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

Percentage Accurate: 94.9% → 97.3%

Time: 10.4s

Alternatives: 21

Speedup: 1.2×

• 36.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.9% 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: 97.3% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in y around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate--l+ N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower--.f64 N/A

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

   7. +-commutative N/A

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

   8. associate--l+ N/A

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

   9. *-commutative N/A

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

   10. lower-fma.f64 N/A

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

   11. lower--.f64 N/A

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

   12. +-commutative N/A

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

   13. associate--r+ N/A

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

   14. fp-cancel-sub-sign-inv N/A

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

   15. +-commutative N/A

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

   16. associate--l+ N/A

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

5. Applied rewrites 99.6%

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

Alternative 2: 55.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.0008:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-248}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right)\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-140}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -1.65e+58)
     t_1
     (if (<= y -0.0008)
       (* (- b a) t)
       (if (<= y 5.6e-248)
         (fma -2.0 b (+ z x))
         (if (<= y 7.1e-140)
           (* (- 1.0 t) a)
           (if (<= y 1.7e-5)
             (fma (- t 2.0) b z)
             (if (<= y 6.5e+95) (* (- (+ t y) 2.0) b) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -1.65e+58) {
		tmp = t_1;
	} else if (y <= -0.0008) {
		tmp = (b - a) * t;
	} else if (y <= 5.6e-248) {
		tmp = fma(-2.0, b, (z + x));
	} else if (y <= 7.1e-140) {
		tmp = (1.0 - t) * a;
	} else if (y <= 1.7e-5) {
		tmp = fma((t - 2.0), b, z);
	} else if (y <= 6.5e+95) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -1.65e+58)
		tmp = t_1;
	elseif (y <= -0.0008)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 5.6e-248)
		tmp = fma(-2.0, b, Float64(z + x));
	elseif (y <= 7.1e-140)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (y <= 1.7e-5)
		tmp = fma(Float64(t - 2.0), b, z);
	elseif (y <= 6.5e+95)
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.65e+58], t$95$1, If[LessEqual[y, -0.0008], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 5.6e-248], N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.1e-140], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 1.7e-5], N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision], If[LessEqual[y, 6.5e+95], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.64999999999999991e58 or 6.5e95 < y

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.9

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

   5. Applied rewrites 64.9%

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

   if -1.64999999999999991e58 < y < -8.00000000000000038e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.0

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

   5. Applied rewrites 68.0%

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

   if -8.00000000000000038e-4 < y < 5.6000000000000002e-248

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 69.6%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 62.2%

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

   if 5.6000000000000002e-248 < y < 7.09999999999999986e-140

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 61.6

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

   5. Applied rewrites 61.6%

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

   if 7.09999999999999986e-140 < y < 1.7e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 79.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 65.6%

