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

Percentage Accurate: 95.5% → 98.6%

Time: 12.8s

Alternatives: 29

Speedup: 0.5×

• 36.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 100.0

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 100.0

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 100.0

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

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

   1. Initial program 0.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 8.3

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 8.3

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 8.3

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lower-+.f64 8.3

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

   4. Applied rewrites 8.3%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 83.3

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

   7. Applied rewrites 83.3%

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

4. Final simplification 99.2%

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

Alternative 2: 50.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ t_2 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-203}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 5.25 \cdot 10^{-263}:\\ \;\;\;\;b \cdot y + a\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-89}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)) (t_2 (* (- 1.0 y) z)))
   (if (<= t -2.3e+18)
     t_1
     (if (<= t -1.12e-203)
       (* (- b z) y)
       (if (<= t 5.25e-263)
         (+ (* b y) a)
         (if (<= t 5.4e-157)
           t_2
           (if (<= t 1.32e-89)
             (* (- y 2.0) b)
             (if (<= t 6.2e+26) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double t_2 = (1.0 - y) * z;
	double tmp;
	if (t <= -2.3e+18) {
		tmp = t_1;
	} else if (t <= -1.12e-203) {
		tmp = (b - z) * y;
	} else if (t <= 5.25e-263) {
		tmp = (b * y) + a;
	} else if (t <= 5.4e-157) {
		tmp = t_2;
	} else if (t <= 1.32e-89) {
		tmp = (y - 2.0) * b;
	} else if (t <= 6.2e+26) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (b - a) * t
    t_2 = (1.0d0 - y) * z
    if (t <= (-2.3d+18)) then
        tmp = t_1
    else if (t <= (-1.12d-203)) then
        tmp = (b - z) * y
    else if (t <= 5.25d-263) then
        tmp = (b * y) + a
    else if (t <= 5.4d-157) then
        tmp = t_2
    else if (t <= 1.32d-89) then
        tmp = (y - 2.0d0) * b
    else if (t <= 6.2d+26) then
        tmp = t_2
    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 t_2 = (1.0 - y) * z;
	double tmp;
	if (t <= -2.3e+18) {
		tmp = t_1;
	} else if (t <= -1.12e-203) {
		tmp = (b - z) * y;
	} else if (t <= 5.25e-263) {
		tmp = (b * y) + a;
	} else if (t <= 5.4e-157) {
		tmp = t_2;
	} else if (t <= 1.32e-89) {
		tmp = (y - 2.0) * b;
	} else if (t <= 6.2e+26) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	t_2 = (1.0 - y) * z
	tmp = 0
	if t <= -2.3e+18:
		tmp = t_1
	elif t <= -1.12e-203:
		tmp = (b - z) * y
	elif t <= 5.25e-263:
		tmp = (b * y) + a
	elif t <= 5.4e-157:
		tmp = t_2
	elif t <= 1.32e-89:
		tmp = (y - 2.0) * b
	elif t <= 6.2e+26:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	t_2 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t <= -2.3e+18)
		tmp = t_1;
	elseif (t <= -1.12e-203)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 5.25e-263)
		tmp = Float64(Float64(b * y) + a);
	elseif (t <= 5.4e-157)
		tmp = t_2;
	elseif (t <= 1.32e-89)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 6.2e+26)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	t_2 = (1.0 - y) * z;
	tmp = 0.0;
	if (t <= -2.3e+18)
		tmp = t_1;
	elseif (t <= -1.12e-203)
		tmp = (b - z) * y;
	elseif (t <= 5.25e-263)
		tmp = (b * y) + a;
	elseif (t <= 5.4e-157)
		tmp = t_2;
	elseif (t <= 1.32e-89)
		tmp = (y - 2.0) * b;
	elseif (t <= 6.2e+26)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t, -2.3e+18], t$95$1, If[LessEqual[t, -1.12e-203], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 5.25e-263], N[(N[(b * y), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 5.4e-157], t$95$2, If[LessEqual[t, 1.32e-89], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 6.2e+26], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.3e18 or 6.1999999999999999e26 < t

   1. Initial program 91.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 70.1

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

   5. Applied rewrites 70.1%

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

   if -2.3e18 < t < -1.12e-203

   1. Initial program 97.5%

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

   3. Taylor expanded in 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 49.6

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

   5. Applied rewrites 49.6%

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

   if -1.12e-203 < t < 5.2499999999999999e-263

   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 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 80.4

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.4%

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

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y + a \]
   10. Step-by-step derivation

   11. Applied rewrites 59.6%

       \[\leadsto b \cdot y + a \]

   if 5.2499999999999999e-263 < t < 5.4e-157 or 1.32e-89 < t < 6.1999999999999999e26

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 50.5

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

   5. Applied rewrites 50.5%

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

   if 5.4e-157 < t < 1.32e-89

   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. +-commutative N/A

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

      5. lower-+.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 83.0%

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

Alternative 3: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (fma (- b a) t (fma (- y 2.0) b x)) a)))
   (if (<= x -3.9e+118)
     t_1
     (if (<= x 1.4e+134)
       (fma (- b z) y (fma (- t 2.0) b (fma (- 1.0 t) a z)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - a), t, fma((y - 2.0), b, x)) + a;
	double tmp;
	if (x <= -3.9e+118) {
		tmp = t_1;
	} else if (x <= 1.4e+134) {
		tmp = fma((b - z), y, fma((t - 2.0), b, fma((1.0 - t), a, z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x)) + a)
	tmp = 0.0
	if (x <= -3.9e+118)
		tmp = t_1;
	elseif (x <= 1.4e+134)
		tmp = fma(Float64(b - z), y, fma(Float64(t - 2.0), b, fma(Float64(1.0 - t), a, z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[x, -3.9e+118], t$95$1, If[LessEqual[x, 1.4e+134], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9e118 or 1.3999999999999999e134 < x

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 84.6

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

   5. Applied rewrites 84.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 85.9%

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

   if -3.9e118 < x < 1.3999999999999999e134

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 97.1%

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

Alternative 4: 48.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 2\right) \cdot b\\ t_2 := \left(1 - y\right) \cdot z\\ t_3 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -75000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 2.0) b)) (t_2 (* (- 1.0 y) z)) (t_3 (* (- b a) t)))
   (if (<= t -75000000.0)
     t_3
     (if (<= t -1.02e-294)
       t_1
       (if (<= t 5.4e-157)
         t_2
         (if (<= t 1.32e-89) t_1 (if (<= t 6.2e+26) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double t_2 = (1.0 - y) * z;
	double t_3 = (b - a) * t;
	double tmp;
	if (t <= -75000000.0) {
		tmp = t_3;
	} else if (t <= -1.02e-294) {
		tmp = t_1;
	} else if (t <= 5.4e-157) {
		tmp = t_2;
	} else if (t <= 1.32e-89) {
		tmp = t_1;
	} else if (t <= 6.2e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y - 2.0d0) * b
    t_2 = (1.0d0 - y) * z
    t_3 = (b - a) * t
    if (t <= (-75000000.0d0)) then
        tmp = t_3
    else if (t <= (-1.02d-294)) then
        tmp = t_1
    else if (t <= 5.4d-157) then
        tmp = t_2
    else if (t <= 1.32d-89) then
        tmp = t_1
    else if (t <= 6.2d+26) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double t_2 = (1.0 - y) * z;
	double t_3 = (b - a) * t;
	double tmp;
	if (t <= -75000000.0) {
		tmp = t_3;
	} else if (t <= -1.02e-294) {
		tmp = t_1;
	} else if (t <= 5.4e-157) {
		tmp = t_2;
	} else if (t <= 1.32e-89) {
		tmp = t_1;
	} else if (t <= 6.2e+26) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y - 2.0) * b
	t_2 = (1.0 - y) * z
	t_3 = (b - a) * t
	tmp = 0
	if t <= -75000000.0:
		tmp = t_3
	elif t <= -1.02e-294:
		tmp = t_1
	elif t <= 5.4e-157:
		tmp = t_2
	elif t <= 1.32e-89:
		tmp = t_1
	elif t <= 6.2e+26:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 2.0) * b)
	t_2 = Float64(Float64(1.0 - y) * z)
	t_3 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -75000000.0)
		tmp = t_3;
	elseif (t <= -1.02e-294)
		tmp = t_1;
	elseif (t <= 5.4e-157)
		tmp = t_2;
	elseif (t <= 1.32e-89)
		tmp = t_1;
	elseif (t <= 6.2e+26)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y - 2.0) * b;
	t_2 = (1.0 - y) * z;
	t_3 = (b - a) * t;
	tmp = 0.0;
	if (t <= -75000000.0)
		tmp = t_3;
	elseif (t <= -1.02e-294)
		tmp = t_1;
	elseif (t <= 5.4e-157)
		tmp = t_2;
	elseif (t <= 1.32e-89)
		tmp = t_1;
	elseif (t <= 6.2e+26)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -75000000.0], t$95$3, If[LessEqual[t, -1.02e-294], t$95$1, If[LessEqual[t, 5.4e-157], t$95$2, If[LessEqual[t, 1.32e-89], t$95$1, If[LessEqual[t, 6.2e+26], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5e7 or 6.1999999999999999e26 < 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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.6

