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

Percentage Accurate: 95.3% → 97.8%

Time: 10.7s

Alternatives: 21

Speedup: 0.5×

• 36.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

4. Final simplification 98.9%

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

Alternative 2: 39.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ t_2 := \left(y - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-211}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-272}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, a\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)) (t_2 (* (- y 2.0) b)))
   (if (<= b -2.6e+96)
     t_2
     (if (<= b -1.08e-42)
       t_1
       (if (<= b -2.3e-211)
         (+ z x)
         (if (<= b 7.2e-272)
           (* (- 1.0 t) a)
           (if (<= b 9.6e-71)
             (fma (- y) z a)
             (if (<= b 2.6e+63) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double t_2 = (y - 2.0) * b;
	double tmp;
	if (b <= -2.6e+96) {
		tmp = t_2;
	} else if (b <= -1.08e-42) {
		tmp = t_1;
	} else if (b <= -2.3e-211) {
		tmp = z + x;
	} else if (b <= 7.2e-272) {
		tmp = (1.0 - t) * a;
	} else if (b <= 9.6e-71) {
		tmp = fma(-y, z, a);
	} else if (b <= 2.6e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	t_2 = Float64(Float64(y - 2.0) * b)
	tmp = 0.0
	if (b <= -2.6e+96)
		tmp = t_2;
	elseif (b <= -1.08e-42)
		tmp = t_1;
	elseif (b <= -2.3e-211)
		tmp = Float64(z + x);
	elseif (b <= 7.2e-272)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (b <= 9.6e-71)
		tmp = fma(Float64(-y), z, a);
	elseif (b <= 2.6e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.6e+96], t$95$2, If[LessEqual[b, -1.08e-42], t$95$1, If[LessEqual[b, -2.3e-211], N[(z + x), $MachinePrecision], If[LessEqual[b, 7.2e-272], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, 9.6e-71], N[((-y) * z + a), $MachinePrecision], If[LessEqual[b, 2.6e+63], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.6e96 or 2.6000000000000001e63 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 54.7%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 52.3%

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

   if -2.6e96 < b < -1.07999999999999996e-42 or 9.6e-71 < b < 2.6000000000000001e63

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 49.5

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

   5. Applied rewrites 49.5%

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

   if -1.07999999999999996e-42 < b < -2.29999999999999988e-211

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 64.0%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 73.7

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

   8. Applied rewrites 73.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 52.7%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 50.3%

       \[\leadsto z + x \]

   if -2.29999999999999988e-211 < b < 7.19999999999999937e-272

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 56.4

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

   5. Applied rewrites 56.4%

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

   if 7.19999999999999937e-272 < b < 9.6e-71

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 82.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 77.3%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 68.5%

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

   12. Taylor expanded in y around inf

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

   14. Applied rewrites 59.9%

       \[\leadsto \mathsf{fma}\left(-y, z, a\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, \left(1 - t\right) \cdot a\right)\\ t_2 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (* (- 1.0 t) a)))
        (t_2 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -1.6e+96)
     t_2
     (if (<= b -1.46e-58)
       t_1
       (if (<= b -2.1e-211)
         (fma (- 1.0 y) z (+ a x))
         (if (<= b 2.9e+62) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, ((1.0 - t) * a));
	double t_2 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -1.6e+96) {
		tmp = t_2;
	} else if (b <= -1.46e-58) {
		tmp = t_1;
	} else if (b <= -2.1e-211) {
		tmp = fma((1.0 - y), z, (a + x));
	} else if (b <= 2.9e+62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, Float64(Float64(1.0 - t) * a))
	t_2 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -1.6e+96)
		tmp = t_2;
	elseif (b <= -1.46e-58)
		tmp = t_1;
	elseif (b <= -2.1e-211)
		tmp = fma(Float64(1.0 - y), z, Float64(a + x));
	elseif (b <= 2.9e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -1.6e+96], t$95$2, If[LessEqual[b, -1.46e-58], t$95$1, If[LessEqual[b, -2.1e-211], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e+62], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.60000000000000003e96 or 2.89999999999999984e62 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.3%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 95.8

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

   8. Applied rewrites 95.8%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 44.7%

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

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 92.0%

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

   if -1.60000000000000003e96 < b < -1.4600000000000001e-58 or -2.10000000000000008e-211 < b < 2.89999999999999984e62

