+120) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -2.4e+97)
		tmp = t_1;
	elseif (b <= 5.2e+120)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+97], t$95$1, If[LessEqual[b, 5.2e+120], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4e97 or 5.1999999999999998e120 < b

   1. Initial program 87.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 83.4

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

   5. Applied rewrites 83.4%

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

   if -2.4e97 < b < 5.1999999999999998e120

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 86.7%

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

Alternative 11: 97.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision] + N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 x around 0

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

5. Applied rewrites 96.5%

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

Alternative 12: 43.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.6e+84)
     t_1
     (if (<= t 7.2e-304)
       (* y (- z))
       (if (<= t 4.9e+64) (* b (+ y -2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.6e+84) {
		tmp = t_1;
	} else if (t <= 7.2e-304) {
		tmp = y * -z;
	} else if (t <= 4.9e+64) {
		tmp = b * (y + -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-3.6d+84)) then
        tmp = t_1
    else if (t <= 7.2d-304) then
        tmp = y * -z
    else if (t <= 4.9d+64) then
        tmp = b * (y + (-2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.6e+84) {
		tmp = t_1;
	} else if (t <= 7.2e-304) {
		tmp = y * -z;
	} else if (t <= 4.9e+64) {
		tmp = b * (y + -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -3.6e+84:
		tmp = t_1
	elif t <= 7.2e-304:
		tmp = y * -z
	elif t <= 4.9e+64:
		tmp = b * (y + -2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.6e+84)
		tmp = t_1;
	elseif (t <= 7.2e-304)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 4.9e+64)
		tmp = Float64(b * Float64(y + -2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.6e+84)
		tmp = t_1;
	elseif (t <= 7.2e-304)
		tmp = y * -z;
	elseif (t <= 4.9e+64)
		tmp = b * (y + -2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+84], t$95$1, If[LessEqual[t, 7.2e-304], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 4.9e+64], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5999999999999999e84 or 4.9000000000000003e64 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   if -3.5999999999999999e84 < t < 7.2000000000000003e-304

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 39.8

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

   5. Applied rewrites 39.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 29.9%

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

   if 7.2000000000000003e-304 < t < 4.9000000000000003e64

   1. Initial program 94.7%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 41.1

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

   5. Applied rewrites 41.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 40.0%

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

Alternative 13: 28.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -3.65 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 10^{+38}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -3.65e+205)
     t_1
     (if (<= t -9e+100) (* t b) (if (<= t 1e+38) (* y (- z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -3.65e+205) {
		tmp = t_1;
	} else if (t <= -9e+100) {
		tmp = t * b;
	} else if (t <= 1e+38) {
		tmp = 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 = t * -a
    if (t <= (-3.65d+205)) then
        tmp = t_1
    else if (t <= (-9d+100)) then
        tmp = t * b
    else if (t <= 1d+38) then
        tmp = 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 = t * -a;
	double tmp;
	if (t <= -3.65e+205) {
		tmp = t_1;
	} else if (t <= -9e+100) {
		tmp = t * b;
	} else if (t <= 1e+38) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -3.65e+205:
		tmp = t_1
	elif t <= -9e+100:
		tmp = t * b
	elif t <= 1e+38:
		tmp = y * -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -3.65e+205)
		tmp = t_1;
	elseif (t <= -9e+100)
		tmp = Float64(t * b);
	elseif (t <= 1e+38)
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -3.65e+205)
		tmp = t_1;
	elseif (t <= -9e+100)
		tmp = t * b;
	elseif (t <= 1e+38)
		tmp = y * -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -3.65e+205], t$95$1, If[LessEqual[t, -9e+100], N[(t * b), $MachinePrecision], If[LessEqual[t, 1e+38], N[(y * (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.64999999999999991e205 or 9.99999999999999977e37 < t

   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 t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 69.9