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

   5. Applied rewrites 69.6%

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

   if -7.5e7 < t < -1.01999999999999998e-294 or 5.4e-157 < t < 1.32e-89

   1. Initial program 98.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 55.5

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

   5. Applied rewrites 55.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 54.8%

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

   if -1.01999999999999998e-294 < t < 5.4e-157 or 1.32e-89 < t < 6.1999999999999999e26

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 48.3

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

   5. Applied rewrites 48.3%

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

Alternative 5: 58.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, x\right)\\ t_2 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9600000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-274}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;b \leq 410000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a x)) (t_2 (* (- (+ t y) 2.0) b)))
   (if (<= b -9600000.0)
     t_2
     (if (<= b -3.4e-161)
       t_1
       (if (<= b 1.5e-274) (* (- 1.0 y) z) (if (<= b 410000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, x);
	double t_2 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -9600000.0) {
		tmp = t_2;
	} else if (b <= -3.4e-161) {
		tmp = t_1;
	} else if (b <= 1.5e-274) {
		tmp = (1.0 - y) * z;
	} else if (b <= 410000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, x)
	t_2 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -9600000.0)
		tmp = t_2;
	elseif (b <= -3.4e-161)
		tmp = t_1;
	elseif (b <= 1.5e-274)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (b <= 410000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9600000.0], t$95$2, If[LessEqual[b, -3.4e-161], t$95$1, If[LessEqual[b, 1.5e-274], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, 410000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.6e6 or 4.1e8 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 72.1

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

   5. Applied rewrites 72.1%

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

   if -9.6e6 < b < -3.39999999999999982e-161 or 1.49999999999999989e-274 < b < 4.1e8

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 65.1

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

   5. Applied rewrites 65.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 54.4%

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

   if -3.39999999999999982e-161 < b < 1.49999999999999989e-274

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 71.4

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

   5. Applied rewrites 71.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9600000:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-161}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-274}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;b \leq 410000000:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -33000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+203}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, b \cdot y\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -33000000000.0)
     t_1
     (if (<= b 2.8e-7)
       (fma (- 1.0 y) z (fma (- 1.0 t) a x))
       (if (<= b 6.5e+203) (+ (fma (- b a) t (* b y)) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -33000000000.0) {
		tmp = t_1;
	} else if (b <= 2.8e-7) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else if (b <= 6.5e+203) {
		tmp = fma((b - a), t, (b * y)) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -33000000000.0)
		tmp = t_1;
	elseif (b <= 2.8e-7)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	elseif (b <= 6.5e+203)
		tmp = Float64(fma(Float64(b - a), t, Float64(b * y)) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -33000000000.0], t$95$1, If[LessEqual[b, 2.8e-7], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+203], N[(N[(N[(b - a), $MachinePrecision] * t + N[(b * y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3e10 or 6.5000000000000003e203 < b

   1. Initial program 90.9%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 91.4

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

   5. Applied rewrites 91.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 89.1%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 88.9%

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

   if -3.3e10 < b < 2.80000000000000019e-7

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 91.5%

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

   if 2.80000000000000019e-7 < b < 6.5000000000000003e203

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 85.3

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 89.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 80.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -33000000000:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+203}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, b \cdot y\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(z - b\right) \cdot y\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -245000000000:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, b \cdot y\right) + a\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+114}:\\ \;\;\;\;x - \mathsf{fma}\left(z, -1, \left(a - b\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (- z b) y))))
   (if (<= y -1.6e+103)
     t_1
     (if (<= y -245000000000.0)
       (+ (fma (- b a) t (* b y)) a)
       (if (<= y 2e+114) (- x (fma z -1.0 (* (- a b) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((z - b) * y);
	double tmp;
	if (y <= -1.6e+103) {
		tmp = t_1;
	} else if (y <= -245000000000.0) {
		tmp = fma((b - a), t, (b * y)) + a;
	} else if (y <= 2e+114) {
		tmp = x - fma(z, -1.0, ((a - b) * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(z - b) * y))
	tmp = 0.0
	if (y <= -1.6e+103)
		tmp = t_1;
	elseif (y <= -245000000000.0)
		tmp = Float64(fma(Float64(b - a), t, Float64(b * y)) + a);
	elseif (y <= 2e+114)
		tmp = Float64(x - fma(z, -1.0, Float64(Float64(a - b) * t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(z - b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+103], t$95$1, If[LessEqual[y, -245000000000.0], N[(N[(N[(b - a), $MachinePrecision] * t + N[(b * y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[y, 2e+114], N[(x - N[(z * -1.0 + N[(N[(a - b), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999996e103 or 2e114 < y

   1. Initial program 91.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 92.7

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 92.7

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 92.7

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lower-+.f64 92.7

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

   4. Applied rewrites 92.7%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. *-lft-identity N/A

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

      6. metadata-eval N/A

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

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

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

      8. lower-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. *-lft-identity N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 87.5

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

   7. Applied rewrites 87.5%

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

   if -1.59999999999999996e103 < y < -2.45e11

   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 z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 74.9

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

   5. Applied rewrites 74.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 74.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 74.9%

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

   if -2.45e11 < y < 2e114

   1. Initial program 97.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 97.3

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 97.3

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 97.3

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lower-+.f64 97.3

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

   4. Applied rewrites 97.3%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. lower--.f64 77.5

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

   7. Applied rewrites 77.5%

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

   8. Taylor expanded in y around 0

      \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{-1}, \left(a - b\right) \cdot t\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 71.4%

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

Alternative 8: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -680000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-99}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+203}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, b \cdot y\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -680000000.0)
     t_1
     (if (<= b 5.2e-99)
       (- x (* z (- y 1.0)))
       (if (<= b 6.5e+203) (+ (fma (- b a) t (* b y)) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -680000000.0) {
		tmp = t_1;
	} else if (b <= 5.2e-99) {
		tmp = x - (z * (y - 1.0));
	} else if (b <= 6.5e+203) {
		tmp = fma((b - a), t, (b * y)) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -680000000.0)
		tmp = t_1;
	elseif (b <= 5.2e-99)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	elseif (b <= 6.5e+203)
		tmp = Float64(fma(Float64(b - a), t, Float64(b * y)) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -680000000.0], t$95$1, If[LessEqual[b, 5.2e-99], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+203], N[(N[(N[(b - a), $MachinePrecision] * t + N[(b * y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.8e8 or 6.5000000000000003e203 < b

   1. Initial program 90.9%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 91.4

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

   5. Applied rewrites 91.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 89.1%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 88.9%