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

   if 1.7e-5 < y < 6.5e95

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 62.2

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

   5. Applied rewrites 62.2%

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 3: 39.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;b \leq -2 \cdot 10^{+68}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2700:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-255}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= b -2e+68)
     (* (- y 2.0) b)
     (if (<= b -2700.0)
       (+ z x)
       (if (<= b -7.8e-255)
         (* (- 1.0 y) z)
         (if (<= b 9e-269)
           t_1
           (if (<= b 1.1e-158)
             (+ z x)
             (if (<= b 2.9e+131) t_1 (* (- t 2.0) b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (b <= -2e+68) {
		tmp = (y - 2.0) * b;
	} else if (b <= -2700.0) {
		tmp = z + x;
	} else if (b <= -7.8e-255) {
		tmp = (1.0 - y) * z;
	} else if (b <= 9e-269) {
		tmp = t_1;
	} else if (b <= 1.1e-158) {
		tmp = z + x;
	} else if (b <= 2.9e+131) {
		tmp = t_1;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - t) * a
    if (b <= (-2d+68)) then
        tmp = (y - 2.0d0) * b
    else if (b <= (-2700.0d0)) then
        tmp = z + x
    else if (b <= (-7.8d-255)) then
        tmp = (1.0d0 - y) * z
    else if (b <= 9d-269) then
        tmp = t_1
    else if (b <= 1.1d-158) then
        tmp = z + x
    else if (b <= 2.9d+131) then
        tmp = t_1
    else
        tmp = (t - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (b <= -2e+68) {
		tmp = (y - 2.0) * b;
	} else if (b <= -2700.0) {
		tmp = z + x;
	} else if (b <= -7.8e-255) {
		tmp = (1.0 - y) * z;
	} else if (b <= 9e-269) {
		tmp = t_1;
	} else if (b <= 1.1e-158) {
		tmp = z + x;
	} else if (b <= 2.9e+131) {
		tmp = t_1;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - t) * a
	tmp = 0
	if b <= -2e+68:
		tmp = (y - 2.0) * b
	elif b <= -2700.0:
		tmp = z + x
	elif b <= -7.8e-255:
		tmp = (1.0 - y) * z
	elif b <= 9e-269:
		tmp = t_1
	elif b <= 1.1e-158:
		tmp = z + x
	elif b <= 2.9e+131:
		tmp = t_1
	else:
		tmp = (t - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (b <= -2e+68)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= -2700.0)
		tmp = Float64(z + x);
	elseif (b <= -7.8e-255)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (b <= 9e-269)
		tmp = t_1;
	elseif (b <= 1.1e-158)
		tmp = Float64(z + x);
	elseif (b <= 2.9e+131)
		tmp = t_1;
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - t) * a;
	tmp = 0.0;
	if (b <= -2e+68)
		tmp = (y - 2.0) * b;
	elseif (b <= -2700.0)
		tmp = z + x;
	elseif (b <= -7.8e-255)
		tmp = (1.0 - y) * z;
	elseif (b <= 9e-269)
		tmp = t_1;
	elseif (b <= 1.1e-158)
		tmp = z + x;
	elseif (b <= 2.9e+131)
		tmp = t_1;
	else
		tmp = (t - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[b, -2e+68], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -2700.0], N[(z + x), $MachinePrecision], If[LessEqual[b, -7.8e-255], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, 9e-269], t$95$1, If[LessEqual[b, 1.1e-158], N[(z + x), $MachinePrecision], If[LessEqual[b, 2.9e+131], t$95$1, N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.99999999999999991e68

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 77.6

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.9%

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

   if -1.99999999999999991e68 < b < -2700 or 9.0000000000000003e-269 < b < 1.1000000000000001e-158

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 65.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 26.1%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 57.5%

       \[\leadsto z + x \]

   if -2700 < b < -7.8000000000000001e-255

   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. lower-*.f64 N/A

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

      3. lower--.f64 48.8

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

   5. Applied rewrites 48.8%

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

   if -7.8000000000000001e-255 < b < 9.0000000000000003e-269 or 1.1000000000000001e-158 < b < 2.9000000000000001e131

   1. Initial program 95.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 47.0

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

   5. Applied rewrites 47.0%

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

   if 2.9000000000000001e131 < b

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 89.9

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 66.5%

      \[\leadsto \left(t - 2\right) \cdot b \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 55.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.0008:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-248}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right)\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-140}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -1.65e+58)
     t_1
     (if (<= y -0.0008)
       (* (- b a) t)
       (if (<= y 5.6e-248)
         (fma -2.0 b (+ z x))
         (if (<= y 7.1e-140)
           (* (- 1.0 t) a)
           (if (<= y 6e+19) (fma (- t 2.0) b z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -1.65e+58) {
		tmp = t_1;
	} else if (y <= -0.0008) {
		tmp = (b - a) * t;
	} else if (y <= 5.6e-248) {
		tmp = fma(-2.0, b, (z + x));
	} else if (y <= 7.1e-140) {
		tmp = (1.0 - t) * a;
	} else if (y <= 6e+19) {
		tmp = fma((t - 2.0), b, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -1.65e+58)
		tmp = t_1;
	elseif (y <= -0.0008)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 5.6e-248)
		tmp = fma(-2.0, b, Float64(z + x));
	elseif (y <= 7.1e-140)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (y <= 6e+19)
		tmp = fma(Float64(t - 2.0), b, z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.65e+58], t$95$1, If[LessEqual[y, -0.0008], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 5.6e-248], N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.1e-140], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 6e+19], N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.64999999999999991e58 or 6e19 < 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 63.6

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

   5. Applied rewrites 63.6%

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

   if -1.64999999999999991e58 < y < -8.00000000000000038e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.0

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

   5. Applied rewrites 68.0%

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

   if -8.00000000000000038e-4 < y < 5.6000000000000002e-248

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 69.6%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 62.2%

