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

Percentage Accurate: 95.2% → 98.2%

Time: 19.2s

Alternatives: 24

Speedup: 0.5×

• 35.9% 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: 95.2% 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: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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. Taylor expanded in t around inf 83.6%

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

4. Final simplification 99.2%

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

Alternative 2: 98.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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. Taylor expanded in t around inf 83.6%

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

4. Final simplification 99.2%

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

Alternative 3: 50.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-296}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-273}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+18}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -4.9e+61)
     t_2
     (if (<= t -2.7e-170)
       (+ x a)
       (if (<= t -7.8e-262)
         t_1
         (if (<= t 1.55e-296)
           (+ x a)
           (if (<= t 3.8e-294)
             t_1
             (if (<= t 3.5e-273)
               (+ x z)
               (if (<= t 3.3e-157)
                 (* b (- y 2.0))
                 (if (<= t 2.5e-118)
                   t_1
                   (if (<= t 5.4e+18) (+ x a) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_2;
	} else if (t <= -2.7e-170) {
		tmp = x + a;
	} else if (t <= -7.8e-262) {
		tmp = t_1;
	} else if (t <= 1.55e-296) {
		tmp = x + a;
	} else if (t <= 3.8e-294) {
		tmp = t_1;
	} else if (t <= 3.5e-273) {
		tmp = x + z;
	} else if (t <= 3.3e-157) {
		tmp = b * (y - 2.0);
	} else if (t <= 2.5e-118) {
		tmp = t_1;
	} else if (t <= 5.4e+18) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-4.9d+61)) then
        tmp = t_2
    else if (t <= (-2.7d-170)) then
        tmp = x + a
    else if (t <= (-7.8d-262)) then
        tmp = t_1
    else if (t <= 1.55d-296) then
        tmp = x + a
    else if (t <= 3.8d-294) then
        tmp = t_1
    else if (t <= 3.5d-273) then
        tmp = x + z
    else if (t <= 3.3d-157) then
        tmp = b * (y - 2.0d0)
    else if (t <= 2.5d-118) then
        tmp = t_1
    else if (t <= 5.4d+18) then
        tmp = x + a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_2;
	} else if (t <= -2.7e-170) {
		tmp = x + a;
	} else if (t <= -7.8e-262) {
		tmp = t_1;
	} else if (t <= 1.55e-296) {
		tmp = x + a;
	} else if (t <= 3.8e-294) {
		tmp = t_1;
	} else if (t <= 3.5e-273) {
		tmp = x + z;
	} else if (t <= 3.3e-157) {
		tmp = b * (y - 2.0);
	} else if (t <= 2.5e-118) {
		tmp = t_1;
	} else if (t <= 5.4e+18) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -4.9e+61:
		tmp = t_2
	elif t <= -2.7e-170:
		tmp = x + a
	elif t <= -7.8e-262:
		tmp = t_1
	elif t <= 1.55e-296:
		tmp = x + a
	elif t <= 3.8e-294:
		tmp = t_1
	elif t <= 3.5e-273:
		tmp = x + z
	elif t <= 3.3e-157:
		tmp = b * (y - 2.0)
	elif t <= 2.5e-118:
		tmp = t_1
	elif t <= 5.4e+18:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.9e+61)
		tmp = t_2;
	elseif (t <= -2.7e-170)
		tmp = Float64(x + a);
	elseif (t <= -7.8e-262)
		tmp = t_1;
	elseif (t <= 1.55e-296)
		tmp = Float64(x + a);
	elseif (t <= 3.8e-294)
		tmp = t_1;
	elseif (t <= 3.5e-273)
		tmp = Float64(x + z);
	elseif (t <= 3.3e-157)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 2.5e-118)
		tmp = t_1;
	elseif (t <= 5.4e+18)
		tmp = Float64(x + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.9e+61)
		tmp = t_2;
	elseif (t <= -2.7e-170)
		tmp = x + a;
	elseif (t <= -7.8e-262)
		tmp = t_1;
	elseif (t <= 1.55e-296)
		tmp = x + a;
	elseif (t <= 3.8e-294)
		tmp = t_1;
	elseif (t <= 3.5e-273)
		tmp = x + z;
	elseif (t <= 3.3e-157)
		tmp = b * (y - 2.0);
	elseif (t <= 2.5e-118)
		tmp = t_1;
	elseif (t <= 5.4e+18)
		tmp = x + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.9e+61], t$95$2, If[LessEqual[t, -2.7e-170], N[(x + a), $MachinePrecision], If[LessEqual[t, -7.8e-262], t$95$1, If[LessEqual[t, 1.55e-296], N[(x + a), $MachinePrecision], If[LessEqual[t, 3.8e-294], t$95$1, If[LessEqual[t, 3.5e-273], N[(x + z), $MachinePrecision], If[LessEqual[t, 3.3e-157], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-118], t$95$1, If[LessEqual[t, 5.4e+18], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.90000000000000025e61 or 5.4e18 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -4.90000000000000025e61 < t < -2.6999999999999999e-170 or -7.79999999999999967e-262 < t < 1.5500000000000001e-296 or 2.50000000000000007e-118 < t < 5.4e18

   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. Step-by-step derivation

      1. +-commutative 98.7%

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

      2. fma-def 99.9%

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

      3. associate--l+ 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. associate--l+ 99.9%

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

      8. *-commutative 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. fma-neg 99.9%

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

      11. neg-sub0 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 99.9%

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

      17. *-commutative 99.9%

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

      18. distribute-rgt-neg-in 99.9%

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

      19. neg-sub0 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 74.8%

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

   5. Taylor expanded in t around 0 71.8%

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

      1. associate-+r+ 71.8%

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

      2. *-commutative 71.8%

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

   7. Simplified 71.8%

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

   8. Taylor expanded in a around inf 51.0%

      \[\leadsto x + \color{blue}{a} \]

   if -2.6999999999999999e-170 < t < -7.79999999999999967e-262 or 1.5500000000000001e-296 < t < 3.8e-294 or 3.29999999999999999e-157 < t < 2.50000000000000007e-118

   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. Taylor expanded in y around inf 67.9%

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

   if 3.8e-294 < t < 3.49999999999999992e-273

   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. Taylor expanded in b around 0 85.8%

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

      1. fma-def 85.8%

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

      2. sub-neg 85.8%

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

      3. metadata-eval 85.8%

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

      4. sub-neg 85.8%

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

      5. metadata-eval 85.8%

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

   4. Simplified 85.8%

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

   5. Taylor expanded in a around 0 72.0%

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

   6. Taylor expanded in y around 0 72.0%

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

      1. sub-neg 72.0%

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

      2. neg-mul-1 72.0%

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

      3. remove-double-neg 72.0%

         \[\leadsto x + \color{blue}{z} \]

      4. +-commutative 72.0%

         \[\leadsto \color{blue}{z + x} \]

   8. Simplified 72.0%

      \[\leadsto \color{blue}{z + x} \]

   if 3.49999999999999992e-273 < t < 3.29999999999999999e-157

   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. Taylor expanded in b around inf 48.0%