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

   if -6.8e8 < b < 5.2000000000000001e-99

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 100.0

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 100.0

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 100.0

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.4

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

   7. Applied rewrites 66.4%

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

   if 5.2000000000000001e-99 < b < 6.5000000000000003e203

   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 z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 81.2%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 71.1%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -680000000:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-99}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+203}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, b \cdot y\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\\ \mathbf{if}\;a \leq -6000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (fma (- b a) t (fma (- y 2.0) b x)) a)))
   (if (<= a -6000.0)
     t_1
     (if (<= a 2e+158) (fma (- b z) y (fma (- t 2.0) b (+ z x))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - a), t, fma((y - 2.0), b, x)) + a;
	double tmp;
	if (a <= -6000.0) {
		tmp = t_1;
	} else if (a <= 2e+158) {
		tmp = fma((b - z), y, fma((t - 2.0), b, (z + x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x)) + a)
	tmp = 0.0
	if (a <= -6000.0)
		tmp = t_1;
	elseif (a <= 2e+158)
		tmp = fma(Float64(b - z), y, fma(Float64(t - 2.0), b, Float64(z + x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[a, -6000.0], t$95$1, If[LessEqual[a, 2e+158], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6e3 or 1.99999999999999991e158 < a

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 86.7

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

   5. Applied rewrites 86.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 87.7%

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

   if -6e3 < a < 1.99999999999999991e158

   1. Initial program 96.8%

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

   3. Taylor expanded in a around 0

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

   5. Applied rewrites 95.0%

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

Alternative 10: 88.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -680000000:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -680000000.0)
   (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))
   (if (<= b 2.2e-7)
     (fma (- 1.0 y) z (fma (- 1.0 t) a x))
     (+ (fma (- b a) t (fma (- y 2.0) b x)) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -680000000.0) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	} else if (b <= 2.2e-7) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = fma((b - a), t, fma((y - 2.0), b, x)) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -680000000.0)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	elseif (b <= 2.2e-7)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = Float64(fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x)) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -680000000.0], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-7], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.8e8

   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 z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 93.8

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

   5. Applied rewrites 93.8%

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

   if -6.8e8 < b < 2.2000000000000001e-7

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 91.5%

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

   if 2.2000000000000001e-7 < b

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 87.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -680000000:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + a\\ \mathbf{if}\;b \leq -680000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (fma (- b a) t (fma (- y 2.0) b x)) a)))
   (if (<= b -680000000.0)
     t_1
     (if (<= b 2.2e-7) (fma (- 1.0 y) z (fma (- 1.0 t) a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - a), t, fma((y - 2.0), b, x)) + a;
	double tmp;
	if (b <= -680000000.0) {
		tmp = t_1;
	} else if (b <= 2.2e-7) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(b - a), t, fma(Float64(y - 2.0), b, x)) + a)
	tmp = 0.0
	if (b <= -680000000.0)
		tmp = t_1;
	elseif (b <= 2.2e-7)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[b, -680000000.0], t$95$1, If[LessEqual[b, 2.2e-7], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.8e8 or 2.2000000000000001e-7 < b

   1. Initial program 91.7%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 89.3

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 89.3%

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

   if -6.8e8 < b < 2.2000000000000001e-7

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

   5. Applied rewrites 91.5%

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

Alternative 12: 34.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 2\right) \cdot b\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-156}:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{elif}\;t \leq 620000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 2.0) b)))
   (if (<= t -1.75e+25)
     (* b t)
     (if (<= t -1.08e-305)
       t_1
       (if (<= t 7.2e-156)
         (- x (- a))
         (if (<= t 620000000000.0) t_1 (* (- a) t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= -1.08e-305) {
		tmp = t_1;
	} else if (t <= 7.2e-156) {
		tmp = x - -a;
	} else if (t <= 620000000000.0) {
		tmp = t_1;
	} else {
		tmp = -a * 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 = (y - 2.0d0) * b
    if (t <= (-1.75d+25)) then
        tmp = b * t
    else if (t <= (-1.08d-305)) then
        tmp = t_1
    else if (t <= 7.2d-156) then
        tmp = x - -a
    else if (t <= 620000000000.0d0) then
        tmp = t_1
    else
        tmp = -a * 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 = (y - 2.0) * b;
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= -1.08e-305) {
		tmp = t_1;
	} else if (t <= 7.2e-156) {
		tmp = x - -a;
	} else if (t <= 620000000000.0) {
		tmp = t_1;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y - 2.0) * b
	tmp = 0
	if t <= -1.75e+25:
		tmp = b * t
	elif t <= -1.08e-305:
		tmp = t_1
	elif t <= 7.2e-156:
		tmp = x - -a
	elif t <= 620000000000.0:
		tmp = t_1
	else:
		tmp = -a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 2.0) * b)
	tmp = 0.0
	if (t <= -1.75e+25)
		tmp = Float64(b * t);
	elseif (t <= -1.08e-305)
		tmp = t_1;
	elseif (t <= 7.2e-156)
		tmp = Float64(x - Float64(-a));
	elseif (t <= 620000000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(-a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y - 2.0) * b;
	tmp = 0.0;
	if (t <= -1.75e+25)
		tmp = b * t;
	elseif (t <= -1.08e-305)
		tmp = t_1;
	elseif (t <= 7.2e-156)
		tmp = x - -a;
	elseif (t <= 620000000000.0)
		tmp = t_1;
	else
		tmp = -a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t, -1.75e+25], N[(b * t), $MachinePrecision], If[LessEqual[t, -1.08e-305], t$95$1, If[LessEqual[t, 7.2e-156], N[(x - (-a)), $MachinePrecision], If[LessEqual[t, 620000000000.0], t$95$1, N[((-a) * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.75e25

   1. Initial program 86.2%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 53.6

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

   5. Applied rewrites 53.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 49.8%

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

   if -1.75e25 < t < -1.08000000000000004e-305 or 7.19999999999999998e-156 < t < 6.2e11

   1. Initial program 99.0%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 44.9

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

   5. Applied rewrites 44.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 43.6%

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

   if -1.08000000000000004e-305 < t < 7.19999999999999998e-156

   1. Initial program 96.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 96.7

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 96.7

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 96.7

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lower-+.f64 96.7

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

   4. Applied rewrites 96.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 46.1

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

   7. Applied rewrites 46.1%

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

   8. Taylor expanded in t around 0

      \[\leadsto x - -1 \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 46.1%

       \[\leadsto x - \left(-a\right) \]

   if 6.2e11 < t

   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 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 65.8

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

   5. Applied rewrites 65.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 39.7%

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

Alternative 13: 65.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -680000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-7}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+89}:\\ \;\;\;\;\left(b - a\right) \cdot t + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -680000000.0)
     t_1
     (if (<= b 2.2e-7)
       (- x (* z (- y 1.0)))
       (if (<= b 6e+89) (+ (* (- b a) t) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -680000000.0) {
		tmp = t_1;
	} else if (b <= 2.2e-7) {
		tmp = x - (z * (y - 1.0));
	} else if (b <= 6e+89) {
		tmp = ((b - a) * t) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -680000000.0)
		tmp = t_1;
	elseif (b <= 2.2e-7)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	elseif (b <= 6e+89)
		tmp = Float64(Float64(Float64(b - a) * t) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -680000000.0], t$95$1, If[LessEqual[b, 2.2e-7], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+89], N[(N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.8e8 or 6.00000000000000025e89 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 91.0

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

   5. Applied rewrites 91.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 90.0%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 85.5%