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 84.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 73.9%

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

   if -1.4600000000000001e-58 < b < -2.10000000000000008e-211

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 60.0%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 75.9

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

   8. Applied rewrites 75.9%

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

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   10. 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. *-commutative N/A

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

       3. remove-double-neg N/A

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

       4. sub-neg N/A

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

       5. metadata-eval N/A

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

       6. distribute-neg-in N/A

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

       7. metadata-eval N/A

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

       8. +-commutative N/A

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

       9. sub-neg N/A

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

       10. mul-1-neg N/A

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

       11. mul-1-neg N/A

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

       12. cancel-sign-sub-inv N/A

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

       13. *-commutative N/A

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

       14. *-commutative N/A

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

   11. Applied rewrites 96.4%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 83.1%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq -1.46 \cdot 10^{-58}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \left(1 - t\right) \cdot a\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \left(1 - t\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ t_2 := \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, b \cdot t\_1\right)\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(t\_1, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0))
        (t_2 (fma (- 1.0 t) a (fma (- 1.0 y) z (* b t_1)))))
   (if (<= a -2e-29)
     t_2
     (if (<= a 7.5e+73) (fma (- 1.0 y) z (fma t_1 b x)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double t_2 = fma((1.0 - t), a, fma((1.0 - y), z, (b * t_1)));
	double tmp;
	if (a <= -2e-29) {
		tmp = t_2;
	} else if (a <= 7.5e+73) {
		tmp = fma((1.0 - y), z, fma(t_1, b, x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	t_2 = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, Float64(b * t_1)))
	tmp = 0.0
	if (a <= -2e-29)
		tmp = t_2;
	elseif (a <= 7.5e+73)
		tmp = fma(Float64(1.0 - y), z, fma(t_1, b, x));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e-29], t$95$2, If[LessEqual[a, 7.5e+73], N[(N[(1.0 - y), $MachinePrecision] * z + N[(t$95$1 * b + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.99999999999999989e-29 or 7.5e73 < a

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.9%

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

   if -1.99999999999999989e-29 < a < 7.5e73

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.6%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 96.6

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

   8. Applied rewrites 96.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, b \cdot \left(\left(t + y\right) - 2\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, b \cdot \left(\left(t + y\right) - 2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 2\right) \cdot b\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-16}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{-141}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 1450000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 2.0) b)) (t_2 (* (- b a) t)))
   (if (<= t -5.5e+64)
     t_2
     (if (<= t -1.15e-16)
       (* (- 1.0 y) z)
       (if (<= t -4.5e-112)
         t_1
         (if (<= t 1.28e-141) (+ z x) (if (<= t 1450000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -5.5e+64) {
		tmp = t_2;
	} else if (t <= -1.15e-16) {
		tmp = (1.0 - y) * z;
	} else if (t <= -4.5e-112) {
		tmp = t_1;
	} else if (t <= 1.28e-141) {
		tmp = z + x;
	} else if (t <= 1450000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - 2.0d0) * b
    t_2 = (b - a) * t
    if (t <= (-5.5d+64)) then
        tmp = t_2
    else if (t <= (-1.15d-16)) then
        tmp = (1.0d0 - y) * z
    else if (t <= (-4.5d-112)) then
        tmp = t_1
    else if (t <= 1.28d-141) then
        tmp = z + x
    else if (t <= 1450000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -5.5e+64) {
		tmp = t_2;
	} else if (t <= -1.15e-16) {
		tmp = (1.0 - y) * z;
	} else if (t <= -4.5e-112) {
		tmp = t_1;
	} else if (t <= 1.28e-141) {
		tmp = z + x;
	} else if (t <= 1450000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y - 2.0) * b
	t_2 = (b - a) * t
	tmp = 0
	if t <= -5.5e+64:
		tmp = t_2
	elif t <= -1.15e-16:
		tmp = (1.0 - y) * z
	elif t <= -4.5e-112:
		tmp = t_1
	elif t <= 1.28e-141:
		tmp = z + x
	elif t <= 1450000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 2.0) * b)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -5.5e+64)
		tmp = t_2;
	elseif (t <= -1.15e-16)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= -4.5e-112)
		tmp = t_1;
	elseif (t <= 1.28e-141)
		tmp = Float64(z + x);
	elseif (t <= 1450000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y - 2.0) * b;
	t_2 = (b - a) * t;
	tmp = 0.0;
	if (t <= -5.5e+64)
		tmp = t_2;
	elseif (t <= -1.15e-16)
		tmp = (1.0 - y) * z;
	elseif (t <= -4.5e-112)
		tmp = t_1;
	elseif (t <= 1.28e-141)
		tmp = z + x;
	elseif (t <= 1450000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.5e+64], t$95$2, If[LessEqual[t, -1.15e-16], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, -4.5e-112], t$95$1, If[LessEqual[t, 1.28e-141], N[(z + x), $MachinePrecision], If[LessEqual[t, 1450000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.4999999999999996e64 or 1.45e6 < t