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

   3. Taylor expanded in t around 0 48.0%

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-262}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-296}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-273}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+18}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 4: 53.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + b \cdot -2\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-264}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* b -2.0)))) (t_2 (* y (- b z))) (t_3 (* t (- b a))))
   (if (<= t -7e+61)
     t_3
     (if (<= t -1.08e-175)
       t_1
       (if (<= t -1.8e-264)
         (* z (- 1.0 y))
         (if (<= t 1.2e-262)
           t_1
           (if (<= t 2.7e-198)
             t_2
             (if (<= t 1.22e-160)
               t_1
               (if (<= t 5.5e-118) t_2 (if (<= t 3.15e+17) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (b * -2.0));
	double t_2 = y * (b - z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -7e+61) {
		tmp = t_3;
	} else if (t <= -1.08e-175) {
		tmp = t_1;
	} else if (t <= -1.8e-264) {
		tmp = z * (1.0 - y);
	} else if (t <= 1.2e-262) {
		tmp = t_1;
	} else if (t <= 2.7e-198) {
		tmp = t_2;
	} else if (t <= 1.22e-160) {
		tmp = t_1;
	} else if (t <= 5.5e-118) {
		tmp = t_2;
	} else if (t <= 3.15e+17) {
		tmp = t_1;
	} 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 = x + (a + (b * (-2.0d0)))
    t_2 = y * (b - z)
    t_3 = t * (b - a)
    if (t <= (-7d+61)) then
        tmp = t_3
    else if (t <= (-1.08d-175)) then
        tmp = t_1
    else if (t <= (-1.8d-264)) then
        tmp = z * (1.0d0 - y)
    else if (t <= 1.2d-262) then
        tmp = t_1
    else if (t <= 2.7d-198) then
        tmp = t_2
    else if (t <= 1.22d-160) then
        tmp = t_1
    else if (t <= 5.5d-118) then
        tmp = t_2
    else if (t <= 3.15d+17) then
        tmp = t_1
    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 = x + (a + (b * -2.0));
	double t_2 = y * (b - z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -7e+61) {
		tmp = t_3;
	} else if (t <= -1.08e-175) {
		tmp = t_1;
	} else if (t <= -1.8e-264) {
		tmp = z * (1.0 - y);
	} else if (t <= 1.2e-262) {
		tmp = t_1;
	} else if (t <= 2.7e-198) {
		tmp = t_2;
	} else if (t <= 1.22e-160) {
		tmp = t_1;
	} else if (t <= 5.5e-118) {
		tmp = t_2;
	} else if (t <= 3.15e+17) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (b * -2.0))
	t_2 = y * (b - z)
	t_3 = t * (b - a)
	tmp = 0
	if t <= -7e+61:
		tmp = t_3
	elif t <= -1.08e-175:
		tmp = t_1
	elif t <= -1.8e-264:
		tmp = z * (1.0 - y)
	elif t <= 1.2e-262:
		tmp = t_1
	elif t <= 2.7e-198:
		tmp = t_2
	elif t <= 1.22e-160:
		tmp = t_1
	elif t <= 5.5e-118:
		tmp = t_2
	elif t <= 3.15e+17:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(b * -2.0)))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7e+61)
		tmp = t_3;
	elseif (t <= -1.08e-175)
		tmp = t_1;
	elseif (t <= -1.8e-264)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 1.2e-262)
		tmp = t_1;
	elseif (t <= 2.7e-198)
		tmp = t_2;
	elseif (t <= 1.22e-160)
		tmp = t_1;
	elseif (t <= 5.5e-118)
		tmp = t_2;
	elseif (t <= 3.15e+17)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (b * -2.0));
	t_2 = y * (b - z);
	t_3 = t * (b - a);
	tmp = 0.0;
	if (t <= -7e+61)
		tmp = t_3;
	elseif (t <= -1.08e-175)
		tmp = t_1;
	elseif (t <= -1.8e-264)
		tmp = z * (1.0 - y);
	elseif (t <= 1.2e-262)
		tmp = t_1;
	elseif (t <= 2.7e-198)
		tmp = t_2;
	elseif (t <= 1.22e-160)
		tmp = t_1;
	elseif (t <= 5.5e-118)
		tmp = t_2;
	elseif (t <= 3.15e+17)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+61], t$95$3, If[LessEqual[t, -1.08e-175], t$95$1, If[LessEqual[t, -1.8e-264], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-262], t$95$1, If[LessEqual[t, 2.7e-198], t$95$2, If[LessEqual[t, 1.22e-160], t$95$1, If[LessEqual[t, 5.5e-118], t$95$2, If[LessEqual[t, 3.15e+17], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.00000000000000036e61 or 3.15e17 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -7.00000000000000036e61 < t < -1.0799999999999999e-175 or -1.8000000000000001e-264 < t < 1.2e-262 or 2.7000000000000002e-198 < t < 1.22000000000000003e-160 or 5.5000000000000003e-118 < t < 3.15e17

   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. Step-by-step derivation

      1. +-commutative 99.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 73.5%

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

   5. Taylor expanded in t around 0 71.2%

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

      1. associate-+r+ 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in z around 0 61.5%

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

      1. *-commutative 61.5%

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

   10. Simplified 61.5%

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

   if -1.0799999999999999e-175 < t < -1.8000000000000001e-264

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 69.5%

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

   if 1.2e-262 < t < 2.7000000000000002e-198 or 1.22000000000000003e-160 < t < 5.5000000000000003e-118

   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. Taylor expanded in y around inf 66.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-175}:\\ \;\;\;\;x + \left(a + b \cdot -2\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-264}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-262}:\\ \;\;\;\;x + \left(a + b \cdot -2\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-160}:\\ \;\;\;\;x + \left(a + b \cdot -2\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{+17}:\\ \;\;\;\;x + \left(a + b \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 5: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + b \cdot -2\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-268}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.1 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* b -2.0)))) (t_2 (* y (- b z))) (t_3 (* t (- b a))))
   (if (<= t -4.9e+61)
     t_3
     (if (<= t -3.05e-173)
       t_1
       (if (<= t -3.5e-268)
         (- z (* y z))
         (if (<= t 1.2e-262)
           t_1
           (if (<= t 1.75e-198)
             t_2
             (if (<= t 8.1e-159)
               t_1
               (if (<= t 2.6e-121) t_2 (if (<= t 3.1e+17) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (b * -2.0));
	double t_2 = y * (b - z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_3;
	} else if (t <= -3.05e-173) {
		tmp = t_1;
	} else if (t <= -3.5e-268) {
		tmp = z - (y * z);
	} else if (t <= 1.2e-262) {
		tmp = t_1;
	} else if (t <= 1.75e-198) {
		tmp = t_2;
	} else if (t <= 8.1e-159) {
		tmp = t_1;
	} else if (t <= 2.6e-121) {
		tmp = t_2;
	} else if (t <= 3.1e+17) {
		tmp = t_1;
	} 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 = x + (a + (b * (-2.0d0)))
    t_2 = y * (b - z)
    t_3 = t * (b - a)
    if (t <= (-4.9d+61)) then
        tmp = t_3
    else if (t <= (-3.05d-173)) then
        tmp = t_1
    else if (t <= (-3.5d-268)) then
        tmp = z - (y * z)
    else if (t <= 1.2d-262) then
        tmp = t_1
    else if (t <= 1.75d-198) then
        tmp = t_2
    else if (t <= 8.1d-159) then
        tmp = t_1
    else if (t <= 2.6d-121) then
        tmp = t_2
    else if (t <= 3.1d+17) then
        tmp = t_1
    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 = x + (a + (b * -2.0));
	double t_2 = y * (b - z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_3;
	} else if (t <= -3.05e-173) {
		tmp = t_1;
	} else if (t <= -3.5e-268) {
		tmp = z - (y * z);
	} else if (t <= 1.2e-262) {
		tmp = t_1;
	} else if (t <= 1.75e-198) {
		tmp = t_2;
	} else if (t <= 8.1e-159) {
		tmp = t_1;
	} else if (t <= 2.6e-121) {
		tmp = t_2;
	} else if (t <= 3.1e+17) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (b * -2.0))
	t_2 = y * (b - z)
	t_3 = t * (b - a)
	tmp = 0
	if t <= -4.9e+61:
		tmp = t_3
	elif t <= -3.05e-173:
		tmp = t_1
	elif t <= -3.5e-268:
		tmp = z - (y * z)
	elif t <= 1.2e-262:
		tmp = t_1
	elif t <= 1.75e-198:
		tmp = t_2
	elif t <= 8.1e-159:
		tmp = t_1
	elif t <= 2.6e-121:
		tmp = t_2
	elif t <= 3.1e+17:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(b * -2.0)))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.9e+61)
		tmp = t_3;
	elseif (t <= -3.05e-173)
		tmp = t_1;
	elseif (t <= -3.5e-268)
		tmp = Float64(z - Float64(y * z));
	elseif (t <= 1.2e-262)
		tmp = t_1;
	elseif (t <= 1.75e-198)
		tmp = t_2;
	elseif (t <= 8.1e-159)
		tmp = t_1;
	elseif (t <= 2.6e-121)
		tmp = t_2;
	elseif (t <= 3.1e+17)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (b * -2.0));
	t_2 = y * (b - z);
	t_3 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.9e+61)
		tmp = t_3;
	elseif (t <= -3.05e-173)
		tmp = t_1;
	elseif (t <= -3.5e-268)
		tmp = z - (y * z);
	elseif (t <= 1.2e-262)
		tmp = t_1;
	elseif (t <= 1.75e-198)
		tmp = t_2;
	elseif (t <= 8.1e-159)
		tmp = t_1;
	elseif (t <= 2.6e-121)
		tmp = t_2;
	elseif (t <= 3.1e+17)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.9e+61], t$95$3, If[LessEqual[t, -3.05e-173], t$95$1, If[LessEqual[t, -3.5e-268], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-262], t$95$1, If[LessEqual[t, 1.75e-198], t$95$2, If[LessEqual[t, 8.1e-159], t$95$1, If[LessEqual[t, 2.6e-121], t$95$2, If[LessEqual[t, 3.1e+17], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.90000000000000025e61 or 3.1e17 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -4.90000000000000025e61 < t < -3.0499999999999999e-173 or -3.50000000000000005e-268 < t < 1.2e-262 or 1.75000000000000013e-198 < t < 8.1000000000000001e-159 or 2.59999999999999986e-121 < t < 3.1e17

   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. Step-by-step derivation

      1. +-commutative 99.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 73.5%

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

   5. Taylor expanded in t around 0 71.2%

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

      1. associate-+r+ 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in z around 0 61.5%

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

      1. *-commutative 61.5%

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

   10. Simplified 61.5%

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

   if -3.0499999999999999e-173 < t < -3.50000000000000005e-268

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 69.5%

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

   3. Taylor expanded in y around 0 69.6%

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

   if 1.2e-262 < t < 1.75000000000000013e-198 or 8.1000000000000001e-159 < t < 2.59999999999999986e-121