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

   if -6.8e8 < b < 2.2000000000000001e-7

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 99.2

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 99.2

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 99.2

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

      17. lift-+.f64 N/A

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

      18. +-commutative N/A

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

      19. lower-+.f64 99.2

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

   4. Applied rewrites 99.2%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 62.8

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

   7. Applied rewrites 62.8%

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

   if 2.2000000000000001e-7 < b < 6.00000000000000025e89

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.6%

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

   9. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(b - a\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 61.9%

       \[\leadsto \left(b - a\right) \cdot t + a \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -680000000:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-7}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+89}:\\ \;\;\;\;\left(b - a\right) \cdot t + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(z - b\right) \cdot y\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (- z b) y))))
   (if (<= y -5.4e+62)
     t_1
     (if (<= y 1.12e+133) (fma (- 1.0 t) a (fma (- t 2.0) b x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((z - b) * y);
	double tmp;
	if (y <= -5.4e+62) {
		tmp = t_1;
	} else if (y <= 1.12e+133) {
		tmp = fma((1.0 - t), a, fma((t - 2.0), b, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(z - b) * y))
	tmp = 0.0
	if (y <= -5.4e+62)
		tmp = t_1;
	elseif (y <= 1.12e+133)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(t - 2.0), b, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(z - b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+62], t$95$1, If[LessEqual[y, 1.12e+133], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4e62 or 1.12e133 < y

   1. Initial program 90.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift--.f64 N/A

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

      5. associate--l- N/A

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

      6. lower--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 92.0

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      13. lower-*.f64 92.0

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      14. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      15. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      16. lower-*.f64 92.0

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      17. lift-+.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right)\right) \]

      18. +-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

      19. lower-+.f64 92.0

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

   4. Applied rewrites 92.0%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   5. Taylor expanded in y around inf

      \[\leadsto x - \color{blue}{y \cdot \left(z - b\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \color{blue}{\left(z - b\right) \cdot y} \]

      2. sub-neg N/A

         \[\leadsto x - \color{blue}{\left(z + \left(\mathsf{neg}\left(b\right)\right)\right)} \cdot y \]

      3. mul-1-neg N/A

         \[\leadsto x - \left(z + \color{blue}{-1 \cdot b}\right) \cdot y \]

      4. +-commutative N/A

         \[\leadsto x - \color{blue}{\left(-1 \cdot b + z\right)} \cdot y \]

      5. *-lft-identity N/A

         \[\leadsto x - \left(-1 \cdot b + \color{blue}{1 \cdot z}\right) \cdot y \]

      6. metadata-eval N/A

         \[\leadsto x - \left(-1 \cdot b + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot z\right) \cdot y \]

      7. cancel-sign-sub-inv N/A

         \[\leadsto x - \color{blue}{\left(-1 \cdot b - -1 \cdot z\right)} \cdot y \]

      8. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\left(-1 \cdot b - -1 \cdot z\right) \cdot y} \]

      9. cancel-sign-sub-inv N/A

         \[\leadsto x - \color{blue}{\left(-1 \cdot b + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} \cdot y \]

      10. metadata-eval N/A

          \[\leadsto x - \left(-1 \cdot b + \color{blue}{1} \cdot z\right) \cdot y \]

      11. *-lft-identity N/A

          \[\leadsto x - \left(-1 \cdot b + \color{blue}{z}\right) \cdot y \]

      12. +-commutative N/A

          \[\leadsto x - \color{blue}{\left(z + -1 \cdot b\right)} \cdot y \]

      13. mul-1-neg N/A

          \[\leadsto x - \left(z + \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \cdot y \]

      14. sub-neg N/A

          \[\leadsto x - \color{blue}{\left(z - b\right)} \cdot y \]

      15. lower--.f64 85.3

          \[\leadsto x - \color{blue}{\left(z - b\right)} \cdot y \]

   7. Applied rewrites 85.3%

      \[\leadsto x - \color{blue}{\left(z - b\right) \cdot y} \]

   if -5.4e62 < y < 1.12e133

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 76.7

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 76.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 73.8%

      \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 62.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -750000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-7}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{+90}:\\ \;\;\;\;\left(b - a\right) \cdot t + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -750000000.0)
     t_1
     (if (<= b 2.2e-7)
       (- x (* z (- y 1.0)))
       (if (<= b 7.4e+90) (+ (* (- b a) t) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -750000000.0) {
		tmp = t_1;
	} else if (b <= 2.2e-7) {
		tmp = x - (z * (y - 1.0));
	} else if (b <= 7.4e+90) {
		tmp = ((b - a) * t) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-750000000.0d0)) then
        tmp = t_1
    else if (b <= 2.2d-7) then
        tmp = x - (z * (y - 1.0d0))
    else if (b <= 7.4d+90) then
        tmp = ((b - a) * t) + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -750000000.0) {
		tmp = t_1;
	} else if (b <= 2.2e-7) {
		tmp = x - (z * (y - 1.0));
	} else if (b <= 7.4e+90) {
		tmp = ((b - a) * t) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -750000000.0:
		tmp = t_1
	elif b <= 2.2e-7:
		tmp = x - (z * (y - 1.0))
	elif b <= 7.4e+90:
		tmp = ((b - a) * t) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -750000000.0)
		tmp = t_1;
	elseif (b <= 2.2e-7)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	elseif (b <= 7.4e+90)
		tmp = Float64(Float64(Float64(b - a) * t) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -750000000.0)
		tmp = t_1;
	elseif (b <= 2.2e-7)
		tmp = x - (z * (y - 1.0));
	elseif (b <= 7.4e+90)
		tmp = ((b - a) * t) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -750000000.0], t$95$1, If[LessEqual[b, 2.2e-7], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.4e+90], N[(N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5e8 or 7.4e90 < b

   1. Initial program 90.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 78.6

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 78.6%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   if -7.5e8 < b < 2.2000000000000001e-7

   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. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l- N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. associate--l- N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto x - \left(\color{blue}{\left(y - 1\right) \cdot z} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x - \left(\color{blue}{z \cdot \left(y - 1\right)} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, \left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      10. lower--.f64 99.2

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      12. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      13. lower-*.f64 99.2

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      14. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      15. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      16. lower-*.f64 99.2

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      17. lift-+.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right)\right) \]

      18. +-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

      19. lower-+.f64 99.2

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

   4. Applied rewrites 99.2%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   5. Taylor expanded in z around inf

      \[\leadsto x - \color{blue}{z \cdot \left(y - 1\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \color{blue}{\left(y - 1\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\left(y - 1\right) \cdot z} \]

      3. lower--.f64 62.8

         \[\leadsto x - \color{blue}{\left(y - 1\right)} \cdot z \]

   7. Applied rewrites 62.8%

      \[\leadsto x - \color{blue}{\left(y - 1\right) \cdot z} \]

   if 2.2000000000000001e-7 < b < 7.4e90

   1. Initial program 96.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 83.0

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 83.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b + -1 \cdot a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 86.6%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(b - a\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 61.9%

       \[\leadsto \left(b - a\right) \cdot t + a \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -750000000:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-7}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{+90}:\\ \;\;\;\;\left(b - a\right) \cdot t + a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+15}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-7}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+60}:\\ \;\;\;\;b \cdot y + a\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.4e+15)
   (* (- y 2.0) b)
   (if (<= b 1.65e-7)
     (* (- 1.0 y) z)
     (if (<= b 2.6e+60) (+ (* b y) a) (* (- t 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.4e+15) {
		tmp = (y - 2.0) * b;
	} else if (b <= 1.65e-7) {
		tmp = (1.0 - y) * z;
	} else if (b <= 2.6e+60) {
		tmp = (b * y) + a;
	} 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 <= (-2.4d+15)) then
        tmp = (y - 2.0d0) * b
    else if (b <= 1.65d-7) then
        tmp = (1.0d0 - y) * z
    else if (b <= 2.6d+60) then
        tmp = (b * y) + a
    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 <= -2.4e+15) {
		tmp = (y - 2.0) * b;
	} else if (b <= 1.65e-7) {
		tmp = (1.0 - y) * z;
	} else if (b <= 2.6e+60) {
		tmp = (b * y) + a;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.4e+15:
		tmp = (y - 2.0) * b
	elif b <= 1.65e-7:
		tmp = (1.0 - y) * z
	elif b <= 2.6e+60:
		tmp = (b * y) + a
	else:
		tmp = (t - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.4e+15)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= 1.65e-7)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (b <= 2.6e+60)
		tmp = Float64(Float64(b * y) + a);
	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 <= -2.4e+15)
		tmp = (y - 2.0) * b;
	elseif (b <= 1.65e-7)
		tmp = (1.0 - y) * z;
	elseif (b <= 2.6e+60)
		tmp = (b * y) + a;
	else
		tmp = (t - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.4e+15], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 1.65e-7], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, 2.6e+60], N[(N[(b * y), $MachinePrecision] + a), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.4e15