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

   if 5.6000000000000002e-248 < y < 7.09999999999999986e-140

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 61.6

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

   5. Applied rewrites 61.6%

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

   if 7.09999999999999986e-140 < y < 6e19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 73.4%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 56.7%

       \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 50.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.0008:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-221}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-140}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -1.65e+58)
     t_1
     (if (<= y -0.0008)
       (* (- b a) t)
       (if (<= y -1.45e-221)
         (+ z x)
         (if (<= y 7.1e-140)
           (* (- 1.0 t) a)
           (if (<= y 6e+19) (fma (- t 2.0) b z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -1.65e+58) {
		tmp = t_1;
	} else if (y <= -0.0008) {
		tmp = (b - a) * t;
	} else if (y <= -1.45e-221) {
		tmp = z + x;
	} else if (y <= 7.1e-140) {
		tmp = (1.0 - t) * a;
	} else if (y <= 6e+19) {
		tmp = fma((t - 2.0), b, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -1.65e+58)
		tmp = t_1;
	elseif (y <= -0.0008)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= -1.45e-221)
		tmp = Float64(z + x);
	elseif (y <= 7.1e-140)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (y <= 6e+19)
		tmp = fma(Float64(t - 2.0), b, z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.65e+58], t$95$1, If[LessEqual[y, -0.0008], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -1.45e-221], N[(z + x), $MachinePrecision], If[LessEqual[y, 7.1e-140], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[y, 6e+19], N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.64999999999999991e58 or 6e19 < 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 63.6

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

   5. Applied rewrites 63.6%

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

   if -1.64999999999999991e58 < y < -8.00000000000000038e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.0

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

   5. Applied rewrites 68.0%

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

   if -8.00000000000000038e-4 < y < -1.44999999999999997e-221

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 78.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 43.2%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 52.5%

       \[\leadsto z + x \]

   if -1.44999999999999997e-221 < y < 7.09999999999999986e-140

   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. lower-*.f64 N/A

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

      3. lower--.f64 54.5

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

   5. Applied rewrites 54.5%

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

   if 7.09999999999999986e-140 < y < 6e19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 73.4%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 56.7%

       \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 6: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.36 \cdot 10^{-40} \lor \neg \left(b \leq 1.15 \cdot 10^{-46}\right):\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.36e-40) (not (<= b 1.15e-46)))
   (fma (- b z) y (fma (- t 2.0) b (fma (- 1.0 t) a z)))
   (fma (- 1.0 y) z (fma (- 1.0 t) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.36e-40) || !(b <= 1.15e-46)) {
		tmp = fma((b - z), y, fma((t - 2.0), b, fma((1.0 - t), a, z)));
	} else {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.36e-40) || !(b <= 1.15e-46))
		tmp = fma(Float64(b - z), y, fma(Float64(t - 2.0), b, fma(Float64(1.0 - t), a, z)));
	else
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.36e-40], N[Not[LessEqual[b, 1.15e-46]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3599999999999999e-40 or 1.15e-46 < b