   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. Taylor expanded in y around inf 66.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-173}:\\ \;\;\;\;x + \left(a + b \cdot -2\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-268}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-262}:\\ \;\;\;\;x + \left(a + b \cdot -2\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 8.1 \cdot 10^{-159}:\\ \;\;\;\;x + \left(a + b \cdot -2\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-121}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+17}:\\ \;\;\;\;x + \left(a + b \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 6: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-36}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-174}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-267}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+18}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.3e+62)
     t_1
     (if (<= t -1.4e-36)
       (- x (* y z))
       (if (<= t -3.05e-71)
         (* b (- y 2.0))
         (if (<= t -5.5e-174)
           (+ x a)
           (if (<= t -1.95e-267)
             (* z (- 1.0 y))
             (if (<= t 2.45e-259)
               (+ x a)
               (if (<= t 2.2e-117)
                 (* y (- b z))
                 (if (<= t 1.45e+18) (+ x a) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.3e+62) {
		tmp = t_1;
	} else if (t <= -1.4e-36) {
		tmp = x - (y * z);
	} else if (t <= -3.05e-71) {
		tmp = b * (y - 2.0);
	} else if (t <= -5.5e-174) {
		tmp = x + a;
	} else if (t <= -1.95e-267) {
		tmp = z * (1.0 - y);
	} else if (t <= 2.45e-259) {
		tmp = x + a;
	} else if (t <= 2.2e-117) {
		tmp = y * (b - z);
	} else if (t <= 1.45e+18) {
		tmp = x + 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 * (b - a)
    if (t <= (-1.3d+62)) then
        tmp = t_1
    else if (t <= (-1.4d-36)) then
        tmp = x - (y * z)
    else if (t <= (-3.05d-71)) then
        tmp = b * (y - 2.0d0)
    else if (t <= (-5.5d-174)) then
        tmp = x + a
    else if (t <= (-1.95d-267)) then
        tmp = z * (1.0d0 - y)
    else if (t <= 2.45d-259) then
        tmp = x + a
    else if (t <= 2.2d-117) then
        tmp = y * (b - z)
    else if (t <= 1.45d+18) then
        tmp = x + 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 * (b - a);
	double tmp;
	if (t <= -1.3e+62) {
		tmp = t_1;
	} else if (t <= -1.4e-36) {
		tmp = x - (y * z);
	} else if (t <= -3.05e-71) {
		tmp = b * (y - 2.0);
	} else if (t <= -5.5e-174) {
		tmp = x + a;
	} else if (t <= -1.95e-267) {
		tmp = z * (1.0 - y);
	} else if (t <= 2.45e-259) {
		tmp = x + a;
	} else if (t <= 2.2e-117) {
		tmp = y * (b - z);
	} else if (t <= 1.45e+18) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.3e+62:
		tmp = t_1
	elif t <= -1.4e-36:
		tmp = x - (y * z)
	elif t <= -3.05e-71:
		tmp = b * (y - 2.0)
	elif t <= -5.5e-174:
		tmp = x + a
	elif t <= -1.95e-267:
		tmp = z * (1.0 - y)
	elif t <= 2.45e-259:
		tmp = x + a
	elif t <= 2.2e-117:
		tmp = y * (b - z)
	elif t <= 1.45e+18:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.3e+62)
		tmp = t_1;
	elseif (t <= -1.4e-36)
		tmp = Float64(x - Float64(y * z));
	elseif (t <= -3.05e-71)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= -5.5e-174)
		tmp = Float64(x + a);
	elseif (t <= -1.95e-267)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 2.45e-259)
		tmp = Float64(x + a);
	elseif (t <= 2.2e-117)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 1.45e+18)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.3e+62)
		tmp = t_1;
	elseif (t <= -1.4e-36)
		tmp = x - (y * z);
	elseif (t <= -3.05e-71)
		tmp = b * (y - 2.0);
	elseif (t <= -5.5e-174)
		tmp = x + a;
	elseif (t <= -1.95e-267)
		tmp = z * (1.0 - y);
	elseif (t <= 2.45e-259)
		tmp = x + a;
	elseif (t <= 2.2e-117)
		tmp = y * (b - z);
	elseif (t <= 1.45e+18)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+62], t$95$1, If[LessEqual[t, -1.4e-36], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.05e-71], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-174], N[(x + a), $MachinePrecision], If[LessEqual[t, -1.95e-267], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e-259], N[(x + a), $MachinePrecision], If[LessEqual[t, 2.2e-117], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+18], N[(x + a), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.29999999999999992e62 or 1.45e18 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -1.29999999999999992e62 < t < -1.4000000000000001e-36

   1. Initial program 99.7%

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

   2. Taylor expanded in b around 0 99.3%

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

      1. fma-def 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. sub-neg 99.4%

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

      5. metadata-eval 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in a around 0 79.8%

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

   6. Taylor expanded in y around inf 66.6%

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

   if -1.4000000000000001e-36 < t < -3.0499999999999999e-71

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 48.4%

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

   3. Taylor expanded in t around 0 48.4%

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

   if -3.0499999999999999e-71 < t < -5.4999999999999999e-174 or -1.94999999999999988e-267 < t < 2.45000000000000011e-259 or 2.2000000000000001e-117 < t < 1.45e18

   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. Step-by-step derivation

      1. +-commutative 98.6%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 75.7%

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

   5. Taylor expanded in t around 0 74.1%

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

      1. associate-+r+ 74.1%

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

      2. *-commutative 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in a around inf 52.3%

      \[\leadsto x + \color{blue}{a} \]

   if -5.4999999999999999e-174 < t < -1.94999999999999988e-267

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 69.5%

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

   if 2.45000000000000011e-259 < t < 2.2000000000000001e-117

   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. Taylor expanded in y around inf 52.7%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-36}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-174}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-267}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+18}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 7: 38.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-45}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-117}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-130}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+77}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.05e+91)
     t_1
     (if (<= a -3.1e-26)
       (* y (- z))
       (if (<= a -6.6e-45)
         (+ x z)
         (if (<= a -3.2e-117)
           (* t b)
           (if (<= a 1.95e-130)
             (+ x z)
             (if (<= a 3.2e-39) (* y b) (if (<= a 1.4e+77) (+ x z) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.05e+91) {
		tmp = t_1;
	} else if (a <= -3.1e-26) {
		tmp = y * -z;
	} else if (a <= -6.6e-45) {
		tmp = x + z;
	} else if (a <= -3.2e-117) {
		tmp = t * b;
	} else if (a <= 1.95e-130) {
		tmp = x + z;
	} else if (a <= 3.2e-39) {
		tmp = y * b;
	} else if (a <= 1.4e+77) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1.05d+91)) then
        tmp = t_1
    else if (a <= (-3.1d-26)) then
        tmp = y * -z
    else if (a <= (-6.6d-45)) then
        tmp = x + z
    else if (a <= (-3.2d-117)) then
        tmp = t * b
    else if (a <= 1.95d-130) then
        tmp = x + z
    else if (a <= 3.2d-39) then
        tmp = y * b
    else if (a <= 1.4d+77) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.05e+91) {
		tmp = t_1;
	} else if (a <= -3.1e-26) {
		tmp = y * -z;
	} else if (a <= -6.6e-45) {
		tmp = x + z;
	} else if (a <= -3.2e-117) {
		tmp = t * b;
	} else if (a <= 1.95e-130) {
		tmp = x + z;
	} else if (a <= 3.2e-39) {
		tmp = y * b;
	} else if (a <= 1.4e+77) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -1.05e+91:
		tmp = t_1
	elif a <= -3.1e-26:
		tmp = y * -z
	elif a <= -6.6e-45:
		tmp = x + z
	elif a <= -3.2e-117:
		tmp = t * b
	elif a <= 1.95e-130:
		tmp = x + z
	elif a <= 3.2e-39:
		tmp = y * b
	elif a <= 1.4e+77:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.05e+91)
		tmp = t_1;
	elseif (a <= -3.1e-26)
		tmp = Float64(y * Float64(-z));
	elseif (a <= -6.6e-45)
		tmp = Float64(x + z);
	elseif (a <= -3.2e-117)
		tmp = Float64(t * b);
	elseif (a <= 1.95e-130)
		tmp = Float64(x + z);
	elseif (a <= 3.2e-39)
		tmp = Float64(y * b);
	elseif (a <= 1.4e+77)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.05e+91)
		tmp = t_1;
	elseif (a <= -3.1e-26)
		tmp = y * -z;
	elseif (a <= -6.6e-45)
		tmp = x + z;
	elseif (a <= -3.2e-117)
		tmp = t * b;
	elseif (a <= 1.95e-130)
		tmp = x + z;
	elseif (a <= 3.2e-39)
		tmp = y * b;
	elseif (a <= 1.4e+77)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+91], t$95$1, If[LessEqual[a, -3.1e-26], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, -6.6e-45], N[(x + z), $MachinePrecision], If[LessEqual[a, -3.2e-117], N[(t * b), $MachinePrecision], If[LessEqual[a, 1.95e-130], N[(x + z), $MachinePrecision], If[LessEqual[a, 3.2e-39], N[(y * b), $MachinePrecision], If[LessEqual[a, 1.4e+77], N[(x + z), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.05000000000000004e91 or 1.4e77 < a

   1. Initial program 92.4%

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

   2. Taylor expanded in a around inf 65.6%

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

   if -1.05000000000000004e91 < a < -3.09999999999999983e-26

   1. Initial program 88.4%

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

   2. Taylor expanded in z around inf 43.6%

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

   3. Taylor expanded in y around inf 32.0%

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

      1. mul-1-neg 32.0%

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

      2. distribute-rgt-neg-in 32.0%

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

   5. Simplified 32.0%

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

   if -3.09999999999999983e-26 < a < -6.6000000000000001e-45 or -3.19999999999999995e-117 < a < 1.95e-130 or 3.1999999999999998e-39 < a < 1.4e77