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 80.0

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 80.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 54.5%

      \[\leadsto \left(y - 2\right) \cdot b \]

   if -2.4e15 < b < 1.6500000000000001e-7

   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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)} \cdot z \]

      3. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} + \left(\mathsf{neg}\left(y\right)\right)\right) \cdot z \]

      4. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(-1 + y\right)\right)\right)} \cdot z \]

      5. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y + -1\right)}\right)\right) \cdot z \]

      6. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(y + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \cdot z \]

      7. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y - 1\right)}\right)\right) \cdot z \]

      8. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} \cdot z \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(y - 1\right)\right) \cdot z} \]

      10. sub-neg N/A

          \[\leadsto \left(-1 \cdot \color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right) \cdot z \]

      11. metadata-eval N/A

          \[\leadsto \left(-1 \cdot \left(y + \color{blue}{-1}\right)\right) \cdot z \]

      12. distribute-lft-in N/A

          \[\leadsto \color{blue}{\left(-1 \cdot y + -1 \cdot -1\right)} \cdot z \]

      13. metadata-eval N/A

          \[\leadsto \left(-1 \cdot y + \color{blue}{1}\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \color{blue}{\left(1 + -1 \cdot y\right)} \cdot z \]

      15. neg-mul-1 N/A

          \[\leadsto \left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \cdot z \]

      16. sub-neg N/A

          \[\leadsto \color{blue}{\left(1 - y\right)} \cdot z \]

      17. lower--.f64 45.8

          \[\leadsto \color{blue}{\left(1 - y\right)} \cdot z \]

   5. Applied rewrites 45.8%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

   if 1.6500000000000001e-7 < b < 2.60000000000000008e60

   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 z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 85.9

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b + -1 \cdot a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 86.0%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y + a \]
   10. Step-by-step derivation

   11. Applied rewrites 52.0%

       \[\leadsto b \cdot y + a \]

   if 2.60000000000000008e60 < b

   1. Initial program 87.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 71.2

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 71.2%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 54.0%

      \[\leadsto \left(t - 2\right) \cdot b \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 17: 38.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -8 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-87}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+186}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -8e+75)
     t_1
     (if (<= a 4.5e-87)
       (* (- t 2.0) b)
       (if (<= a 4.8e+186) (* (- y 2.0) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -8e+75) {
		tmp = t_1;
	} else if (a <= 4.5e-87) {
		tmp = (t - 2.0) * b;
	} else if (a <= 4.8e+186) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (1.0d0 - t) * a
    if (a <= (-8d+75)) then
        tmp = t_1
    else if (a <= 4.5d-87) then
        tmp = (t - 2.0d0) * b
    else if (a <= 4.8d+186) then
        tmp = (y - 2.0d0) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -8e+75) {
		tmp = t_1;
	} else if (a <= 4.5e-87) {
		tmp = (t - 2.0) * b;
	} else if (a <= 4.8e+186) {
		tmp = (y - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - t) * a
	tmp = 0
	if a <= -8e+75:
		tmp = t_1
	elif a <= 4.5e-87:
		tmp = (t - 2.0) * b
	elif a <= 4.8e+186:
		tmp = (y - 2.0) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -8e+75)
		tmp = t_1;
	elseif (a <= 4.5e-87)
		tmp = Float64(Float64(t - 2.0) * b);
	elseif (a <= 4.8e+186)
		tmp = Float64(Float64(y - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - t) * a;
	tmp = 0.0;
	if (a <= -8e+75)
		tmp = t_1;
	elseif (a <= 4.5e-87)
		tmp = (t - 2.0) * b;
	elseif (a <= 4.8e+186)
		tmp = (y - 2.0) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -8e+75], t$95$1, If[LessEqual[a, 4.5e-87], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 4.8e+186], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.99999999999999941e75 or 4.7999999999999999e186 < a

   1. Initial program 91.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)} \cdot a \]

      3. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot a \]

      4. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(-1 + t\right)\right)\right)} \cdot a \]

      5. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t + -1\right)}\right)\right) \cdot a \]

      6. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \cdot a \]

      7. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right)}\right)\right) \cdot a \]

      8. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right) \cdot a} \]

      10. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} \cdot a \]

      11. sub-neg N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) \cdot a \]

      12. metadata-eval N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right)\right) \cdot a \]

      13. +-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right)\right) \cdot a \]

      14. distribute-neg-in N/A

          \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right)} \cdot a \]

      15. metadata-eval N/A

          \[\leadsto \left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot a \]

      16. sub-neg N/A

          \[\leadsto \color{blue}{\left(1 - t\right)} \cdot a \]

      17. lower--.f64 62.8

          \[\leadsto \color{blue}{\left(1 - t\right)} \cdot a \]

   5. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   if -7.99999999999999941e75 < a < 4.49999999999999958e-87

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 48.4

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 48.4%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 36.1%

      \[\leadsto \left(t - 2\right) \cdot b \]

   if 4.49999999999999958e-87 < a < 4.7999999999999999e186

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 49.7

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 49.7%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 38.3%

      \[\leadsto \left(y - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 36.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-238}:\\ \;\;\;\;b \cdot y + a\\ \mathbf{elif}\;t \leq 620000000000:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+25)
   (* b t)
   (if (<= t 2.7e-238)
     (+ (* b y) a)
     (if (<= t 620000000000.0) (- x (- a)) (* (- a) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= 2.7e-238) {
		tmp = (b * y) + a;
	} else if (t <= 620000000000.0) {
		tmp = x - -a;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.75d+25)) then
        tmp = b * t
    else if (t <= 2.7d-238) then
        tmp = (b * y) + a
    else if (t <= 620000000000.0d0) then
        tmp = x - -a
    else
        tmp = -a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= 2.7e-238) {
		tmp = (b * y) + a;
	} else if (t <= 620000000000.0) {
		tmp = x - -a;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+25:
		tmp = b * t
	elif t <= 2.7e-238:
		tmp = (b * y) + a
	elif t <= 620000000000.0:
		tmp = x - -a
	else:
		tmp = -a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+25)
		tmp = Float64(b * t);
	elseif (t <= 2.7e-238)
		tmp = Float64(Float64(b * y) + a);
	elseif (t <= 620000000000.0)
		tmp = Float64(x - Float64(-a));
	else
		tmp = Float64(Float64(-a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.75e+25)
		tmp = b * t;
	elseif (t <= 2.7e-238)
		tmp = (b * y) + a;
	elseif (t <= 620000000000.0)
		tmp = x - -a;
	else
		tmp = -a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+25], N[(b * t), $MachinePrecision], If[LessEqual[t, 2.7e-238], N[(N[(b * y), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 620000000000.0], N[(x - (-a)), $MachinePrecision], N[((-a) * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.75e25

   1. Initial program 86.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 53.6

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 53.6%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.8%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -1.75e25 < t < 2.69999999999999991e-238

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 68.7

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 68.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b + -1 \cdot a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 68.6%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y + a \]
   10. Step-by-step derivation