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 91.9%

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

   if -1.3599999999999999e-40 < b < 1.15e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 100.0%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.36 \cdot 10^{-40} \lor \neg \left(b \leq 1.15 \cdot 10^{-46}\right):\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;b \leq -2 \cdot 10^{+68}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-255}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-158}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= b -2e+68)
     (* (- y 2.0) b)
     (if (<= b -4.1e-255)
       (+ z x)
       (if (<= b 9e-269)
         t_1
         (if (<= b 1.1e-158)
           (+ z x)
           (if (<= b 2.9e+131) t_1 (* (- t 2.0) b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (b <= -2e+68) {
		tmp = (y - 2.0) * b;
	} else if (b <= -4.1e-255) {
		tmp = z + x;
	} else if (b <= 9e-269) {
		tmp = t_1;
	} else if (b <= 1.1e-158) {
		tmp = z + x;
	} else if (b <= 2.9e+131) {
		tmp = t_1;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - t) * a
    if (b <= (-2d+68)) then
        tmp = (y - 2.0d0) * b
    else if (b <= (-4.1d-255)) then
        tmp = z + x
    else if (b <= 9d-269) then
        tmp = t_1
    else if (b <= 1.1d-158) then
        tmp = z + x
    else if (b <= 2.9d+131) then
        tmp = t_1
    else
        tmp = (t - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (b <= -2e+68) {
		tmp = (y - 2.0) * b;
	} else if (b <= -4.1e-255) {
		tmp = z + x;
	} else if (b <= 9e-269) {
		tmp = t_1;
	} else if (b <= 1.1e-158) {
		tmp = z + x;
	} else if (b <= 2.9e+131) {
		tmp = t_1;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - t) * a
	tmp = 0
	if b <= -2e+68:
		tmp = (y - 2.0) * b
	elif b <= -4.1e-255:
		tmp = z + x
	elif b <= 9e-269:
		tmp = t_1
	elif b <= 1.1e-158:
		tmp = z + x
	elif b <= 2.9e+131:
		tmp = t_1
	else:
		tmp = (t - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (b <= -2e+68)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= -4.1e-255)
		tmp = Float64(z + x);
	elseif (b <= 9e-269)
		tmp = t_1;
	elseif (b <= 1.1e-158)
		tmp = Float64(z + x);
	elseif (b <= 2.9e+131)
		tmp = t_1;
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - t) * a;
	tmp = 0.0;
	if (b <= -2e+68)
		tmp = (y - 2.0) * b;
	elseif (b <= -4.1e-255)
		tmp = z + x;
	elseif (b <= 9e-269)
		tmp = t_1;
	elseif (b <= 1.1e-158)
		tmp = z + x;
	elseif (b <= 2.9e+131)
		tmp = t_1;
	else
		tmp = (t - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[b, -2e+68], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -4.1e-255], N[(z + x), $MachinePrecision], If[LessEqual[b, 9e-269], t$95$1, If[LessEqual[b, 1.1e-158], N[(z + x), $MachinePrecision], If[LessEqual[b, 2.9e+131], t$95$1, N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.99999999999999991e68

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 77.6

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.9%

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

   if -1.99999999999999991e68 < b < -4.1e-255 or 9.0000000000000003e-269 < b < 1.1000000000000001e-158

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 53.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 25.4%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 46.6%

       \[\leadsto z + x \]

   if -4.1e-255 < b < 9.0000000000000003e-269 or 1.1000000000000001e-158 < b < 2.9000000000000001e131

   1. Initial program 95.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 47.0

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

   5. Applied rewrites 47.0%

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

   if 2.9000000000000001e131 < b

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 89.9

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 66.5%

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

Alternative 8: 87.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{if}\;b \leq -2000 \lor \neg \left(b \leq 2.4 \cdot 10^{-27}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a x)))
   (if (or (<= b -2000.0) (not (<= b 2.4e-27)))
     (fma (- (+ t y) 2.0) b t_1)
     (fma (- 1.0 y) z 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, x);
	double tmp;
	if ((b <= -2000.0) || !(b <= 2.4e-27)) {
		tmp = fma(((t + y) - 2.0), b, t_1);
	} else {
		tmp = fma((1.0 - y), z, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, x)
	tmp = 0.0
	if ((b <= -2000.0) || !(b <= 2.4e-27))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, t_1);
	else
		tmp = fma(Float64(1.0 - y), z, 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 + x), $MachinePrecision]}, If[Or[LessEqual[b, -2000.0], N[Not[LessEqual[b, 2.4e-27]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + t$95$1), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2e3 or 2.40000000000000002e-27 < b

   1. Initial program 93.2%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 91.9%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 87.3%

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

   if -2e3 < b < 2.40000000000000002e-27

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 96.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2000 \lor \neg \left(b \leq 2.4 \cdot 10^{-27}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ t_2 := \mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{if}\;b \leq -1.72 \cdot 10^{-40}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x - \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)) (t_2 (fma (- 1.0 t) a x)))
   (if (<= b -1.72e-40)
     (fma t_1 b (- x (* (- y 1.0) z)))
     (if (<= b 2.4e-27) (fma (- 1.0 y) z t_2) (fma t_1 b 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, x);
	double tmp;
	if (b <= -1.72e-40) {
		tmp = fma(t_1, b, (x - ((y - 1.0) * z)));
	} else if (b <= 2.4e-27) {
		tmp = fma((1.0 - y), z, t_2);
	} else {
		tmp = fma(t_1, b, 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, x)
	tmp = 0.0
	if (b <= -1.72e-40)
		tmp = fma(t_1, b, Float64(x - Float64(Float64(y - 1.0) * z)));
	elseif (b <= 2.4e-27)
		tmp = fma(Float64(1.0 - y), z, t_2);
	else
		tmp = fma(t_1, b, 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 + x), $MachinePrecision]}, If[LessEqual[b, -1.72e-40], N[(t$95$1 * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-27], N[(N[(1.0 - y), $MachinePrecision] * z + t$95$2), $MachinePrecision], N[(t$95$1 * b + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7199999999999999e-40