   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. Taylor expanded in b around 0 64.3%

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

      1. fma-def 64.3%

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

      2. sub-neg 64.3%

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

      3. metadata-eval 64.3%

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

      4. sub-neg 64.3%

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

      5. metadata-eval 64.3%

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

   4. Simplified 64.3%

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

   5. Taylor expanded in a around 0 58.4%

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

   6. Taylor expanded in y around 0 44.0%

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

      1. sub-neg 44.0%

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

      2. neg-mul-1 44.0%

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

      3. remove-double-neg 44.0%

         \[\leadsto x + \color{blue}{z} \]

      4. +-commutative 44.0%

         \[\leadsto \color{blue}{z + x} \]

   8. Simplified 44.0%

      \[\leadsto \color{blue}{z + x} \]

   if -6.6000000000000001e-45 < a < -3.19999999999999995e-117

   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. Taylor expanded in a around 0 93.7%

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

   3. Taylor expanded in t around inf 54.8%

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

   if 1.95e-130 < a < 3.1999999999999998e-39

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 59.5%

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

   3. Taylor expanded in b around inf 41.3%

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

      1. *-commutative 41.3%

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

   5. Simplified 41.3%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-45}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-117}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-130}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-39}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+77}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 8: 54.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-50}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 122000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -4.5e+53)
     t_1
     (if (<= b -2.1e-14)
       (+ x a)
       (if (<= b -2.65e-42)
         (* y (- b z))
         (if (<= b -1.12e-50)
           (+ x z)
           (if (<= b -3.8e-112)
             (* a (- 1.0 t))
             (if (<= b 122000000.0) (- x (* y z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -4.5e+53) {
		tmp = t_1;
	} else if (b <= -2.1e-14) {
		tmp = x + a;
	} else if (b <= -2.65e-42) {
		tmp = y * (b - z);
	} else if (b <= -1.12e-50) {
		tmp = x + z;
	} else if (b <= -3.8e-112) {
		tmp = a * (1.0 - t);
	} else if (b <= 122000000.0) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-4.5d+53)) then
        tmp = t_1
    else if (b <= (-2.1d-14)) then
        tmp = x + a
    else if (b <= (-2.65d-42)) then
        tmp = y * (b - z)
    else if (b <= (-1.12d-50)) then
        tmp = x + z
    else if (b <= (-3.8d-112)) then
        tmp = a * (1.0d0 - t)
    else if (b <= 122000000.0d0) then
        tmp = x - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -4.5e+53) {
		tmp = t_1;
	} else if (b <= -2.1e-14) {
		tmp = x + a;
	} else if (b <= -2.65e-42) {
		tmp = y * (b - z);
	} else if (b <= -1.12e-50) {
		tmp = x + z;
	} else if (b <= -3.8e-112) {
		tmp = a * (1.0 - t);
	} else if (b <= 122000000.0) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -4.5e+53:
		tmp = t_1
	elif b <= -2.1e-14:
		tmp = x + a
	elif b <= -2.65e-42:
		tmp = y * (b - z)
	elif b <= -1.12e-50:
		tmp = x + z
	elif b <= -3.8e-112:
		tmp = a * (1.0 - t)
	elif b <= 122000000.0:
		tmp = x - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -4.5e+53)
		tmp = t_1;
	elseif (b <= -2.1e-14)
		tmp = Float64(x + a);
	elseif (b <= -2.65e-42)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= -1.12e-50)
		tmp = Float64(x + z);
	elseif (b <= -3.8e-112)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 122000000.0)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -4.5e+53)
		tmp = t_1;
	elseif (b <= -2.1e-14)
		tmp = x + a;
	elseif (b <= -2.65e-42)
		tmp = y * (b - z);
	elseif (b <= -1.12e-50)
		tmp = x + z;
	elseif (b <= -3.8e-112)
		tmp = a * (1.0 - t);
	elseif (b <= 122000000.0)
		tmp = x - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -4.5e+53], t$95$1, If[LessEqual[b, -2.1e-14], N[(x + a), $MachinePrecision], If[LessEqual[b, -2.65e-42], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.12e-50], N[(x + z), $MachinePrecision], If[LessEqual[b, -3.8e-112], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 122000000.0], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.5000000000000002e53 or 1.22e8 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in b around inf 75.5%

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

   if -4.5000000000000002e53 < b < -2.0999999999999999e-14

   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. Step-by-step derivation

      1. +-commutative 90.9%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 73.7%

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

   5. Taylor expanded in t around 0 65.3%

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

      1. associate-+r+ 65.3%

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

      2. *-commutative 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in a around inf 56.5%

      \[\leadsto x + \color{blue}{a} \]

   if -2.0999999999999999e-14 < b < -2.65e-42

   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. Taylor expanded in y around inf 76.2%

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

   if -2.65e-42 < b < -1.12e-50

   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. Taylor expanded in b around 0 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. remove-double-neg 100.0%

         \[\leadsto x + \color{blue}{z} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{z + x} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{z + x} \]

   if -1.12e-50 < b < -3.79999999999999995e-112

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 47.6%

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

   if -3.79999999999999995e-112 < b < 1.22e8

   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. Taylor expanded in b around 0 94.9%

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

      1. fma-def 94.9%

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

      2. sub-neg 94.9%

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

      3. metadata-eval 94.9%

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

      4. sub-neg 94.9%

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

      5. metadata-eval 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in a around 0 60.8%

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

   6. Taylor expanded in y around inf 49.3%

      \[\leadsto x - \color{blue}{y \cdot z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-50}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-112}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 122000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 9: 86.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+49} \lor \neg \left(b \leq 5 \cdot 10^{+69}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -4.7e+49) (not (<= b 5e+69)))
     (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
     (+ x (+ (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -4.7e+49) || !(b <= 5e+69)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((b <= (-4.7d+49)) .or. (.not. (b <= 5d+69))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else
        tmp = x + ((a * (1.0d0 - t)) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((b <= -4.7e+49) || !(b <= 5e+69)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -4.7e+49) or not (b <= 5e+69):
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	else:
		tmp = x + ((a * (1.0 - t)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((b <= -4.7e+49) || !(b <= 5e+69))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((b <= -4.7e+49) || ~((b <= 5e+69)))
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	else
		tmp = x + ((a * (1.0 - t)) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -4.7e+49], N[Not[LessEqual[b, 5e+69]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.6999999999999997e49 or 5.00000000000000036e69 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in a around 0 86.9%

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

   if -4.6999999999999997e49 < b < 5.00000000000000036e69

   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. Taylor expanded in b around 0 92.0%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+49} \lor \neg \left(b \leq 5 \cdot 10^{+69}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 10: 34.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-173}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -5.5e+213)
     t_1
     (if (<= t -5.5e+63)
       (* t b)
       (if (<= t -2.45e-173)
         (+ x a)
         (if (<= t -4.9e-261)
           (* y (- z))
           (if (<= t 4.8e-261)
             (+ x a)
             (if (<= t 5.2e-200)
               (* y b)
               (if (<= t 1.65e+58) (+ x a) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -5.5e+213) {
		tmp = t_1;
	} else if (t <= -5.5e+63) {
		tmp = t * b;
	} else if (t <= -2.45e-173) {
		tmp = x + a;
	} else if (t <= -4.9e-261) {
		tmp = y * -z;
	} else if (t <= 4.8e-261) {
		tmp = x + a;
	} else if (t <= 5.2e-200) {
		tmp = y * b;
	} else if (t <= 1.65e+58) {
		tmp = x + 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 * -a
    if (t <= (-5.5d+213)) then
        tmp = t_1
    else if (t <= (-5.5d+63)) then
        tmp = t * b
    else if (t <= (-2.45d-173)) then
        tmp = x + a
    else if (t <= (-4.9d-261)) then
        tmp = y * -z
    else if (t <= 4.8d-261) then
        tmp = x + a
    else if (t <= 5.2d-200) then
        tmp = y * b
    else if (t <= 1.65d+58) then
        tmp = x + 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 * -a;
	double tmp;
	if (t <= -5.5e+213) {
		tmp = t_1;
	} else if (t <= -5.5e+63) {
		tmp = t * b;
	} else if (t <= -2.45e-173) {
		tmp = x + a;
	} else if (t <= -4.9e-261) {
		tmp = y * -z;
	} else if (t <= 4.8e-261) {
		tmp = x + a;
	} else if (t <= 5.2e-200) {
		tmp = y * b;
	} else if (t <= 1.65e+58) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -5.5e+213:
		tmp = t_1
	elif t <= -5.5e+63:
		tmp = t * b
	elif t <= -2.45e-173:
		tmp = x + a
	elif t <= -4.9e-261:
		tmp = y * -z
	elif t <= 4.8e-261:
		tmp = x + a
	elif t <= 5.2e-200:
		tmp = y * b
	elif t <= 1.65e+58:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -5.5e+213)
		tmp = t_1;
	elseif (t <= -5.5e+63)
		tmp = Float64(t * b);
	elseif (t <= -2.45e-173)
		tmp = Float64(x + a);
	elseif (t <= -4.9e-261)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 4.8e-261)
		tmp = Float64(x + a);
	elseif (t <= 5.2e-200)
		tmp = Float64(y * b);
	elseif (t <= 1.65e+58)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -5.5e+213)
		tmp = t_1;
	elseif (t <= -5.5e+63)
		tmp = t * b;
	elseif (t <= -2.45e-173)
		tmp = x + a;
	elseif (t <= -4.9e-261)
		tmp = y * -z;
	elseif (t <= 4.8e-261)
		tmp = x + a;
	elseif (t <= 5.2e-200)
		tmp = y * b;
	elseif (t <= 1.65e+58)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -5.5e+213], t$95$1, If[LessEqual[t, -5.5e+63], N[(t * b), $MachinePrecision], If[LessEqual[t, -2.45e-173], N[(x + a), $MachinePrecision], If[LessEqual[t, -4.9e-261], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 4.8e-261], N[(x + a), $MachinePrecision], If[LessEqual[t, 5.2e-200], N[(y * b), $MachinePrecision], If[LessEqual[t, 1.65e+58], N[(x + a), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.50000000000000059e213 or 1.64999999999999991e58 < t