   11. Applied rewrites 44.0%

       \[\leadsto b \cdot y + a \]

   if 2.69999999999999991e-238 < t < 6.2e11

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l- N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. associate--l- N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto x - \left(\color{blue}{\left(y - 1\right) \cdot z} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x - \left(\color{blue}{z \cdot \left(y - 1\right)} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, \left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      10. lower--.f64 98.1

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      12. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      13. lower-*.f64 98.1

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      14. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      15. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      16. lower-*.f64 98.1

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      17. lift-+.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right)\right) \]

      18. +-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

      19. lower-+.f64 98.1

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

   4. Applied rewrites 98.1%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{a \cdot \left(t - 1\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \color{blue}{\left(t - 1\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. lower--.f64 33.4

         \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]

   7. Applied rewrites 33.4%

      \[\leadsto x - \color{blue}{\left(t - 1\right) \cdot a} \]

   8. Taylor expanded in t around 0

      \[\leadsto x - -1 \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 32.2%

       \[\leadsto x - \left(-a\right) \]

   if 6.2e11 < t

   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 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 65.8

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 65.8%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in b around 0

      \[\leadsto \left(-1 \cdot a\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 39.7%

      \[\leadsto \left(-a\right) \cdot t \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 19: 32.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-285}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 620000000000:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+25)
   (* b t)
   (if (<= t -3.15e-285)
     (* b y)
     (if (<= t 620000000000.0) (- x (- a)) (* (- a) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= -3.15e-285) {
		tmp = b * y;
	} else if (t <= 620000000000.0) {
		tmp = x - -a;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.75d+25)) then
        tmp = b * t
    else if (t <= (-3.15d-285)) then
        tmp = b * y
    else if (t <= 620000000000.0d0) then
        tmp = x - -a
    else
        tmp = -a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= -3.15e-285) {
		tmp = b * y;
	} else if (t <= 620000000000.0) {
		tmp = x - -a;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+25:
		tmp = b * t
	elif t <= -3.15e-285:
		tmp = b * y
	elif t <= 620000000000.0:
		tmp = x - -a
	else:
		tmp = -a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+25)
		tmp = Float64(b * t);
	elseif (t <= -3.15e-285)
		tmp = Float64(b * y);
	elseif (t <= 620000000000.0)
		tmp = Float64(x - Float64(-a));
	else
		tmp = Float64(Float64(-a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.75e+25)
		tmp = b * t;
	elseif (t <= -3.15e-285)
		tmp = b * y;
	elseif (t <= 620000000000.0)
		tmp = x - -a;
	else
		tmp = -a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+25], N[(b * t), $MachinePrecision], If[LessEqual[t, -3.15e-285], N[(b * y), $MachinePrecision], If[LessEqual[t, 620000000000.0], N[(x - (-a)), $MachinePrecision], N[((-a) * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.75e25

   1. Initial program 86.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 53.6

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 53.6%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.8%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -1.75e25 < t < -3.14999999999999994e-285

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 72.4

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 72.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.5%

      \[\leadsto b \cdot \color{blue}{y} \]

   if -3.14999999999999994e-285 < t < 6.2e11

   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. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l- N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. associate--l- N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto x - \left(\color{blue}{\left(y - 1\right) \cdot z} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x - \left(\color{blue}{z \cdot \left(y - 1\right)} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, \left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      10. lower--.f64 98.6

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      12. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      13. lower-*.f64 98.6

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      14. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      15. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      16. lower-*.f64 98.6

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      17. lift-+.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right)\right) \]

      18. +-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

      19. lower-+.f64 98.6

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

   4. Applied rewrites 98.6%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{a \cdot \left(t - 1\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \color{blue}{\left(t - 1\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. lower--.f64 36.3

         \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]

   7. Applied rewrites 36.3%

      \[\leadsto x - \color{blue}{\left(t - 1\right) \cdot a} \]

   8. Taylor expanded in t around 0

      \[\leadsto x - -1 \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 35.5%

       \[\leadsto x - \left(-a\right) \]

   if 6.2e11 < t

   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 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 65.8

         \[\leadsto \color{blue}{\left(b - a\right)} \cdot t \]

   5. Applied rewrites 65.8%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   6. Taylor expanded in b around 0

      \[\leadsto \left(-1 \cdot a\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 39.7%

      \[\leadsto \left(-a\right) \cdot t \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 20: 71.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(a - b\right) \cdot t\\ \mathbf{if}\;t \leq -75000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 500000000000:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (- a b) t))))
   (if (<= t -75000000.0)
     t_1
     (if (<= t 500000000000.0) (fma (- y 2.0) b (+ a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((a - b) * t);
	double tmp;
	if (t <= -75000000.0) {
		tmp = t_1;
	} else if (t <= 500000000000.0) {
		tmp = fma((y - 2.0), b, (a + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(a - b) * t))
	tmp = 0.0
	if (t <= -75000000.0)
		tmp = t_1;
	elseif (t <= 500000000000.0)
		tmp = fma(Float64(y - 2.0), b, Float64(a + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(a - b), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -75000000.0], t$95$1, If[LessEqual[t, 500000000000.0], N[(N[(y - 2.0), $MachinePrecision] * b + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5e7 or 5e11 < t

   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. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l- N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. associate--l- N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto x - \left(\color{blue}{\left(y - 1\right) \cdot z} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x - \left(\color{blue}{z \cdot \left(y - 1\right)} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, \left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      10. lower--.f64 93.1

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      12. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      13. lower-*.f64 93.1

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      14. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      15. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      16. lower-*.f64 93.1

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      17. lift-+.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right)\right) \]

      18. +-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

      19. lower-+.f64 93.1

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

   4. Applied rewrites 93.1%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x - \color{blue}{t \cdot \left(a - b\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \color{blue}{\left(a - b\right) \cdot t} \]

      2. sub-neg N/A

         \[\leadsto x - \color{blue}{\left(a + \left(\mathsf{neg}\left(b\right)\right)\right)} \cdot t \]

      3. mul-1-neg N/A

         \[\leadsto x - \left(a + \color{blue}{-1 \cdot b}\right) \cdot t \]

      4. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\left(a + -1 \cdot b\right) \cdot t} \]

      5. mul-1-neg N/A

         \[\leadsto x - \left(a + \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \cdot t \]

      6. sub-neg N/A

         \[\leadsto x - \color{blue}{\left(a - b\right)} \cdot t \]

      7. lower--.f64 74.5

         \[\leadsto x - \color{blue}{\left(a - b\right)} \cdot t \]

   7. Applied rewrites 74.5%

      \[\leadsto x - \color{blue}{\left(a - b\right) \cdot t} \]

   if -7.5e7 < t < 5e11

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 67.1

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 67.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 65.9%

      \[\leadsto \mathsf{fma}\left(y - 2, \color{blue}{b}, a + x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 32.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-285}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 17000000000000:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+25)
   (* b t)
   (if (<= t -3.15e-285)
     (* b y)
     (if (<= t 17000000000000.0) (- x (- a)) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= -3.15e-285) {
		tmp = b * y;
	} else if (t <= 17000000000000.0) {
		tmp = x - -a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.75d+25)) then
        tmp = b * t
    else if (t <= (-3.15d-285)) then
        tmp = b * y
    else if (t <= 17000000000000.0d0) then
        tmp = x - -a
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= -3.15e-285) {
		tmp = b * y;
	} else if (t <= 17000000000000.0) {
		tmp = x - -a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+25:
		tmp = b * t
	elif t <= -3.15e-285:
		tmp = b * y
	elif t <= 17000000000000.0:
		tmp = x - -a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+25)
		tmp = Float64(b * t);
	elseif (t <= -3.15e-285)
		tmp = Float64(b * y);
	elseif (t <= 17000000000000.0)
		tmp = Float64(x - Float64(-a));
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.75e+25)
		tmp = b * t;
	elseif (t <= -3.15e-285)
		tmp = b * y;
	elseif (t <= 17000000000000.0)
		tmp = x - -a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+25], N[(b * t), $MachinePrecision], If[LessEqual[t, -3.15e-285], N[(b * y), $MachinePrecision], If[LessEqual[t, 17000000000000.0], N[(x - (-a)), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e25 or 1.7e13 < 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. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 45.7