   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 a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 85.8

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

   5. Applied rewrites 85.8%

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

   if -1.7199999999999999e-40 < b < 2.40000000000000002e-27

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 99.1%

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

   if 2.40000000000000002e-27 < b

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 92.1%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 88.7%

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

Alternative 10: 51.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -58000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-202}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-7}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -58000000000000.0)
     t_1
     (if (<= t -1.1e-202)
       (+ z x)
       (if (<= t 1.85e-7) (* (- b z) y) (if (<= t 4.4e+42) (+ z x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -58000000000000.0) {
		tmp = t_1;
	} else if (t <= -1.1e-202) {
		tmp = z + x;
	} else if (t <= 1.85e-7) {
		tmp = (b - z) * y;
	} else if (t <= 4.4e+42) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-58000000000000.0d0)) then
        tmp = t_1
    else if (t <= (-1.1d-202)) then
        tmp = z + x
    else if (t <= 1.85d-7) then
        tmp = (b - z) * y
    else if (t <= 4.4d+42) then
        tmp = z + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -58000000000000.0) {
		tmp = t_1;
	} else if (t <= -1.1e-202) {
		tmp = z + x;
	} else if (t <= 1.85e-7) {
		tmp = (b - z) * y;
	} else if (t <= 4.4e+42) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -58000000000000.0:
		tmp = t_1
	elif t <= -1.1e-202:
		tmp = z + x
	elif t <= 1.85e-7:
		tmp = (b - z) * y
	elif t <= 4.4e+42:
		tmp = z + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -58000000000000.0)
		tmp = t_1;
	elseif (t <= -1.1e-202)
		tmp = Float64(z + x);
	elseif (t <= 1.85e-7)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 4.4e+42)
		tmp = Float64(z + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -58000000000000.0)
		tmp = t_1;
	elseif (t <= -1.1e-202)
		tmp = z + x;
	elseif (t <= 1.85e-7)
		tmp = (b - z) * y;
	elseif (t <= 4.4e+42)
		tmp = z + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -58000000000000.0], t$95$1, If[LessEqual[t, -1.1e-202], N[(z + x), $MachinePrecision], If[LessEqual[t, 1.85e-7], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 4.4e+42], N[(z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8e13 or 4.4000000000000003e42 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

      1. *-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 68.6

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

   5. Applied rewrites 68.6%

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

   if -5.8e13 < t < -1.10000000000000004e-202 or 1.85000000000000002e-7 < t < 4.4000000000000003e42

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 62.4%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 19.9%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 54.1%

       \[\leadsto z + x \]

   if -1.10000000000000004e-202 < t < 1.85000000000000002e-7

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 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 41.6

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

   5. Applied rewrites 41.6%

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

Alternative 11: 49.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -58000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-292}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -58000000000000.0)
     t_1
     (if (<= t -5.4e-292)
       (+ z x)
       (if (<= t 1.75e-7) (* (- y 2.0) b) (if (<= t 4.4e+42) (+ z x) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -58000000000000.0) {
		tmp = t_1;
	} else if (t <= -5.4e-292) {
		tmp = z + x;
	} else if (t <= 1.75e-7) {
		tmp = (y - 2.0) * b;
	} else if (t <= 4.4e+42) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-58000000000000.0d0)) then
        tmp = t_1
    else if (t <= (-5.4d-292)) then
        tmp = z + x
    else if (t <= 1.75d-7) then
        tmp = (y - 2.0d0) * b
    else if (t <= 4.4d+42) then
        tmp = z + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -58000000000000.0) {
		tmp = t_1;
	} else if (t <= -5.4e-292) {
		tmp = z + x;
	} else if (t <= 1.75e-7) {
		tmp = (y - 2.0) * b;
	} else if (t <= 4.4e+42) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -58000000000000.0:
		tmp = t_1
	elif t <= -5.4e-292:
		tmp = z + x
	elif t <= 1.75e-7:
		tmp = (y - 2.0) * b
	elif t <= 4.4e+42:
		tmp = z + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -58000000000000.0)
		tmp = t_1;
	elseif (t <= -5.4e-292)
		tmp = Float64(z + x);
	elseif (t <= 1.75e-7)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 4.4e+42)
		tmp = Float64(z + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -58000000000000.0)
		tmp = t_1;
	elseif (t <= -5.4e-292)
		tmp = z + x;
	elseif (t <= 1.75e-7)
		tmp = (y - 2.0) * b;
	elseif (t <= 4.4e+42)
		tmp = z + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -58000000000000.0], t$95$1, If[LessEqual[t, -5.4e-292], N[(z + x), $MachinePrecision], If[LessEqual[t, 1.75e-7], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 4.4e+42], N[(z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8e13 or 4.4000000000000003e42 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