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 45.4%

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

   if -3.64999999999999991e205 < t < -9.00000000000000073e100

   1. Initial program 92.3%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 81.2

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 62.6%

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

   if -9.00000000000000073e100 < t < 9.99999999999999977e37

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 42.8

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

   5. Applied rewrites 42.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 28.2%

      \[\leadsto y \cdot \left(-z\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 10^{+38}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -3.65 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -3.65e+205)
     t_1
     (if (<= t -5e+84) (* t b) (if (<= t 7.2e+91) (* y b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -3.65e+205) {
		tmp = t_1;
	} else if (t <= -5e+84) {
		tmp = t * b;
	} else if (t <= 7.2e+91) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-3.65d+205)) then
        tmp = t_1
    else if (t <= (-5d+84)) then
        tmp = t * b
    else if (t <= 7.2d+91) then
        tmp = y * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -3.65e+205) {
		tmp = t_1;
	} else if (t <= -5e+84) {
		tmp = t * b;
	} else if (t <= 7.2e+91) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -3.65e+205:
		tmp = t_1
	elif t <= -5e+84:
		tmp = t * b
	elif t <= 7.2e+91:
		tmp = y * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -3.65e+205)
		tmp = t_1;
	elseif (t <= -5e+84)
		tmp = Float64(t * b);
	elseif (t <= 7.2e+91)
		tmp = Float64(y * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -3.65e+205)
		tmp = t_1;
	elseif (t <= -5e+84)
		tmp = t * b;
	elseif (t <= 7.2e+91)
		tmp = y * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -3.65e+205], t$95$1, If[LessEqual[t, -5e+84], N[(t * b), $MachinePrecision], If[LessEqual[t, 7.2e+91], N[(y * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.64999999999999991e205 or 7.2e91 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 71.9

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

   5. Applied rewrites 71.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 48.9%

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

   if -3.64999999999999991e205 < t < -5.0000000000000001e84

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 76.6

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 56.4%

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

   if -5.0000000000000001e84 < t < 7.2e91

   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 b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 33.0

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

   5. Applied rewrites 33.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 20.9%

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

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{+205}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+120}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -2.4e+97)
     t_1
     (if (<= b 4.6e+120) (+ a (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -2.4e+97) {
		tmp = t_1;
	} else if (b <= 4.6e+120) {
		tmp = a + fma(z, (1.0 - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -2.4e+97)
		tmp = t_1;
	elseif (b <= 4.6e+120)
		tmp = Float64(a + fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+97], t$95$1, If[LessEqual[b, 4.6e+120], N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4e97 or 4.59999999999999985e120 < b

   1. Initial program 87.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 83.4

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

   5. Applied rewrites 83.4%

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

   if -2.4e97 < b < 4.59999999999999985e120

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 67.0%

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

Alternative 16: 66.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+25}:\\ \;\;\;\;a + \left(x + \mathsf{fma}\left(b, -2, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* y (- b z)))))
   (if (<= y -5.8e+28)
     t_1
     (if (<= y 1.25e+25) (+ a (+ x (fma b -2.0 z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (y * (b - z));
	double tmp;
	if (y <= -5.8e+28) {
		tmp = t_1;
	} else if (y <= 1.25e+25) {
		tmp = a + (x + fma(b, -2.0, z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(y * Float64(b - z)))
	tmp = 0.0
	if (y <= -5.8e+28)
		tmp = t_1;
	elseif (y <= 1.25e+25)
		tmp = Float64(a + Float64(x + fma(b, -2.0, z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+28], t$95$1, If[LessEqual[y, 1.25e+25], N[(a + N[(x + N[(b * -2.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000002e28 or 1.25000000000000006e25 < y

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 77.8%

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

   if -5.8000000000000002e28 < y < 1.25000000000000006e25

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 61.9%

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

Alternative 17: 61.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -2.05e+52) t_1 (if (<= b 3.6e+24) (fma z (- 1.0 y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -2.05e+52) {
		tmp = t_1;
	} else if (b <= 3.6e+24) {
		tmp = fma(z, (1.0 - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -2.05e+52)
		tmp = t_1;
	elseif (b <= 3.6e+24)
		tmp = fma(z, Float64(1.0 - y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+52], t$95$1, If[LessEqual[b, 3.6e+24], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.05e52 or 3.59999999999999983e24 < b

   1. Initial program 88.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 74.1

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

   5. Applied rewrites 74.1%

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

   if -2.05e52 < b < 3.59999999999999983e24

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 90.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 57.4%