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.6%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -1.75e25 < t < -3.14999999999999994e-285

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 72.4

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 72.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.5%

      \[\leadsto b \cdot \color{blue}{y} \]

   if -3.14999999999999994e-285 < t < 1.7e13

   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. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l- N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. associate--l- N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto x - \left(\color{blue}{\left(y - 1\right) \cdot z} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x - \left(\color{blue}{z \cdot \left(y - 1\right)} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, \left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      10. lower--.f64 98.6

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      12. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      13. lower-*.f64 98.6

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      14. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      15. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      16. lower-*.f64 98.6

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      17. lift-+.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right)\right) \]

      18. +-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

      19. lower-+.f64 98.6

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

   4. Applied rewrites 98.6%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   5. Taylor expanded in a around inf

      \[\leadsto x - \color{blue}{a \cdot \left(t - 1\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \color{blue}{\left(t - 1\right) \cdot a} \]

      2. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\left(t - 1\right) \cdot a} \]

      3. lower--.f64 36.3

         \[\leadsto x - \color{blue}{\left(t - 1\right)} \cdot a \]

   7. Applied rewrites 36.3%

      \[\leadsto x - \color{blue}{\left(t - 1\right) \cdot a} \]

   8. Taylor expanded in t around 0

      \[\leadsto x - -1 \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 35.5%

       \[\leadsto x - \left(-a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 26.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-154}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 490000000000:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+25)
   (* b t)
   (if (<= t 1.3e-154) (* b y) (if (<= t 490000000000.0) (* -2.0 b) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= 1.3e-154) {
		tmp = b * y;
	} else if (t <= 490000000000.0) {
		tmp = -2.0 * b;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.75d+25)) then
        tmp = b * t
    else if (t <= 1.3d-154) then
        tmp = b * y
    else if (t <= 490000000000.0d0) then
        tmp = (-2.0d0) * b
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= 1.3e-154) {
		tmp = b * y;
	} else if (t <= 490000000000.0) {
		tmp = -2.0 * b;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+25:
		tmp = b * t
	elif t <= 1.3e-154:
		tmp = b * y
	elif t <= 490000000000.0:
		tmp = -2.0 * b
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+25)
		tmp = Float64(b * t);
	elseif (t <= 1.3e-154)
		tmp = Float64(b * y);
	elseif (t <= 490000000000.0)
		tmp = Float64(-2.0 * b);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.75e+25)
		tmp = b * t;
	elseif (t <= 1.3e-154)
		tmp = b * y;
	elseif (t <= 490000000000.0)
		tmp = -2.0 * b;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+25], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.3e-154], N[(b * y), $MachinePrecision], If[LessEqual[t, 490000000000.0], N[(-2.0 * b), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e25 or 4.9e11 < 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. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 45.7

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.6%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -1.75e25 < t < 1.3e-154

   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 z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 66.9

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 66.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 27.2%

      \[\leadsto b \cdot \color{blue}{y} \]

   if 1.3e-154 < t < 4.9e11

   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. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 38.9

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 38.9%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 38.9%

      \[\leadsto \left(y - 2\right) \cdot b \]

   9. Taylor expanded in y around 0

      \[\leadsto -2 \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 29.4%

       \[\leadsto -2 \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 27.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-288}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 300000:\\ \;\;\;\;1 \cdot a\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+25)
   (* b t)
   (if (<= t -5.9e-288) (* b y) (if (<= t 300000.0) (* 1.0 a) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= -5.9e-288) {
		tmp = b * y;
	} else if (t <= 300000.0) {
		tmp = 1.0 * a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.75d+25)) then
        tmp = b * t
    else if (t <= (-5.9d-288)) then
        tmp = b * y
    else if (t <= 300000.0d0) then
        tmp = 1.0d0 * a
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= -5.9e-288) {
		tmp = b * y;
	} else if (t <= 300000.0) {
		tmp = 1.0 * a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+25:
		tmp = b * t
	elif t <= -5.9e-288:
		tmp = b * y
	elif t <= 300000.0:
		tmp = 1.0 * a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+25)
		tmp = Float64(b * t);
	elseif (t <= -5.9e-288)
		tmp = Float64(b * y);
	elseif (t <= 300000.0)
		tmp = Float64(1.0 * a);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.75e+25)
		tmp = b * t;
	elseif (t <= -5.9e-288)
		tmp = b * y;
	elseif (t <= 300000.0)
		tmp = 1.0 * a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+25], N[(b * t), $MachinePrecision], If[LessEqual[t, -5.9e-288], N[(b * y), $MachinePrecision], If[LessEqual[t, 300000.0], N[(1.0 * a), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e25 or 3e5 < t

   1. Initial program 92.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 46.1

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 46.1%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.2%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -1.75e25 < t < -5.90000000000000014e-288

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 72.4

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 72.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.5%

      \[\leadsto b \cdot \color{blue}{y} \]

   if -5.90000000000000014e-288 < t < 3e5

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(1 + \left(\mathsf{neg}\left(t\right)\right)\right)} \cdot a \]

      3. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot a \]

      4. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(-1 + t\right)\right)\right)} \cdot a \]

      5. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t + -1\right)}\right)\right) \cdot a \]

      6. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \cdot a \]

      7. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right)}\right)\right) \cdot a \]

      8. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right) \cdot a} \]

      10. mul-1-neg N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} \cdot a \]

      11. sub-neg N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right)\right) \cdot a \]

      12. metadata-eval N/A

          \[\leadsto \left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right)\right) \cdot a \]

      13. +-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right)\right) \cdot a \]

      14. distribute-neg-in N/A

          \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right)} \cdot a \]

      15. metadata-eval N/A

          \[\leadsto \left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot a \]

      16. sub-neg N/A

          \[\leadsto \color{blue}{\left(1 - t\right)} \cdot a \]

      17. lower--.f64 20.0

          \[\leadsto \color{blue}{\left(1 - t\right)} \cdot a \]

   5. Applied rewrites 20.0%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   6. Taylor expanded in t around 0

      \[\leadsto 1 \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 19.4%

      \[\leadsto 1 \cdot a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 24: 60.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+115}:\\ \;\;\;\;x - \left(a - b\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3.7e+60) t_1 (if (<= y 5.5e+115) (- x (* (- a b) t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.7e+60) {
		tmp = t_1;
	} else if (y <= 5.5e+115) {
		tmp = x - ((a - b) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-3.7d+60)) then
        tmp = t_1
    else if (y <= 5.5d+115) then
        tmp = x - ((a - b) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.7e+60) {
		tmp = t_1;
	} else if (y <= 5.5e+115) {
		tmp = x - ((a - b) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -3.7e+60:
		tmp = t_1
	elif y <= 5.5e+115:
		tmp = x - ((a - b) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -3.7e+60)
		tmp = t_1;
	elseif (y <= 5.5e+115)
		tmp = Float64(x - Float64(Float64(a - b) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -3.7e+60)
		tmp = t_1;
	elseif (y <= 5.5e+115)
		tmp = x - ((a - b) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.7e+60], t$95$1, If[LessEqual[y, 5.5e+115], N[(x - N[(N[(a - b), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.69999999999999988e60 or 5.5e115 < y

   1. Initial program 91.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      3. lower--.f64 76.0

         \[\leadsto \color{blue}{\left(b - z\right)} \cdot y \]

   5. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -3.69999999999999988e60 < y < 5.5e115

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b} \]

      2. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l- N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right)} - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. associate--l- N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\left(y - 1\right) \cdot z + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto x - \left(\color{blue}{\left(y - 1\right) \cdot z} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      8. *-commutative N/A

         \[\leadsto x - \left(\color{blue}{z \cdot \left(y - 1\right)} + \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(z, y - 1, \left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      10. lower--.f64 97.5