   1. Initial program 87.1%

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

   2. Taylor expanded in a around inf 47.2%

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

   3. Taylor expanded in t around inf 47.2%

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

      1. associate-*r* 47.2%

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

      2. mul-1-neg 47.2%

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

   5. Simplified 47.2%

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

   if -5.50000000000000059e213 < t < -5.50000000000000004e63

   1. Initial program 96.7%

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

   2. Taylor expanded in a around 0 90.4%

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

   3. Taylor expanded in t around inf 52.9%

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

   if -5.50000000000000004e63 < t < -2.44999999999999996e-173 or -4.90000000000000005e-261 < t < 4.80000000000000028e-261 or 5.19999999999999979e-200 < t < 1.64999999999999991e58

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 68.5%

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

   5. Taylor expanded in t around 0 65.8%

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

      1. associate-+r+ 65.8%

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

      2. *-commutative 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in a around inf 44.6%

      \[\leadsto x + \color{blue}{a} \]

   if -2.44999999999999996e-173 < t < -4.90000000000000005e-261

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 66.1%

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

   3. Taylor expanded in y around inf 41.1%

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

      1. mul-1-neg 41.1%

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

      2. distribute-rgt-neg-in 41.1%

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

   5. Simplified 41.1%

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

   if 4.80000000000000028e-261 < t < 5.19999999999999979e-200

   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. Taylor expanded in y around inf 62.8%

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

   3. Taylor expanded in b around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+213}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-173}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]

Alternative 11: 39.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-116}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-142}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+77}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= a -1e+89)
     t_2
     (if (<= a -1.7e-17)
       t_1
       (if (<= a -1e-116)
         (* t b)
         (if (<= a 1.42e-142)
           (+ x z)
           (if (<= a 2.25e-39) t_1 (if (<= a 1.35e+77) (+ x z) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1e+89) {
		tmp = t_2;
	} else if (a <= -1.7e-17) {
		tmp = t_1;
	} else if (a <= -1e-116) {
		tmp = t * b;
	} else if (a <= 1.42e-142) {
		tmp = x + z;
	} else if (a <= 2.25e-39) {
		tmp = t_1;
	} else if (a <= 1.35e+77) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (a <= (-1d+89)) then
        tmp = t_2
    else if (a <= (-1.7d-17)) then
        tmp = t_1
    else if (a <= (-1d-116)) then
        tmp = t * b
    else if (a <= 1.42d-142) then
        tmp = x + z
    else if (a <= 2.25d-39) then
        tmp = t_1
    else if (a <= 1.35d+77) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1e+89) {
		tmp = t_2;
	} else if (a <= -1.7e-17) {
		tmp = t_1;
	} else if (a <= -1e-116) {
		tmp = t * b;
	} else if (a <= 1.42e-142) {
		tmp = x + z;
	} else if (a <= 2.25e-39) {
		tmp = t_1;
	} else if (a <= 1.35e+77) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -1e+89:
		tmp = t_2
	elif a <= -1.7e-17:
		tmp = t_1
	elif a <= -1e-116:
		tmp = t * b
	elif a <= 1.42e-142:
		tmp = x + z
	elif a <= 2.25e-39:
		tmp = t_1
	elif a <= 1.35e+77:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1e+89)
		tmp = t_2;
	elseif (a <= -1.7e-17)
		tmp = t_1;
	elseif (a <= -1e-116)
		tmp = Float64(t * b);
	elseif (a <= 1.42e-142)
		tmp = Float64(x + z);
	elseif (a <= 2.25e-39)
		tmp = t_1;
	elseif (a <= 1.35e+77)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1e+89)
		tmp = t_2;
	elseif (a <= -1.7e-17)
		tmp = t_1;
	elseif (a <= -1e-116)
		tmp = t * b;
	elseif (a <= 1.42e-142)
		tmp = x + z;
	elseif (a <= 2.25e-39)
		tmp = t_1;
	elseif (a <= 1.35e+77)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+89], t$95$2, If[LessEqual[a, -1.7e-17], t$95$1, If[LessEqual[a, -1e-116], N[(t * b), $MachinePrecision], If[LessEqual[a, 1.42e-142], N[(x + z), $MachinePrecision], If[LessEqual[a, 2.25e-39], t$95$1, If[LessEqual[a, 1.35e+77], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.99999999999999995e88 or 1.3499999999999999e77 < a

   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. Taylor expanded in a around inf 65.0%

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

   if -9.99999999999999995e88 < a < -1.6999999999999999e-17 or 1.42000000000000007e-142 < a < 2.25e-39

   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. Taylor expanded in b around inf 56.7%

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

   3. Taylor expanded in t around 0 45.4%

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

   if -1.6999999999999999e-17 < a < -9.9999999999999999e-117

   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. Taylor expanded in a around 0 87.8%

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

   3. Taylor expanded in t around inf 43.3%

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

   if -9.9999999999999999e-117 < a < 1.42000000000000007e-142 or 2.25e-39 < a < 1.3499999999999999e77

   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. Taylor expanded in b around 0 63.4%

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

      1. fma-def 63.4%

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

      2. sub-neg 63.4%

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

      3. metadata-eval 63.4%

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

      4. sub-neg 63.4%

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

      5. metadata-eval 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in a around 0 59.2%

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

   6. Taylor expanded in y around 0 44.1%

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

      1. sub-neg 44.1%

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

      2. neg-mul-1 44.1%

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

      3. remove-double-neg 44.1%

         \[\leadsto x + \color{blue}{z} \]

      4. +-commutative 44.1%

         \[\leadsto \color{blue}{z + x} \]

   8. Simplified 44.1%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-116}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-142}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+77}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 12: 49.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{+18}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -4.9e+61)
     t_2
     (if (<= t -7.6e-170)
       (+ x a)
       (if (<= t -9e-289)
         t_1
         (if (<= t 1.2e-261)
           (+ x a)
           (if (<= t 1.56e-125) t_1 (if (<= t 1.86e+18) (+ x a) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_2;
	} else if (t <= -7.6e-170) {
		tmp = x + a;
	} else if (t <= -9e-289) {
		tmp = t_1;
	} else if (t <= 1.2e-261) {
		tmp = x + a;
	} else if (t <= 1.56e-125) {
		tmp = t_1;
	} else if (t <= 1.86e+18) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-4.9d+61)) then
        tmp = t_2
    else if (t <= (-7.6d-170)) then
        tmp = x + a
    else if (t <= (-9d-289)) then
        tmp = t_1
    else if (t <= 1.2d-261) then
        tmp = x + a
    else if (t <= 1.56d-125) then
        tmp = t_1
    else if (t <= 1.86d+18) then
        tmp = x + a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_2;
	} else if (t <= -7.6e-170) {
		tmp = x + a;
	} else if (t <= -9e-289) {
		tmp = t_1;
	} else if (t <= 1.2e-261) {
		tmp = x + a;
	} else if (t <= 1.56e-125) {
		tmp = t_1;
	} else if (t <= 1.86e+18) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -4.9e+61:
		tmp = t_2
	elif t <= -7.6e-170:
		tmp = x + a
	elif t <= -9e-289:
		tmp = t_1
	elif t <= 1.2e-261:
		tmp = x + a
	elif t <= 1.56e-125:
		tmp = t_1
	elif t <= 1.86e+18:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.9e+61)
		tmp = t_2;
	elseif (t <= -7.6e-170)
		tmp = Float64(x + a);
	elseif (t <= -9e-289)
		tmp = t_1;
	elseif (t <= 1.2e-261)
		tmp = Float64(x + a);
	elseif (t <= 1.56e-125)
		tmp = t_1;
	elseif (t <= 1.86e+18)
		tmp = Float64(x + a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.9e+61)
		tmp = t_2;
	elseif (t <= -7.6e-170)
		tmp = x + a;
	elseif (t <= -9e-289)
		tmp = t_1;
	elseif (t <= 1.2e-261)
		tmp = x + a;
	elseif (t <= 1.56e-125)
		tmp = t_1;
	elseif (t <= 1.86e+18)
		tmp = x + a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.9e+61], t$95$2, If[LessEqual[t, -7.6e-170], N[(x + a), $MachinePrecision], If[LessEqual[t, -9e-289], t$95$1, If[LessEqual[t, 1.2e-261], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.56e-125], t$95$1, If[LessEqual[t, 1.86e+18], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.90000000000000025e61 or 1.86e18 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -4.90000000000000025e61 < t < -7.5999999999999995e-170 or -9.0000000000000003e-289 < t < 1.20000000000000007e-261 or 1.5599999999999999e-125 < t < 1.86e18