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

Alternative 18: 51.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.7e+86) t_1 (if (<= t 5.6e+67) (* y (- b z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.7e+86) {
		tmp = t_1;
	} else if (t <= 5.6e+67) {
		tmp = y * (b - 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 = t * (b - a)
    if (t <= (-1.7d+86)) then
        tmp = t_1
    else if (t <= 5.6d+67) then
        tmp = y * (b - 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 = t * (b - a);
	double tmp;
	if (t <= -1.7e+86) {
		tmp = t_1;
	} else if (t <= 5.6e+67) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.7e+86:
		tmp = t_1
	elif t <= 5.6e+67:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.7e+86)
		tmp = t_1;
	elseif (t <= 5.6e+67)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.7e+86)
		tmp = t_1;
	elseif (t <= 5.6e+67)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+86], t$95$1, If[LessEqual[t, 5.6e+67], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e86 or 5.5999999999999995e67 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   if -1.6999999999999999e86 < t < 5.5999999999999995e67

   1. Initial program 94.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 43.7

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

   5. Applied rewrites 43.7%

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

Alternative 19: 30.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= z -4.5e+97) t_1 (if (<= z 2.75e+110) (* b (+ t -2.0)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (z <= -4.5e+97) {
		tmp = t_1;
	} else if (z <= 2.75e+110) {
		tmp = b * (t + -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (z <= (-4.5d+97)) then
        tmp = t_1
    else if (z <= 2.75d+110) then
        tmp = b * (t + (-2.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (z <= -4.5e+97) {
		tmp = t_1;
	} else if (z <= 2.75e+110) {
		tmp = b * (t + -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if z <= -4.5e+97:
		tmp = t_1
	elif z <= 2.75e+110:
		tmp = b * (t + -2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -4.5e+97)
		tmp = t_1;
	elseif (z <= 2.75e+110)
		tmp = Float64(b * Float64(t + -2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (z <= -4.5e+97)
		tmp = t_1;
	elseif (z <= 2.75e+110)
		tmp = b * (t + -2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -4.5e+97], t$95$1, If[LessEqual[z, 2.75e+110], N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999976e97 or 2.74999999999999998e110 < z

   1. Initial program 88.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 57.3

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

   5. Applied rewrites 57.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 53.0%

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

   if -4.49999999999999976e97 < z < 2.74999999999999998e110

   1. Initial program 97.6%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 46.9

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

   5. Applied rewrites 46.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 32.6%

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

Alternative 20: 27.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+65}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5e+84) (* t b) (if (<= t 6.8e+65) (* y b) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e+84) {
		tmp = t * b;
	} else if (t <= 6.8e+65) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5d+84)) then
        tmp = t * b
    else if (t <= 6.8d+65) then
        tmp = y * b
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e+84) {
		tmp = t * b;
	} else if (t <= 6.8e+65) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5e+84:
		tmp = t * b
	elif t <= 6.8e+65:
		tmp = y * b
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5e+84)
		tmp = Float64(t * b);
	elseif (t <= 6.8e+65)
		tmp = Float64(y * b);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5e+84)
		tmp = t * b;
	elseif (t <= 6.8e+65)
		tmp = y * b;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5e+84], N[(t * b), $MachinePrecision], If[LessEqual[t, 6.8e+65], N[(y * b), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000001e84 or 6.7999999999999999e65 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 42.0%

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

   if -5.0000000000000001e84 < t < 6.7999999999999999e65

   1. Initial program 94.7%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 32.3

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

   5. Applied rewrites 32.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 21.0%

      \[\leadsto b \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+65}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 18.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ y \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* y b))

C

double code(double x, double y, double z, double t, double a, double b) {
	return y * 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 = y * b
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return y * b

Julia

function code(x, y, z, t, a, b)
	return Float64(y * b)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(y * b), $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 b around inf

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

   1. lower-*.f64 N/A

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

   2. +-commutative N/A

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

   3. associate-+r- N/A

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

   4. lower-+.f64 N/A

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

   5. sub-neg N/A

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

   6. lower-+.f64 N/A

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

   7. metadata-eval 37.3

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

5. Applied rewrites 37.3%

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

6. Taylor expanded in y around inf

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

8. Applied rewrites 16.4%

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

9. Final simplification 16.4%

   \[\leadsto y \cdot b \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024238 
(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)))