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.3

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

   5. Applied rewrites 67.3%

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

   if -5.4999999999999996e64 < t < -1.15e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 58.6

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

   5. Applied rewrites 58.6%

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

   if -1.15e-16 < t < -4.50000000000000012e-112 or 1.2799999999999999e-141 < t < 1.45e6

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 79.1%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 53.4%

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

   if -4.50000000000000012e-112 < t < 1.2799999999999999e-141

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 79.4

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

   8. Applied rewrites 79.4%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 50.4%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 42.7%

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

Alternative 6: 39.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-211}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-272}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 2.0) b)))
   (if (<= b -4.7e+153)
     t_1
     (if (<= b -6.2e+86)
       (* b t)
       (if (<= b -2.3e-211)
         (+ z x)
         (if (<= b 7.2e-272)
           (* (- 1.0 t) a)
           (if (<= b 1.22e+123) (fma (- y) z a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double tmp;
	if (b <= -4.7e+153) {
		tmp = t_1;
	} else if (b <= -6.2e+86) {
		tmp = b * t;
	} else if (b <= -2.3e-211) {
		tmp = z + x;
	} else if (b <= 7.2e-272) {
		tmp = (1.0 - t) * a;
	} else if (b <= 1.22e+123) {
		tmp = fma(-y, z, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 2.0) * b)
	tmp = 0.0
	if (b <= -4.7e+153)
		tmp = t_1;
	elseif (b <= -6.2e+86)
		tmp = Float64(b * t);
	elseif (b <= -2.3e-211)
		tmp = Float64(z + x);
	elseif (b <= 7.2e-272)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (b <= 1.22e+123)
		tmp = fma(Float64(-y), z, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.7e+153], t$95$1, If[LessEqual[b, -6.2e+86], N[(b * t), $MachinePrecision], If[LessEqual[b, -2.3e-211], N[(z + x), $MachinePrecision], If[LessEqual[b, 7.2e-272], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, 1.22e+123], N[((-y) * z + a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.69999999999999968e153 or 1.22e123 < b

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.0%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 59.5%

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

   if -4.69999999999999968e153 < b < -6.2000000000000004e86

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 87.1

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

   8. Applied rewrites 87.1%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 48.2%

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

   if -6.2000000000000004e86 < b < -2.29999999999999988e-211

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 71.1%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 72.9

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

   8. Applied rewrites 72.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 51.9%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 44.9%

       \[\leadsto z + x \]

   if -2.29999999999999988e-211 < b < 7.19999999999999937e-272

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 56.4

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

   5. Applied rewrites 56.4%

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

   if 7.19999999999999937e-272 < b < 1.22e123

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 80.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 56.0%

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

   12. Taylor expanded in y around inf

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

   14. Applied rewrites 45.3%

       \[\leadsto \mathsf{fma}\left(-y, z, a\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 7: 87.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-30}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (fma (- (+ t y) 2.0) b x))))
   (if (<= b -1.45e+16)
     t_1
     (if (<= b 1.9e-30) (- x (fma z (- y 1.0) (* a (- t 1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, fma(((t + y) - 2.0), b, x));
	double tmp;
	if (b <= -1.45e+16) {
		tmp = t_1;
	} else if (b <= 1.9e-30) {
		tmp = x - fma(z, (y - 1.0), (a * (t - 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, fma(Float64(Float64(t + y) - 2.0), b, x))
	tmp = 0.0
	if (b <= -1.45e+16)
		tmp = t_1;
	elseif (b <= 1.9e-30)
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(a * Float64(t - 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+16], t$95$1, If[LessEqual[b, 1.9e-30], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.45e16 or 1.9000000000000002e-30 < b