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{\left(t - 1\right) \cdot a} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      12. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      13. lower-*.f64 97.5

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, \color{blue}{a \cdot \left(t - 1\right)} - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      14. lift-*.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b}\right) \]

      15. *-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      16. lower-*.f64 97.5

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - \color{blue}{b \cdot \left(\left(y + t\right) - 2\right)}\right) \]

      17. lift-+.f64 N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right)\right) \]

      18. +-commutative N/A

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

      19. lower-+.f64 97.5

          \[\leadsto x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\color{blue}{\left(t + y\right)} - 2\right)\right) \]

   4. Applied rewrites 97.5%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(z, y - 1, a \cdot \left(t - 1\right) - b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto x - \color{blue}{t \cdot \left(a - b\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \color{blue}{\left(a - b\right) \cdot t} \]

      2. sub-neg N/A

         \[\leadsto x - \color{blue}{\left(a + \left(\mathsf{neg}\left(b\right)\right)\right)} \cdot t \]

      3. mul-1-neg N/A

         \[\leadsto x - \left(a + \color{blue}{-1 \cdot b}\right) \cdot t \]

      4. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\left(a + -1 \cdot b\right) \cdot t} \]

      5. mul-1-neg N/A

         \[\leadsto x - \left(a + \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \cdot t \]

      6. sub-neg N/A

         \[\leadsto x - \color{blue}{\left(a - b\right)} \cdot t \]

      7. lower--.f64 55.7

         \[\leadsto x - \color{blue}{\left(a - b\right)} \cdot t \]

   7. Applied rewrites 55.7%

      \[\leadsto x - \color{blue}{\left(a - b\right) \cdot t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 56.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+114}:\\ \;\;\;\;\left(b - a\right) \cdot t + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -5.4e+62) t_1 (if (<= y 3.3e+114) (+ (* (- b a) t) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -5.4e+62) {
		tmp = t_1;
	} else if (y <= 3.3e+114) {
		tmp = ((b - a) * t) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-5.4d+62)) then
        tmp = t_1
    else if (y <= 3.3d+114) then
        tmp = ((b - a) * t) + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -5.4e+62) {
		tmp = t_1;
	} else if (y <= 3.3e+114) {
		tmp = ((b - a) * t) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -5.4e+62:
		tmp = t_1
	elif y <= 3.3e+114:
		tmp = ((b - a) * t) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -5.4e+62)
		tmp = t_1;
	elseif (y <= 3.3e+114)
		tmp = Float64(Float64(Float64(b - a) * t) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -5.4e+62)
		tmp = t_1;
	elseif (y <= 3.3e+114)
		tmp = ((b - a) * t) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -5.4e+62], t$95$1, If[LessEqual[y, 3.3e+114], N[(N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4e62 or 3.3000000000000001e114 < y

   1. Initial program 91.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      3. lower--.f64 76.8

         \[\leadsto \color{blue}{\left(b - z\right)} \cdot y \]

   5. Applied rewrites 76.8%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -5.4e62 < y < 3.3000000000000001e114

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 77.1

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 77.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b + -1 \cdot a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.3%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in t around inf

      \[\leadsto t \cdot \left(b - a\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 50.3%

       \[\leadsto \left(b - a\right) \cdot t + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 57.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -5.4e+62) t_1 (if (<= y 5.1e+35) (fma (- 1.0 t) a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -5.4e+62) {
		tmp = t_1;
	} else if (y <= 5.1e+35) {
		tmp = fma((1.0 - t), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -5.4e+62)
		tmp = t_1;
	elseif (y <= 5.1e+35)
		tmp = fma(Float64(1.0 - t), a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -5.4e+62], t$95$1, If[LessEqual[y, 5.1e+35], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4e62 or 5.10000000000000017e35 < y

   1. Initial program 92.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      3. lower--.f64 71.2

         \[\leadsto \color{blue}{\left(b - z\right)} \cdot y \]

   5. Applied rewrites 71.2%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -5.4e62 < y < 5.10000000000000017e35

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 77.4

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 46.0%

      \[\leadsto \mathsf{fma}\left(1 - t, \color{blue}{a}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 27: 34.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot y + a\\ \mathbf{if}\;y \leq -0.0034:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+129}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* b y) a)))
   (if (<= y -0.0034) t_1 (if (<= y 1.35e+129) (* (- t 2.0) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * y) + a;
	double tmp;
	if (y <= -0.0034) {
		tmp = t_1;
	} else if (y <= 1.35e+129) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * y) + a
    if (y <= (-0.0034d0)) then
        tmp = t_1
    else if (y <= 1.35d+129) then
        tmp = (t - 2.0d0) * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * y) + a;
	double tmp;
	if (y <= -0.0034) {
		tmp = t_1;
	} else if (y <= 1.35e+129) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * y) + a
	tmp = 0
	if y <= -0.0034:
		tmp = t_1
	elif y <= 1.35e+129:
		tmp = (t - 2.0) * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * y) + a)
	tmp = 0.0
	if (y <= -0.0034)
		tmp = t_1;
	elseif (y <= 1.35e+129)
		tmp = Float64(Float64(t - 2.0) * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * y) + a;
	tmp = 0.0;
	if (y <= -0.0034)
		tmp = t_1;
	elseif (y <= 1.35e+129)
		tmp = (t - 2.0) * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * y), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[y, -0.0034], t$95$1, If[LessEqual[y, 1.35e+129], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00339999999999999981 or 1.35e129 < y

   1. Initial program 92.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 66.1

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 66.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b + -1 \cdot a\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 64.2%

      \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right)\right) + \color{blue}{a} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y + a \]
   10. Step-by-step derivation

   11. Applied rewrites 45.1%

       \[\leadsto b \cdot y + a \]

   if -0.00339999999999999981 < y < 1.35e129

   1. Initial program 97.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 40.0

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 40.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 37.4%

      \[\leadsto \left(t - 2\right) \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 28: 27.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 17500000000000:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+25) (* b t) (if (<= t 17500000000000.0) (* b y) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= 17500000000000.0) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.75d+25)) then
        tmp = b * t
    else if (t <= 17500000000000.0d0) then
        tmp = b * y
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+25) {
		tmp = b * t;
	} else if (t <= 17500000000000.0) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+25:
		tmp = b * t
	elif t <= 17500000000000.0:
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+25)
		tmp = Float64(b * t);
	elseif (t <= 17500000000000.0)
		tmp = Float64(b * y);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.75e+25)
		tmp = b * t;
	elseif (t <= 17500000000000.0)
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+25], N[(b * t), $MachinePrecision], If[LessEqual[t, 17500000000000.0], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75e25 or 1.75e13 < 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. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 45.7

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 45.7%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 41.6%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -1.75e25 < t < 1.75e13

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - 1\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\left(t + \color{blue}{-1}\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(-1 + t\right)}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(-1\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + \left(\mathsf{neg}\left(t\right)\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 67.9

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 67.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 23.0%

      \[\leadsto b \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 29: 18.0% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ b \cdot t \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* b t))

C

double code(double x, double y, double z, double t, double a, double b) {
	return b * t;
}

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 = b * t
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return b * t;
}

Python

def code(x, y, z, t, a, b):
	return b * t

Julia

function code(x, y, z, t, a, b)
	return Float64(b * t)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = b * t;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(b * t), $MachinePrecision]

Derivation

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 b around inf

   \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

   3. lower--.f64 N/A

      \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

   4. +-commutative N/A

      \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. lower-+.f64 41.8

      \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

5. Applied rewrites 41.8%

   \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

6. Taylor expanded in t around inf

   \[\leadsto b \cdot \color{blue}{t} \]
7. Step-by-step derivation

8. Applied rewrites 21.9%

   \[\leadsto b \cdot \color{blue}{t} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024255 
(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)))