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 99.9%

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

      3. associate--l+ 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. associate--l+ 99.9%

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

      8. *-commutative 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. fma-neg 99.9%

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

      11. neg-sub0 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 99.9%

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

      17. *-commutative 99.9%

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

      18. distribute-rgt-neg-in 99.9%

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

      19. neg-sub0 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 99.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 72.1%

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

   5. Taylor expanded in t around 0 69.4%

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

      1. associate-+r+ 69.4%

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

      2. *-commutative 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in a around inf 51.2%

      \[\leadsto x + \color{blue}{a} \]

   if -7.5999999999999995e-170 < t < -9.0000000000000003e-289 or 1.20000000000000007e-261 < t < 1.5599999999999999e-125

   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. Taylor expanded in b around inf 44.1%

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

   3. Taylor expanded in t around 0 44.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-289}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-261}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-125}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{+18}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 13: 50.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-171}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-267}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+17}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.9e+61)
     t_1
     (if (<= t -1.35e-171)
       (+ x a)
       (if (<= t -5.9e-267)
         (* z (- 1.0 y))
         (if (<= t 1.2e-259)
           (+ x a)
           (if (<= t 6.2e-119)
             (* y (- b z))
             (if (<= t 4e+17) (+ x a) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_1;
	} else if (t <= -1.35e-171) {
		tmp = x + a;
	} else if (t <= -5.9e-267) {
		tmp = z * (1.0 - y);
	} else if (t <= 1.2e-259) {
		tmp = x + a;
	} else if (t <= 6.2e-119) {
		tmp = y * (b - z);
	} else if (t <= 4e+17) {
		tmp = x + 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 * (b - a)
    if (t <= (-4.9d+61)) then
        tmp = t_1
    else if (t <= (-1.35d-171)) then
        tmp = x + a
    else if (t <= (-5.9d-267)) then
        tmp = z * (1.0d0 - y)
    else if (t <= 1.2d-259) then
        tmp = x + a
    else if (t <= 6.2d-119) then
        tmp = y * (b - z)
    else if (t <= 4d+17) then
        tmp = x + 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 * (b - a);
	double tmp;
	if (t <= -4.9e+61) {
		tmp = t_1;
	} else if (t <= -1.35e-171) {
		tmp = x + a;
	} else if (t <= -5.9e-267) {
		tmp = z * (1.0 - y);
	} else if (t <= 1.2e-259) {
		tmp = x + a;
	} else if (t <= 6.2e-119) {
		tmp = y * (b - z);
	} else if (t <= 4e+17) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.9e+61:
		tmp = t_1
	elif t <= -1.35e-171:
		tmp = x + a
	elif t <= -5.9e-267:
		tmp = z * (1.0 - y)
	elif t <= 1.2e-259:
		tmp = x + a
	elif t <= 6.2e-119:
		tmp = y * (b - z)
	elif t <= 4e+17:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.9e+61)
		tmp = t_1;
	elseif (t <= -1.35e-171)
		tmp = Float64(x + a);
	elseif (t <= -5.9e-267)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 1.2e-259)
		tmp = Float64(x + a);
	elseif (t <= 6.2e-119)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 4e+17)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.9e+61)
		tmp = t_1;
	elseif (t <= -1.35e-171)
		tmp = x + a;
	elseif (t <= -5.9e-267)
		tmp = z * (1.0 - y);
	elseif (t <= 1.2e-259)
		tmp = x + a;
	elseif (t <= 6.2e-119)
		tmp = y * (b - z);
	elseif (t <= 4e+17)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.9e+61], t$95$1, If[LessEqual[t, -1.35e-171], N[(x + a), $MachinePrecision], If[LessEqual[t, -5.9e-267], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-259], N[(x + a), $MachinePrecision], If[LessEqual[t, 6.2e-119], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+17], N[(x + a), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.90000000000000025e61 or 4e17 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 71.7%

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

   if -4.90000000000000025e61 < t < -1.35000000000000007e-171 or -5.89999999999999974e-267 < t < 1.2e-259 or 6.19999999999999956e-119 < t < 4e17

   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. Step-by-step derivation

      1. +-commutative 98.9%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 72.5%

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

   5. Taylor expanded in t around 0 70.0%

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

      1. associate-+r+ 70.0%

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

      2. *-commutative 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in a around inf 49.7%

      \[\leadsto x + \color{blue}{a} \]

   if -1.35000000000000007e-171 < t < -5.89999999999999974e-267

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 69.5%

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

   if 1.2e-259 < t < 6.19999999999999956e-119

   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. Taylor expanded in y around inf 52.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-171}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-267}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-259}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+17}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 14: 71.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(1 - t\right) - y \cdot z\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y))))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -9.2e+51)
     t_2
     (if (<= b -1.6e-260)
       t_1
       (if (<= b 2.2e-284)
         (- (* a (- 1.0 t)) (* y z))
         (if (<= b 1.75e-21) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -9.2e+51) {
		tmp = t_2;
	} else if (b <= -1.6e-260) {
		tmp = t_1;
	} else if (b <= 2.2e-284) {
		tmp = (a * (1.0 - t)) - (y * z);
	} else if (b <= 1.75e-21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a + (z * (1.0d0 - y)))
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-9.2d+51)) then
        tmp = t_2
    else if (b <= (-1.6d-260)) then
        tmp = t_1
    else if (b <= 2.2d-284) then
        tmp = (a * (1.0d0 - t)) - (y * z)
    else if (b <= 1.75d-21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -9.2e+51) {
		tmp = t_2;
	} else if (b <= -1.6e-260) {
		tmp = t_1;
	} else if (b <= 2.2e-284) {
		tmp = (a * (1.0 - t)) - (y * z);
	} else if (b <= 1.75e-21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -9.2e+51:
		tmp = t_2
	elif b <= -1.6e-260:
		tmp = t_1
	elif b <= 2.2e-284:
		tmp = (a * (1.0 - t)) - (y * z)
	elif b <= 1.75e-21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -9.2e+51)
		tmp = t_2;
	elseif (b <= -1.6e-260)
		tmp = t_1;
	elseif (b <= 2.2e-284)
		tmp = Float64(Float64(a * Float64(1.0 - t)) - Float64(y * z));
	elseif (b <= 1.75e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -9.2e+51)
		tmp = t_2;
	elseif (b <= -1.6e-260)
		tmp = t_1;
	elseif (b <= 2.2e-284)
		tmp = (a * (1.0 - t)) - (y * z);
	elseif (b <= 1.75e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+51], t$95$2, If[LessEqual[b, -1.6e-260], t$95$1, If[LessEqual[b, 2.2e-284], N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.75e-21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.2000000000000002e51 or 1.7500000000000002e-21 < b

   1. Initial program 91.0%

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

   2. Taylor expanded in a around 0 82.6%

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

   3. Taylor expanded in z around 0 77.5%

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

   if -9.2000000000000002e51 < b < -1.59999999999999997e-260 or 2.2000000000000001e-284 < b < 1.7500000000000002e-21

   1. Initial program 99.1%

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

   2. Taylor expanded in b around 0 95.1%

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

      1. fma-def 95.2%

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

      2. sub-neg 95.2%

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

      3. metadata-eval 95.2%

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

      4. sub-neg 95.2%

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

      5. metadata-eval 95.2%

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

   4. Simplified 95.2%

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

   5. Taylor expanded in t around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. neg-mul-1 80.4%

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

      3. unsub-neg 80.4%

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

      4. sub-neg 80.4%

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

      5. metadata-eval 80.4%

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

   7. Simplified 80.4%

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

   if -1.59999999999999997e-260 < b < 2.2000000000000001e-284

   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. Taylor expanded in b around 0 99.9%

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

      1. fma-def 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in y around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. neg-mul-1 75.7%

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

   8. Simplified 75.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-260}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-284}:\\ \;\;\;\;a \cdot \left(1 - t\right) - y \cdot z\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-21}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 15: 83.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+52} \lor \neg \left(b \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.35e+52) (not (<= b 2e+70)))
   (+ x (* (- (+ y t) 2.0) b))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.35e+52) || !(b <= 2e+70)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.35d+52)) .or. (.not. (b <= 2d+70))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.35e+52) || !(b <= 2e+70)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.35e+52) or not (b <= 2e+70):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.35e+52) || !(b <= 2e+70))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.35e+52) || ~((b <= 2e+70)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.35e+52], N[Not[LessEqual[b, 2e+70]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35e52 or 2.00000000000000015e70 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in a around 0 86.9%