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.2%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 92.6

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

   8. Applied rewrites 92.6%

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

   if -1.45e16 < b < 1.9000000000000002e-30

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 93.0

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

   8. Applied rewrites 93.0%

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

Alternative 8: 87.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+62}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))))
   (if (<= b -2.6e+96)
     t_1
     (if (<= b 1.8e+62) (- x (fma z (- y 1.0) (* a (- t 1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	double tmp;
	if (b <= -2.6e+96) {
		tmp = t_1;
	} else if (b <= 1.8e+62) {
		tmp = x - fma(z, (y - 1.0), (a * (t - 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x))
	tmp = 0.0
	if (b <= -2.6e+96)
		tmp = t_1;
	elseif (b <= 1.8e+62)
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(a * Float64(t - 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+96], t$95$1, If[LessEqual[b, 1.8e+62], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.6e96 or 1.8e62 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 94.2

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

   5. Applied rewrites 94.2%

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

   if -2.6e96 < b < 1.8e62

   1. Initial program 97.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.6%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 89.5

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

   8. Applied rewrites 89.5%

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

Alternative 9: 49.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-81}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-206}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 3950:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -7.5e+25)
     t_1
     (if (<= y -2.9e-81)
       (+ z x)
       (if (<= y 3.8e-206) (* (- b a) t) (if (<= y 3950.0) (+ z x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -7.5e+25) {
		tmp = t_1;
	} else if (y <= -2.9e-81) {
		tmp = z + x;
	} else if (y <= 3.8e-206) {
		tmp = (b - a) * t;
	} else if (y <= 3950.0) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-7.5d+25)) then
        tmp = t_1
    else if (y <= (-2.9d-81)) then
        tmp = z + x
    else if (y <= 3.8d-206) then
        tmp = (b - a) * t
    else if (y <= 3950.0d0) then
        tmp = z + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -7.5e+25) {
		tmp = t_1;
	} else if (y <= -2.9e-81) {
		tmp = z + x;
	} else if (y <= 3.8e-206) {
		tmp = (b - a) * t;
	} else if (y <= 3950.0) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -7.5e+25:
		tmp = t_1
	elif y <= -2.9e-81:
		tmp = z + x
	elif y <= 3.8e-206:
		tmp = (b - a) * t
	elif y <= 3950.0:
		tmp = z + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -7.5e+25)
		tmp = t_1;
	elseif (y <= -2.9e-81)
		tmp = Float64(z + x);
	elseif (y <= 3.8e-206)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 3950.0)
		tmp = Float64(z + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -7.5e+25)
		tmp = t_1;
	elseif (y <= -2.9e-81)
		tmp = z + x;
	elseif (y <= 3.8e-206)
		tmp = (b - a) * t;
	elseif (y <= 3950.0)
		tmp = z + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -7.5e+25], t$95$1, If[LessEqual[y, -2.9e-81], N[(z + x), $MachinePrecision], If[LessEqual[y, 3.8e-206], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 3950.0], N[(z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.49999999999999993e25 or 3950 < y

   1. Initial program 91.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.8

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

   5. Applied rewrites 68.8%

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

   if -7.49999999999999993e25 < y < -2.89999999999999989e-81 or 3.80000000000000003e-206 < y < 3950

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 67.4%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 75.7

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

   8. Applied rewrites 75.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 72.0%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 50.2%

       \[\leadsto z + x \]

   if -2.89999999999999989e-81 < y < 3.80000000000000003e-206

   1. Initial program 98.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 50.9

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

   5. Applied rewrites 50.9%

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

Alternative 10: 38.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-246}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+123}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 2.0) b)))
   (if (<= b -4.7e+153)
     t_1
     (if (<= b -6.2e+86)
       (* b t)
       (if (<= b -4.6e-246)
         (+ z x)
         (if (<= b 1.22e+123) (fma (- y) z a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double tmp;
	if (b <= -4.7e+153) {
		tmp = t_1;
	} else if (b <= -6.2e+86) {
		tmp = b * t;
	} else if (b <= -4.6e-246) {
		tmp = z + x;
	} else if (b <= 1.22e+123) {
		tmp = fma(-y, z, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 2.0) * b)
	tmp = 0.0
	if (b <= -4.7e+153)
		tmp = t_1;
	elseif (b <= -6.2e+86)
		tmp = Float64(b * t);
	elseif (b <= -4.6e-246)
		tmp = Float64(z + x);
	elseif (b <= 1.22e+123)
		tmp = fma(Float64(-y), z, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.7e+153], t$95$1, If[LessEqual[b, -6.2e+86], N[(b * t), $MachinePrecision], If[LessEqual[b, -4.6e-246], N[(z + x), $MachinePrecision], If[LessEqual[b, 1.22e+123], N[((-y) * z + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.69999999999999968e153 or 1.22e123 < b