      1. *-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 68.6

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

   5. Applied rewrites 68.6%

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

   if -5.8e13 < t < -5.3999999999999998e-292 or 1.74999999999999992e-7 < t < 4.4000000000000003e42

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 71.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 56.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 20.9%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 48.6%

       \[\leadsto z + x \]

   if -5.3999999999999998e-292 < t < 1.74999999999999992e-7

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 35.8

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

   5. Applied rewrites 35.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 35.8%

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

Alternative 12: 34.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -5 \cdot 10^{+256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.66 \cdot 10^{+103}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+77}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a) t)))
   (if (<= t -5e+256)
     t_1
     (if (<= t -1.66e+103)
       (* b t)
       (if (<= t 6.8e+77) (+ z x) (if (<= t 9e+166) t_1 (* b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -5e+256) {
		tmp = t_1;
	} else if (t <= -1.66e+103) {
		tmp = b * t;
	} else if (t <= 6.8e+77) {
		tmp = z + x;
	} else if (t <= 9e+166) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -a * t
    if (t <= (-5d+256)) then
        tmp = t_1
    else if (t <= (-1.66d+103)) then
        tmp = b * t
    else if (t <= 6.8d+77) then
        tmp = z + x
    else if (t <= 9d+166) then
        tmp = t_1
    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 t_1 = -a * t;
	double tmp;
	if (t <= -5e+256) {
		tmp = t_1;
	} else if (t <= -1.66e+103) {
		tmp = b * t;
	} else if (t <= 6.8e+77) {
		tmp = z + x;
	} else if (t <= 9e+166) {
		tmp = t_1;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a * t
	tmp = 0
	if t <= -5e+256:
		tmp = t_1
	elif t <= -1.66e+103:
		tmp = b * t
	elif t <= 6.8e+77:
		tmp = z + x
	elif t <= 9e+166:
		tmp = t_1
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -5e+256)
		tmp = t_1;
	elseif (t <= -1.66e+103)
		tmp = Float64(b * t);
	elseif (t <= 6.8e+77)
		tmp = Float64(z + x);
	elseif (t <= 9e+166)
		tmp = t_1;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a * t;
	tmp = 0.0;
	if (t <= -5e+256)
		tmp = t_1;
	elseif (t <= -1.66e+103)
		tmp = b * t;
	elseif (t <= 6.8e+77)
		tmp = z + x;
	elseif (t <= 9e+166)
		tmp = t_1;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -5e+256], t$95$1, If[LessEqual[t, -1.66e+103], N[(b * t), $MachinePrecision], If[LessEqual[t, 6.8e+77], N[(z + x), $MachinePrecision], If[LessEqual[t, 9e+166], t$95$1, N[(b * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.00000000000000015e256 or 6.79999999999999993e77 < t < 9.00000000000000061e166

   1. Initial program 88.8%

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

   3. Taylor expanded in 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 78.1

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 57.2%

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

   if -5.00000000000000015e256 < t < -1.6600000000000001e103 or 9.00000000000000061e166 < t

   1. Initial program 94.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 61.2

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

   5. Applied rewrites 61.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 61.4%

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

   if -1.6600000000000001e103 < t < 6.79999999999999993e77

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 45.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 21.7%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 34.9%

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

Alternative 13: 81.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+68} \lor \neg \left(b \leq 2.5 \cdot 10^{+145}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-a\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.8e+68) (not (<= b 2.5e+145)))
   (fma (- (+ t y) 2.0) b (* (- a) t))
   (fma (- 1.0 y) z (fma (- 1.0 t) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.8e+68) || !(b <= 2.5e+145)) {
		tmp = fma(((t + y) - 2.0), b, (-a * t));
	} else {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.8e+68) || !(b <= 2.5e+145))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(-a) * t));
	else
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.8e+68], N[Not[LessEqual[b, 2.5e+145]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-a) * t), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.80000000000000023e68 or 2.49999999999999983e145 < b