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

   3. Taylor expanded in z around 0 82.7%

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

   if -1.35e52 < b < 2.00000000000000015e70

   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. Taylor expanded in b around 0 92.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+52} \lor \neg \left(b \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 16: 53.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) + t \cdot b\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -9.6 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x z) (* t b))) (t_2 (* a (- 1.0 t))))
   (if (<= a -9.6e+98)
     t_2
     (if (<= a 3.05e-127)
       t_1
       (if (<= a 5.8e-49) (* y (- b z)) (if (<= a 2e+79) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (t * b);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -9.6e+98) {
		tmp = t_2;
	} else if (a <= 3.05e-127) {
		tmp = t_1;
	} else if (a <= 5.8e-49) {
		tmp = y * (b - z);
	} else if (a <= 2e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + z) + (t * b)
    t_2 = a * (1.0d0 - t)
    if (a <= (-9.6d+98)) then
        tmp = t_2
    else if (a <= 3.05d-127) then
        tmp = t_1
    else if (a <= 5.8d-49) then
        tmp = y * (b - z)
    else if (a <= 2d+79) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (t * b);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -9.6e+98) {
		tmp = t_2;
	} else if (a <= 3.05e-127) {
		tmp = t_1;
	} else if (a <= 5.8e-49) {
		tmp = y * (b - z);
	} else if (a <= 2e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) + (t * b)
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -9.6e+98:
		tmp = t_2
	elif a <= 3.05e-127:
		tmp = t_1
	elif a <= 5.8e-49:
		tmp = y * (b - z)
	elif a <= 2e+79:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) + Float64(t * b))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -9.6e+98)
		tmp = t_2;
	elseif (a <= 3.05e-127)
		tmp = t_1;
	elseif (a <= 5.8e-49)
		tmp = Float64(y * Float64(b - z));
	elseif (a <= 2e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + z) + (t * b);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -9.6e+98)
		tmp = t_2;
	elseif (a <= 3.05e-127)
		tmp = t_1;
	elseif (a <= 5.8e-49)
		tmp = y * (b - z);
	elseif (a <= 2e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + z), $MachinePrecision] + N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.6e+98], t$95$2, If[LessEqual[a, 3.05e-127], t$95$1, If[LessEqual[a, 5.8e-49], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+79], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5999999999999995e98 or 1.99999999999999993e79 < a

   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. Taylor expanded in a around inf 66.9%

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

   if -9.5999999999999995e98 < a < 3.0499999999999999e-127 or 5.8e-49 < a < 1.99999999999999993e79

   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. Step-by-step derivation

      1. +-commutative 96.6%

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

      2. fma-def 97.3%

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

      3. associate--l+ 97.3%

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

      4. sub-neg 97.3%

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

      5. metadata-eval 97.3%

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

      6. sub-neg 97.3%

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

      7. associate--l+ 97.3%

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

      8. *-commutative 97.3%

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

      9. distribute-rgt-neg-in 97.3%

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

      10. fma-neg 97.3%

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

      11. neg-sub0 97.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 97.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 97.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 97.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 97.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 97.3%

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

      17. *-commutative 97.3%

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

      18. distribute-rgt-neg-in 97.3%

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

      19. neg-sub0 97.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 97.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 97.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 97.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 97.3%

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

   4. Taylor expanded in y around 0 70.2%

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

   5. Taylor expanded in t around -inf 61.4%

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

      1. associate-*r* 61.4%

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

      2. mul-1-neg 61.4%

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

      3. mul-1-neg 61.4%

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

      4. unsub-neg 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in a around 0 58.1%

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

      1. associate-+r+ 58.1%

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

      2. +-commutative 58.1%

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

   10. Simplified 58.1%

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

   if 3.0499999999999999e-127 < a < 5.8e-49

   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. Taylor expanded in y around inf 66.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+98}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-127}:\\ \;\;\;\;\left(x + z\right) + t \cdot b\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+79}:\\ \;\;\;\;\left(x + z\right) + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 17: 61.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(t + -1\right) \cdot a\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ t -1.0) a))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.6e+50)
     t_2
     (if (<= b -1.7e-14)
       t_1
       (if (<= b -4.2e-59) (* z (- 1.0 y)) (if (<= b 6.5e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((t + -1.0) * a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.6e+50) {
		tmp = t_2;
	} else if (b <= -1.7e-14) {
		tmp = t_1;
	} else if (b <= -4.2e-59) {
		tmp = z * (1.0 - y);
	} else if (b <= 6.5e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((t + (-1.0d0)) * a)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-2.6d+50)) then
        tmp = t_2
    else if (b <= (-1.7d-14)) then
        tmp = t_1
    else if (b <= (-4.2d-59)) then
        tmp = z * (1.0d0 - y)
    else if (b <= 6.5d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((t + -1.0) * a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.6e+50) {
		tmp = t_2;
	} else if (b <= -1.7e-14) {
		tmp = t_1;
	} else if (b <= -4.2e-59) {
		tmp = z * (1.0 - y);
	} else if (b <= 6.5e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((t + -1.0) * a)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -2.6e+50:
		tmp = t_2
	elif b <= -1.7e-14:
		tmp = t_1
	elif b <= -4.2e-59:
		tmp = z * (1.0 - y)
	elif b <= 6.5e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(t + -1.0) * a))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.6e+50)
		tmp = t_2;
	elseif (b <= -1.7e-14)
		tmp = t_1;
	elseif (b <= -4.2e-59)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 6.5e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((t + -1.0) * a);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.6e+50)
		tmp = t_2;
	elseif (b <= -1.7e-14)
		tmp = t_1;
	elseif (b <= -4.2e-59)
		tmp = z * (1.0 - y);
	elseif (b <= 6.5e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.6e+50], t$95$2, If[LessEqual[b, -1.7e-14], t$95$1, If[LessEqual[b, -4.2e-59], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6000000000000002e50 or 6.5000000000000001e69 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in b around inf 80.4%

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

   if -2.6000000000000002e50 < b < -1.70000000000000001e-14 or -4.19999999999999993e-59 < b < 6.5000000000000001e69

   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. Taylor expanded in b around 0 92.8%

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

      1. fma-def 92.8%

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

      2. sub-neg 92.8%

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

      3. metadata-eval 92.8%

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

      4. sub-neg 92.8%

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

      5. metadata-eval 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in a around inf 64.1%

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

   if -1.70000000000000001e-14 < b < -4.19999999999999993e-59

   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. Taylor expanded in z around inf 64.4%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+50}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-14}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+69}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 18: 62.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(t + -1\right) \cdot a\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-88}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ t -1.0) a))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -8.5e+51)
     t_2
     (if (<= b 2.95e-282)
       t_1
       (if (<= b 4.7e-88)
         (- x (* (+ y -1.0) z))
         (if (<= b 1.36e+70) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((t + -1.0) * a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -8.5e+51) {
		tmp = t_2;
	} else if (b <= 2.95e-282) {
		tmp = t_1;
	} else if (b <= 4.7e-88) {
		tmp = x - ((y + -1.0) * z);
	} else if (b <= 1.36e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((t + (-1.0d0)) * a)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-8.5d+51)) then
        tmp = t_2
    else if (b <= 2.95d-282) then
        tmp = t_1
    else if (b <= 4.7d-88) then
        tmp = x - ((y + (-1.0d0)) * z)
    else if (b <= 1.36d+70) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((t + -1.0) * a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -8.5e+51) {
		tmp = t_2;
	} else if (b <= 2.95e-282) {
		tmp = t_1;
	} else if (b <= 4.7e-88) {
		tmp = x - ((y + -1.0) * z);
	} else if (b <= 1.36e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((t + -1.0) * a)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -8.5e+51:
		tmp = t_2
	elif b <= 2.95e-282:
		tmp = t_1
	elif b <= 4.7e-88:
		tmp = x - ((y + -1.0) * z)
	elif b <= 1.36e+70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(t + -1.0) * a))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -8.5e+51)
		tmp = t_2;
	elseif (b <= 2.95e-282)
		tmp = t_1;
	elseif (b <= 4.7e-88)
		tmp = Float64(x - Float64(Float64(y + -1.0) * z));
	elseif (b <= 1.36e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((t + -1.0) * a);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -8.5e+51)
		tmp = t_2;
	elseif (b <= 2.95e-282)
		tmp = t_1;
	elseif (b <= 4.7e-88)
		tmp = x - ((y + -1.0) * z);
	elseif (b <= 1.36e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -8.5e+51], t$95$2, If[LessEqual[b, 2.95e-282], t$95$1, If[LessEqual[b, 4.7e-88], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.36e+70], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.4999999999999999e51 or 1.35999999999999995e70 < b

   1. Initial program 90.3%

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

   2. Taylor expanded in b around inf 80.4%

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

   if -8.4999999999999999e51 < b < 2.9499999999999998e-282 or 4.7e-88 < b < 1.35999999999999995e70

   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. Taylor expanded in b around 0 89.7%

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

      1. fma-def 89.7%

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

      2. sub-neg 89.7%

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

      3. metadata-eval 89.7%

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

      4. sub-neg 89.7%

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

      5. metadata-eval 89.7%

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

   4. Simplified 89.7%

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

   5. Taylor expanded in a around inf 63.6%

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

   if 2.9499999999999998e-282 < b < 4.7e-88

   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. Taylor expanded in b around 0 100.0%