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.0%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 59.5%

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

   if -4.69999999999999968e153 < b < -6.2000000000000004e86

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 87.1

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

   8. Applied rewrites 87.1%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 48.2%

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

   if -6.2000000000000004e86 < b < -4.5999999999999995e-246

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 72.4%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 69.7

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

   8. Applied rewrites 69.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 49.3%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 43.2%

       \[\leadsto z + x \]

   if -4.5999999999999995e-246 < b < 1.22e123

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 71.6%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 53.5%

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

   12. Taylor expanded in y around inf

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

   14. Applied rewrites 44.1%

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

Alternative 11: 84.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+62}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -2.7e+96)
     t_1
     (if (<= b 7.2e+62) (- x (fma z (- y 1.0) (* a (- t 1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -2.7e+96) {
		tmp = t_1;
	} else if (b <= 7.2e+62) {
		tmp = x - fma(z, (y - 1.0), (a * (t - 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -2.7e+96)
		tmp = t_1;
	elseif (b <= 7.2e+62)
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(a * Float64(t - 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -2.7e+96], t$95$1, If[LessEqual[b, 7.2e+62], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.70000000000000022e96 or 7.2e62 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.3%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 95.8

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

   8. Applied rewrites 95.8%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 44.7%

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

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 92.0%

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

   if -2.70000000000000022e96 < b < 7.2e62

   1. Initial program 97.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.6%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 89.5

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

   8. Applied rewrites 89.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+62}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-50}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 1450000:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -6e+64)
     t_1
     (if (<= t -5.8e-50)
       (* (- b z) y)
       (if (<= t 1450000.0) (fma (- y 2.0) b a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -6e+64) {
		tmp = t_1;
	} else if (t <= -5.8e-50) {
		tmp = (b - z) * y;
	} else if (t <= 1450000.0) {
		tmp = fma((y - 2.0), b, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -6e+64)
		tmp = t_1;
	elseif (t <= -5.8e-50)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 1450000.0)
		tmp = fma(Float64(y - 2.0), b, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6e+64], t$95$1, If[LessEqual[t, -5.8e-50], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1450000.0], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.0000000000000004e64 or 1.45e6 < t

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.3

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

   5. Applied rewrites 67.3%

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

   if -6.0000000000000004e64 < t < -5.80000000000000016e-50

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.6

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

   5. Applied rewrites 73.6%

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

   if -5.80000000000000016e-50 < t < 1.45e6

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 77.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 74.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 50.7%

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

Alternative 13: 56.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-119}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -6e+64)
     t_1
     (if (<= t -6.2e-119)
       (* (- b z) y)
       (if (<= t 6.5e+31) (fma (- 1.0 y) z a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -6e+64) {
		tmp = t_1;
	} else if (t <= -6.2e-119) {
		tmp = (b - z) * y;
	} else if (t <= 6.5e+31) {
		tmp = fma((1.0 - y), z, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -6e+64)
		tmp = t_1;
	elseif (t <= -6.2e-119)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 6.5e+31)
		tmp = fma(Float64(1.0 - y), z, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6e+64], t$95$1, If[LessEqual[t, -6.2e-119], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 6.5e+31], N[(N[(1.0 - y), $MachinePrecision] * z + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.0000000000000004e64 or 6.5000000000000004e31 < t

   1. Initial program 91.2%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.0

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

   5. Applied rewrites 69.0%

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

   if -6.0000000000000004e64 < t < -6.19999999999999956e-119

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.1

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

   5. Applied rewrites 64.1%

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

   if -6.19999999999999956e-119 < t < 6.5000000000000004e31

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 51.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 50.1%