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 97.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 93.6%

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

   12. Taylor expanded in t around inf

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

   14. Applied rewrites 90.1%

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

   if -5.80000000000000023e68 < b < 2.49999999999999983e145

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 86.9%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+68} \lor \neg \left(b \leq 2.5 \cdot 10^{+145}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-a\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+70} \lor \neg \left(b \leq 2.5 \cdot 10^{+145}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.5e+70) (not (<= b 2.5e+145)))
   (* (- (+ t y) 2.0) b)
   (fma (- 1.0 y) z (fma (- 1.0 t) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e+70) || !(b <= 2.5e+145)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.5e+70) || !(b <= 2.5e+145))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.5e+70], N[Not[LessEqual[b, 2.5e+145]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.49999999999999988e70 or 2.49999999999999983e145 < b

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -1.49999999999999988e70 < b < 2.49999999999999983e145

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. fp-cancel-sub-sign-inv N/A

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 86.9%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+70} \lor \neg \left(b \leq 2.5 \cdot 10^{+145}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+68} \lor \neg \left(b \leq 2.5 \cdot 10^{+145}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.3e+68) (not (<= b 2.5e+145)))
   (* (- (+ t y) 2.0) b)
   (+ (fma (- 1.0 t) a z) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.3e+68) || !(b <= 2.5e+145)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = fma((1.0 - t), a, z) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.3e+68) || !(b <= 2.5e+145))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = Float64(fma(Float64(1.0 - t), a, z) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.3e+68], N[Not[LessEqual[b, 2.5e+145]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(N[(1.0 - t), $MachinePrecision] * a + z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3e68 or 2.49999999999999983e145 < b

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -2.3e68 < b < 2.49999999999999983e145

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 76.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 45.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 22.6%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 68.7%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+68} \lor \neg \left(b \leq 2.5 \cdot 10^{+145}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -58000000000000 \lor \neg \left(t \leq 4.4 \cdot 10^{+42}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -58000000000000.0) (not (<= t 4.4e+42)))
   (* (- b a) t)
   (+ (fma -2.0 b (+ z x)) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -58000000000000.0) || !(t <= 4.4e+42)) {
		tmp = (b - a) * t;
	} else {
		tmp = fma(-2.0, b, (z + x)) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -58000000000000.0) || !(t <= 4.4e+42))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(fma(-2.0, b, Float64(z + x)) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -58000000000000.0], N[Not[LessEqual[t, 4.4e+42]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.8e13 or 4.4000000000000003e42 < t

   1. Initial program 94.2%

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

   3. Taylor expanded in t around inf

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

      1. *-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 68.6

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

   5. Applied rewrites 68.6%

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

   if -5.8e13 < t < 4.4000000000000003e42

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 64.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 63.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -58000000000000 \lor \neg \left(t \leq 4.4 \cdot 10^{+42}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+68} \lor \neg \left(b \leq 2.6 \cdot 10^{-31}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.7e+68) (not (<= b 2.6e-31))) (* (- t 2.0) b) (+ z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.7e+68) || !(b <= 2.6e-31)) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.7d+68)) .or. (.not. (b <= 2.6d-31))) then
        tmp = (t - 2.0d0) * b
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.7e+68) || !(b <= 2.6e-31)) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.7e+68) or not (b <= 2.6e-31):
		tmp = (t - 2.0) * b
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.7e+68) || !(b <= 2.6e-31))
		tmp = Float64(Float64(t - 2.0) * b);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.7e+68) || ~((b <= 2.6e-31)))
		tmp = (t - 2.0) * b;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.7e+68], N[Not[LessEqual[b, 2.6e-31]], $MachinePrecision]], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.70000000000000008e68 or 2.59999999999999995e-31 < b