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

      1. fma-def 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around 0 68.5%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+51}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-282}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-88}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{+70}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 19: 65.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-281}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-21}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -3.6e+49)
     t_1
     (if (<= b 2.8e-281)
       (- x (* (+ t -1.0) a))
       (if (<= b 1.4e-21) (- x (* (+ y -1.0) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.6e+49) {
		tmp = t_1;
	} else if (b <= 2.8e-281) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 1.4e-21) {
		tmp = x - ((y + -1.0) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-3.6d+49)) then
        tmp = t_1
    else if (b <= 2.8d-281) then
        tmp = x - ((t + (-1.0d0)) * a)
    else if (b <= 1.4d-21) then
        tmp = x - ((y + (-1.0d0)) * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -3.6e+49) {
		tmp = t_1;
	} else if (b <= 2.8e-281) {
		tmp = x - ((t + -1.0) * a);
	} else if (b <= 1.4e-21) {
		tmp = x - ((y + -1.0) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -3.6e+49:
		tmp = t_1
	elif b <= 2.8e-281:
		tmp = x - ((t + -1.0) * a)
	elif b <= 1.4e-21:
		tmp = x - ((y + -1.0) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -3.6e+49)
		tmp = t_1;
	elseif (b <= 2.8e-281)
		tmp = Float64(x - Float64(Float64(t + -1.0) * a));
	elseif (b <= 1.4e-21)
		tmp = Float64(x - Float64(Float64(y + -1.0) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -3.6e+49)
		tmp = t_1;
	elseif (b <= 2.8e-281)
		tmp = x - ((t + -1.0) * a);
	elseif (b <= 1.4e-21)
		tmp = x - ((y + -1.0) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e+49], t$95$1, If[LessEqual[b, 2.8e-281], N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-21], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.59999999999999996e49 or 1.40000000000000002e-21 < b

   1. Initial program 91.0%

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

   2. Taylor expanded in a around 0 82.6%

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

   3. Taylor expanded in z around 0 77.5%

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

   if -3.59999999999999996e49 < b < 2.80000000000000005e-281

   1. Initial program 98.8%

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

   2. Taylor expanded in b around 0 94.9%

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

      1. fma-def 95.0%

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

      2. sub-neg 95.0%

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

      3. metadata-eval 95.0%

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

      4. sub-neg 95.0%

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

      5. metadata-eval 95.0%

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

   4. Simplified 95.0%

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

   5. Taylor expanded in a around inf 65.5%

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

   if 2.80000000000000005e-281 < b < 1.40000000000000002e-21

   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. Taylor expanded in b around 0 97.8%

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

      1. fma-def 97.8%

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

      2. sub-neg 97.8%

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

      3. metadata-eval 97.8%

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

      4. sub-neg 97.8%

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

      5. metadata-eval 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in a around 0 66.8%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+49}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-281}:\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-21}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 20: 72.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+51} \lor \neg \left(b \leq 5.2 \cdot 10^{-21}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.6e+51) (not (<= b 5.2e-21)))
   (+ x (* (- (+ y t) 2.0) b))
   (+ x (+ a (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.6e+51) || !(b <= 5.2e-21)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.6d+51)) .or. (.not. (b <= 5.2d-21))) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else
        tmp = x + (a + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.6e+51) || !(b <= 5.2e-21)) {
		tmp = x + (((y + t) - 2.0) * b);
	} else {
		tmp = x + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.6e+51) or not (b <= 5.2e-21):
		tmp = x + (((y + t) - 2.0) * b)
	else:
		tmp = x + (a + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.6e+51) || !(b <= 5.2e-21))
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	else
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.6e+51) || ~((b <= 5.2e-21)))
		tmp = x + (((y + t) - 2.0) * b);
	else
		tmp = x + (a + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.6e+51], N[Not[LessEqual[b, 5.2e-21]], $MachinePrecision]], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6000000000000001e51 or 5.20000000000000035e-21 < b

   1. Initial program 91.0%

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

   2. Taylor expanded in a around 0 82.6%

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

   3. Taylor expanded in z around 0 77.5%

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

   if -1.6000000000000001e51 < b < 5.20000000000000035e-21

   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. Taylor expanded in b around 0 95.9%

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

      1. fma-def 95.9%

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

      2. sub-neg 95.9%

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

      3. metadata-eval 95.9%

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

      4. sub-neg 95.9%

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

      5. metadata-eval 95.9%

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

   4. Simplified 95.9%

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

   5. Taylor expanded in t around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. neg-mul-1 76.6%

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

      3. unsub-neg 76.6%

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

      4. sub-neg 76.6%

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

      5. metadata-eval 76.6%

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

   7. Simplified 76.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+51} \lor \neg \left(b \leq 5.2 \cdot 10^{-21}\right):\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 21: 34.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+114}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+162} \lor \neg \left(b \leq 4 \cdot 10^{+270}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.6e+114)
   (* t b)
   (if (<= b 5.2e+37)
     (+ x a)
     (if (or (<= b 5.5e+162) (not (<= b 4e+270))) (* t b) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.6e+114) {
		tmp = t * b;
	} else if (b <= 5.2e+37) {
		tmp = x + a;
	} else if ((b <= 5.5e+162) || !(b <= 4e+270)) {
		tmp = t * b;
	} else {
		tmp = y * 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 <= (-6.6d+114)) then
        tmp = t * b
    else if (b <= 5.2d+37) then
        tmp = x + a
    else if ((b <= 5.5d+162) .or. (.not. (b <= 4d+270))) then
        tmp = t * b
    else
        tmp = y * 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 <= -6.6e+114) {
		tmp = t * b;
	} else if (b <= 5.2e+37) {
		tmp = x + a;
	} else if ((b <= 5.5e+162) || !(b <= 4e+270)) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.6e+114:
		tmp = t * b
	elif b <= 5.2e+37:
		tmp = x + a
	elif (b <= 5.5e+162) or not (b <= 4e+270):
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.6e+114)
		tmp = Float64(t * b);
	elseif (b <= 5.2e+37)
		tmp = Float64(x + a);
	elseif ((b <= 5.5e+162) || !(b <= 4e+270))
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.6e+114)
		tmp = t * b;
	elseif (b <= 5.2e+37)
		tmp = x + a;
	elseif ((b <= 5.5e+162) || ~((b <= 4e+270)))
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.6e+114], N[(t * b), $MachinePrecision], If[LessEqual[b, 5.2e+37], N[(x + a), $MachinePrecision], If[Or[LessEqual[b, 5.5e+162], N[Not[LessEqual[b, 4e+270]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.6000000000000001e114 or 5.1999999999999998e37 < b < 5.49999999999999966e162 or 4.0000000000000002e270 < b

   1. Initial program 86.8%

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

   2. Taylor expanded in a around 0 80.0%

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

   3. Taylor expanded in t around inf 42.0%

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

   if -6.6000000000000001e114 < b < 5.1999999999999998e37

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 71.8%

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

   5. Taylor expanded in t around 0 51.6%

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

      1. associate-+r+ 51.6%

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

      2. *-commutative 51.6%

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

   7. Simplified 51.6%

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

   8. Taylor expanded in a around inf 40.6%

      \[\leadsto x + \color{blue}{a} \]

   if 5.49999999999999966e162 < b < 4.0000000000000002e270

   1. Initial program 93.3%

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

   2. Taylor expanded in y around inf 48.9%

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

   3. Taylor expanded in b around inf 48.8%

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

      1. *-commutative 48.8%

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

   5. Simplified 48.8%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+114}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+162} \lor \neg \left(b \leq 4 \cdot 10^{+270}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 22: 27.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{+53} \lor \neg \left(b \leq 1.15 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.56e+53) (not (<= b 1.15e+23))) (* t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.56e+53) || !(b <= 1.15e+23)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.56d+53)) .or. (.not. (b <= 1.15d+23))) then
        tmp = t * b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.56e+53) || !(b <= 1.15e+23)) {
		tmp = t * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.56e+53) or not (b <= 1.15e+23):
		tmp = t * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.56e+53) || !(b <= 1.15e+23))
		tmp = Float64(t * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.56e+53) || ~((b <= 1.15e+23)))
		tmp = t * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.56e+53], N[Not[LessEqual[b, 1.15e+23]], $MachinePrecision]], N[(t * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -1.56e53 or 1.15e23 < b

   1. Initial program 90.2%

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

   2. Taylor expanded in a around 0 83.5%

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

   3. Taylor expanded in t around inf 37.7%

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

   if -1.56e53 < b < 1.15e23

   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. Taylor expanded in x around inf 24.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{+53} \lor \neg \left(b \leq 1.15 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 20.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.5e+161) x (if (<= x 4.8e-26) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+161) {
		tmp = x;
	} else if (x <= 4.8e-26) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.5d+161)) then
        tmp = x
    else if (x <= 4.8d-26) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+161) {
		tmp = x;
	} else if (x <= 4.8e-26) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.5e+161:
		tmp = x
	elif x <= 4.8e-26:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.5e+161)
		tmp = x;
	elseif (x <= 4.8e-26)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.5e+161)
		tmp = x;
	elseif (x <= 4.8e-26)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.5e+161], x, If[LessEqual[x, 4.8e-26], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5e161 or 4.8000000000000002e-26 < x

   1. Initial program 92.8%

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

   2. Taylor expanded in x around inf 36.6%

      \[\leadsto \color{blue}{x} \]

   if -6.5e161 < x < 4.8000000000000002e-26

   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. Taylor expanded in a around inf 34.3%

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

   3. Taylor expanded in t around 0 19.8%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 10.6% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

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. Taylor expanded in a around inf 28.6%

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

3. Taylor expanded in t around 0 14.3%

   \[\leadsto \color{blue}{a} \]

4. Final simplification 14.3%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023318 
(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)))