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

Alternative 14: 34.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-246}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.2e+86)
   (* b t)
   (if (<= b -4.6e-246) (+ z x) (if (<= b 5.9e+85) (fma (- y) z a) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+86) {
		tmp = b * t;
	} else if (b <= -4.6e-246) {
		tmp = z + x;
	} else if (b <= 5.9e+85) {
		tmp = fma(-y, z, a);
	} else {
		tmp = b * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.2e+86)
		tmp = Float64(b * t);
	elseif (b <= -4.6e-246)
		tmp = Float64(z + x);
	elseif (b <= 5.9e+85)
		tmp = fma(Float64(-y), z, a);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.2e+86], N[(b * t), $MachinePrecision], If[LessEqual[b, -4.6e-246], N[(z + x), $MachinePrecision], If[LessEqual[b, 5.9e+85], N[((-y) * z + a), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.2000000000000004e86 or 5.9e85 < b

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 91.6%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 95.0

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

   8. Applied rewrites 95.0%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 45.4%

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

   if -6.2000000000000004e86 < b < -4.5999999999999995e-246

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 72.4%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 69.7

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

   8. Applied rewrites 69.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 49.3%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 43.2%

       \[\leadsto z + x \]

   if -4.5999999999999995e-246 < b < 5.9e85

   1. Initial program 97.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 73.0%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 56.1%

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

   12. Taylor expanded in y around inf

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

   14. Applied rewrites 45.9%

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

Alternative 15: 71.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -4.7e+86) t_1 (if (<= b 1.2e+32) (fma (- 1.0 y) z (+ a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -4.7e+86) {
		tmp = t_1;
	} else if (b <= 1.2e+32) {
		tmp = fma((1.0 - y), z, (a + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -4.7e+86)
		tmp = t_1;
	elseif (b <= 1.2e+32)
		tmp = fma(Float64(1.0 - y), z, Float64(a + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -4.7e+86], t$95$1, If[LessEqual[b, 1.2e+32], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.7000000000000002e86 or 1.19999999999999996e32 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.3%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 93.5

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

   8. Applied rewrites 93.5%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 43.5%

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

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 87.5%

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

   if -4.7000000000000002e86 < b < 1.19999999999999996e32

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 77.8%

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

   6. Taylor expanded in a around 0

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

      1. cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

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

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

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

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

      5. sub-neg N/A

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

      6. metadata-eval N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. lower--.f64 N/A

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

      16. +-commutative N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 66.9

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

   8. Applied rewrites 66.9%

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

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   10. 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. *-commutative N/A

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

       3. remove-double-neg N/A

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

       4. sub-neg N/A

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

       5. metadata-eval N/A

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

       6. distribute-neg-in N/A

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

       7. metadata-eval N/A

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

       8. +-commutative N/A

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

       9. sub-neg N/A

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

       10. mul-1-neg N/A

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

       11. mul-1-neg N/A

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

       12. cancel-sign-sub-inv N/A

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

       13. *-commutative N/A

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

       14. *-commutative N/A

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

   11. Applied rewrites 90.8%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 72.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 64.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -2.5e+86) t_1 (if (<= b 8.5e+30) (fma (- 1.0 y) z x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -2.5e+86) {
		tmp = t_1;
	} else if (b <= 8.5e+30) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -2.5e+86)
		tmp = t_1;
	elseif (b <= 8.5e+30)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -2.5e+86], t$95$1, If[LessEqual[b, 8.5e+30], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4999999999999999e86 or 8.4999999999999995e30 < b

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   7. Step-by-step derivation

      1. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto z \cdot \left(\color{blue}{-1 \cdot y} + \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto z \cdot \color{blue}{\left(1 + -1 \cdot y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. sub-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      19. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      20. lower-+.f64 93.5

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   8. Applied rewrites 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   10. Step-by-step derivation

   11. Applied rewrites 43.5%

       \[\leadsto b \cdot \color{blue}{t} \]

   12. Taylor expanded in z around 0

       \[\leadsto x + \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   13. Step-by-step derivation

   14. Applied rewrites 87.5%

       \[\leadsto \mathsf{fma}\left(\left(y + t\right) - 2, \color{blue}{b}, x\right) \]

   if -2.4999999999999999e86 < b < 8.4999999999999995e30

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   7. Step-by-step derivation

      1. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto z \cdot \left(\color{blue}{-1 \cdot y} + \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto z \cdot \color{blue}{\left(1 + -1 \cdot y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. sub-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      19. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      20. lower-+.f64 66.9