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 69.6

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

   5. Applied rewrites 69.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 47.6%

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

   if -1.70000000000000008e68 < b < 2.59999999999999995e-31

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 44.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 18.4%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 40.6%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+68} \lor \neg \left(b \leq 2.6 \cdot 10^{-31}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+68}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-31}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+68)
   (* (- y 2.0) b)
   (if (<= b 2.6e-31) (+ z x) (* (- t 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+68) {
		tmp = (y - 2.0) * b;
	} else if (b <= 2.6e-31) {
		tmp = z + x;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d+68)) then
        tmp = (y - 2.0d0) * b
    else if (b <= 2.6d-31) then
        tmp = z + x
    else
        tmp = (t - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+68) {
		tmp = (y - 2.0) * b;
	} else if (b <= 2.6e-31) {
		tmp = z + x;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+68:
		tmp = (y - 2.0) * b
	elif b <= 2.6e-31:
		tmp = z + x
	else:
		tmp = (t - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+68)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= 2.6e-31)
		tmp = Float64(z + x);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e+68)
		tmp = (y - 2.0) * b;
	elseif (b <= 2.6e-31)
		tmp = z + x;
	else
		tmp = (t - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+68], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 2.6e-31], N[(z + x), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.99999999999999991e68

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 77.6

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 57.9%

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

   if -1.99999999999999991e68 < b < 2.59999999999999995e-31

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 44.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 18.4%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 40.6%

       \[\leadsto z + x \]

   if 2.59999999999999995e-31 < b

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 64.7

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

   5. Applied rewrites 64.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 47.1%

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

Alternative 19: 34.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.66 \cdot 10^{+103} \lor \neg \left(t \leq 2.7 \cdot 10^{+101}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.66e+103) (not (<= t 2.7e+101))) (* b t) (+ z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.66e+103) || !(t <= 2.7e+101)) {
		tmp = b * t;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.66d+103)) .or. (.not. (t <= 2.7d+101))) then
        tmp = b * t
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.66e+103) || !(t <= 2.7e+101)) {
		tmp = b * t;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.66e+103) or not (t <= 2.7e+101):
		tmp = b * t
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.66e+103) || !(t <= 2.7e+101))
		tmp = Float64(b * t);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.66e+103) || ~((t <= 2.7e+101)))
		tmp = b * t;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.66e+103], N[Not[LessEqual[t, 2.7e+101]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6600000000000001e103 or 2.70000000000000006e101 < t

   1. Initial program 92.0%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 49.9

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

   5. Applied rewrites 49.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 49.0%

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

   if -1.6600000000000001e103 < t < 2.70000000000000006e101

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 44.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 21.4%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 34.3%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.66 \cdot 10^{+103} \lor \neg \left(t \leq 2.7 \cdot 10^{+101}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 32.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+78}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-31}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.12e+78) (* b y) (if (<= b 2.6e-31) (+ z x) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.12e+78) {
		tmp = b * y;
	} else if (b <= 2.6e-31) {
		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 <= (-1.12d+78)) then
        tmp = b * y
    else if (b <= 2.6d-31) 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 <= -1.12e+78) {
		tmp = b * y;
	} else if (b <= 2.6e-31) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.12e+78:
		tmp = b * y
	elif b <= 2.6e-31:
		tmp = z + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.12e+78)
		tmp = Float64(b * y);
	elseif (b <= 2.6e-31)
		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 <= -1.12e+78)
		tmp = b * y;
	elseif (b <= 2.6e-31)
		tmp = z + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.12e+78], N[(b * y), $MachinePrecision], If[LessEqual[b, 2.6e-31], N[(z + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.12e78

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 76.5

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

   5. Applied rewrites 76.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 37.2%

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

   if -1.12e78 < b < 2.59999999999999995e-31

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. associate--r+ N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 77.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 45.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 19.6%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 40.1%

       \[\leadsto z + x \]

   if 2.59999999999999995e-31 < b

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 64.7

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

   5. Applied rewrites 64.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 41.2%

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

Alternative 21: 24.7% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ z + x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ z x))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = z + x
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return z + x

Julia

function code(x, y, z, t, a, b)
	return Float64(z + x)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + x), $MachinePrecision]

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. lower--.f64 N/A

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

   6. +-commutative N/A

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

   7. associate--r+ N/A

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

   8. fp-cancel-sub-sign-inv N/A

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

   9. +-commutative N/A

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

   10. associate--l+ N/A

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

5. Applied rewrites 73.5%

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

6. Taylor expanded in a around 0

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

8. Applied rewrites 49.5%

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

9. Taylor expanded in x around 0

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

11. Applied rewrites 33.2%

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

12. Taylor expanded in b around 0

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

14. Applied rewrites 26.7%

    \[\leadsto z + x \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024326 
(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)))