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   8. Applied rewrites 66.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{z \cdot \left(1 - y\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 59.8%

       \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 66.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.9e+26) t_1 (if (<= y 7.5e+22) (+ (fma (- t 2.0) b z) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4.9e+26) {
		tmp = t_1;
	} else if (y <= 7.5e+22) {
		tmp = fma((t - 2.0), b, z) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4.9e+26)
		tmp = t_1;
	elseif (y <= 7.5e+22)
		tmp = Float64(fma(Float64(t - 2.0), b, z) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.9e+26], t$95$1, If[LessEqual[y, 7.5e+22], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.89999999999999974e26 or 7.5000000000000002e22 < y

   1. Initial program 90.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      3. lower--.f64 71.4

         \[\leadsto \color{blue}{\left(b - z\right)} \cdot y \]

   5. Applied rewrites 71.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -4.89999999999999974e26 < y < 7.5000000000000002e22

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   7. Step-by-step derivation

      1. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto z \cdot \left(\color{blue}{-1 \cdot y} + \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto z \cdot \color{blue}{\left(1 + -1 \cdot y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. sub-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      19. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      20. lower-+.f64 74.9

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   8. Applied rewrites 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{\left(z + b \cdot \left(t - 2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 71.7%

       \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 57.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.9e+26) t_1 (if (<= y 7.5e+22) (fma (- t 2.0) b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4.9e+26) {
		tmp = t_1;
	} else if (y <= 7.5e+22) {
		tmp = fma((t - 2.0), b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4.9e+26)
		tmp = t_1;
	elseif (y <= 7.5e+22)
		tmp = fma(Float64(t - 2.0), b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.9e+26], t$95$1, If[LessEqual[y, 7.5e+22], N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.89999999999999974e26 or 7.5000000000000002e22 < y

   1. Initial program 90.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      3. lower--.f64 71.4

         \[\leadsto \color{blue}{\left(b - z\right)} \cdot y \]

   5. Applied rewrites 71.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -4.89999999999999974e26 < y < 7.5000000000000002e22

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   7. Step-by-step derivation

      1. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto z \cdot \left(\color{blue}{-1 \cdot y} + \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto z \cdot \color{blue}{\left(1 + -1 \cdot y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. sub-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      19. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      20. lower-+.f64 74.9

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   8. Applied rewrites 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{\left(z + b \cdot \left(t - 2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 71.7%

       \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \color{blue}{x} \]

   12. Taylor expanded in z around 0

       \[\leadsto x + b \cdot \color{blue}{\left(t - 2\right)} \]
   13. Step-by-step derivation

   14. Applied rewrites 55.8%

       \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 33.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+98}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.2e+86) (* b t) (if (<= b 4.2e+98) (+ z x) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+86) {
		tmp = b * t;
	} else if (b <= 4.2e+98) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.2d+86)) then
        tmp = b * t
    else if (b <= 4.2d+98) then
        tmp = z + x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+86) {
		tmp = b * t;
	} else if (b <= 4.2e+98) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.2e+86:
		tmp = b * t
	elif b <= 4.2e+98:
		tmp = z + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.2e+86)
		tmp = Float64(b * t);
	elseif (b <= 4.2e+98)
		tmp = Float64(z + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.2e+86)
		tmp = b * t;
	elseif (b <= 4.2e+98)
		tmp = z + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.2e+86], N[(b * t), $MachinePrecision], If[LessEqual[b, 4.2e+98], N[(z + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.2000000000000004e86 or 4.20000000000000008e98 < b

   1. Initial program 90.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 92.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   7. Step-by-step derivation

      1. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto z \cdot \left(\color{blue}{-1 \cdot y} + \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto z \cdot \color{blue}{\left(1 + -1 \cdot y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. sub-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      19. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      20. lower-+.f64 95.8

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   8. Applied rewrites 95.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   10. Step-by-step derivation

   11. Applied rewrites 46.2%

       \[\leadsto b \cdot \color{blue}{t} \]

   if -6.2000000000000004e86 < b < 4.20000000000000008e98

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   7. Step-by-step derivation

      1. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto z \cdot \left(\color{blue}{-1 \cdot y} + \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto z \cdot \color{blue}{\left(1 + -1 \cdot y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. sub-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      19. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      20. lower-+.f64 66.9

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   8. Applied rewrites 66.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{\left(z + b \cdot \left(t - 2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 39.9%

       \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \color{blue}{x} \]

   12. Taylor expanded in b around 0

       \[\leadsto x + z \]
   13. Step-by-step derivation

   14. Applied rewrites 35.9%

       \[\leadsto z + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 30.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+177}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+133}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.3e+177) (+ a z) (if (<= a 4.4e+133) (+ z x) (+ a z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.3e+177) {
		tmp = a + z;
	} else if (a <= 4.4e+133) {
		tmp = z + x;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3.3d+177)) then
        tmp = a + z
    else if (a <= 4.4d+133) then
        tmp = z + x
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.3e+177) {
		tmp = a + z;
	} else if (a <= 4.4e+133) {
		tmp = z + x;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.3e+177:
		tmp = a + z
	elif a <= 4.4e+133:
		tmp = z + x
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.3e+177)
		tmp = Float64(a + z);
	elseif (a <= 4.4e+133)
		tmp = Float64(z + x);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.3e+177)
		tmp = a + z;
	elseif (a <= 4.4e+133)
		tmp = z + x;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.3e+177], N[(a + z), $MachinePrecision], If[LessEqual[a, 4.4e+133], N[(z + x), $MachinePrecision], N[(a + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3000000000000001e177 or 4.4e133 < a

   1. Initial program 89.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 93.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto a \cdot \left(1 - t\right) + \color{blue}{z \cdot \left(1 - y\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 77.9%

      \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, \left(1 - t\right) \cdot a\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto a + z \cdot \color{blue}{\left(1 - y\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 41.8%

       \[\leadsto \mathsf{fma}\left(1 - y, z, a\right) \]

   12. Taylor expanded in y around 0

       \[\leadsto a + z \]
   13. Step-by-step derivation

   14. Applied rewrites 30.5%

       \[\leadsto z + a \]

   if -3.3000000000000001e177 < a < 4.4e133

   1. Initial program 96.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]
   7. Step-by-step derivation

      1. cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z\right)\right) \cdot \left(y - 1\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. sub-neg N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\left(y + \color{blue}{-1}\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + \left(\mathsf{neg}\left(-1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto z \cdot \left(\color{blue}{-1 \cdot y} + \left(\mathsf{neg}\left(-1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto z \cdot \left(-1 \cdot y + \color{blue}{1}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto z \cdot \color{blue}{\left(1 + -1 \cdot y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. sub-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(1 - y\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      18. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      19. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      20. lower-+.f64 90.4

          \[\leadsto \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   8. Applied rewrites 90.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{\left(z + b \cdot \left(t - 2\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 59.3%

       \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \color{blue}{x} \]

   12. Taylor expanded in b around 0

       \[\leadsto x + z \]
   13. Step-by-step derivation

   14. Applied rewrites 31.4%

       \[\leadsto z + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+177}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+133}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 20.4% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ a + z \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ a z))

C

double code(double x, double y, double z, double t, double a, double b) {
	return a + z;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a + z
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a + z;
}

Python

def code(x, y, z, t, a, b):
	return a + z

Julia

function code(x, y, z, t, a, b)
	return Float64(a + z)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a + z;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + z), $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

   \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

5. Applied rewrites 83.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, \left(\left(t + y\right) - 2\right) \cdot b\right)\right)} \]

6. Taylor expanded in b around 0

   \[\leadsto a \cdot \left(1 - t\right) + \color{blue}{z \cdot \left(1 - y\right)} \]
7. Step-by-step derivation

8. Applied rewrites 51.0%

   \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, \left(1 - t\right) \cdot a\right) \]

9. Taylor expanded in t around 0

   \[\leadsto a + z \cdot \color{blue}{\left(1 - y\right)} \]
10. Step-by-step derivation

11. Applied rewrites 36.2%

    \[\leadsto \mathsf{fma}\left(1 - y, z, a\right) \]

12. Taylor expanded in y around 0

    \[\leadsto a + z \]
13. Step-by-step derivation

14. Applied rewrites 18.6%

    \[\leadsto z + a \]

15. Final simplification 18.6%

    \[\leadsto a + z \]
16. Add Preprocessing

Reproduce

herbie shell --seed 2024298 
(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)))