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

Percentage Accurate: 95.1% → 98.4%

Time: 15.0s

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: 95.1% 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: 98.4% accurate, 0.2× speedup

Math

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

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
     (+ (+ (* b -2.0) (fma y (- b z) (* t b))) (+ z (+ x 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 = ((b * -2.0) + fma(y, (b - z), (t * b))) + (z + (x + 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(Float64(Float64(b * -2.0) + fma(y, Float64(b - z), Float64(t * b))) + Float64(z + Float64(x + a)));
	end
	return 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[(N[(N[(b * -2.0), $MachinePrecision] + N[(y * N[(b - z), $MachinePrecision] + N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z + N[(x + a), $MachinePrecision]), $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 y around 0 38.5%

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

   3. Taylor expanded in t around 0 61.5%

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

      1. sub-neg 61.5%

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

      2. +-commutative 61.5%

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

      3. associate-+l+ 61.5%

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

      4. *-commutative 61.5%

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

      5. fma-def 61.5%

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

      6. +-commutative 61.5%

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

      7. fma-def 76.9%

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

      8. distribute-neg-in 76.9%

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

      9. neg-mul-1 76.9%

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

      10. remove-double-neg 76.9%

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

      11. mul-1-neg 76.9%

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

      12. remove-double-neg 76.9%

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

      13. associate-+l+ 76.9%

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

      14. +-commutative 76.9%

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

      15. +-commutative 76.9%

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

   5. Simplified 76.9%

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

      1. fma-udef 76.9%

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

   7. Applied egg-rr 76.9%

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

   8. Taylor expanded in b around inf 84.6%

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

      1. *-commutative 84.6%

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

   10. Simplified 84.6%

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

4. Final simplification 99.2%

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

Alternative 2: 98.1% accurate, 0.5× speedup

Math

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

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 (+ z (+ x (+ (* b (- t 2.0)) (* y (- b z))))))))

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 = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((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 = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	}
	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 = z + (x + ((b * (t - 2.0)) + (y * (b - z))))
	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(z + Float64(x + Float64(Float64(b * Float64(t - 2.0)) + Float64(y * Float64(b - z)))));
	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 = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(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[(z + N[(x + N[(N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 y around 0 38.5%

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

   3. Taylor expanded in a around 0 69.2%

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

4. Final simplification 98.4%

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

Alternative 3: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(\left(y \cdot z - z\right) - a\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := t_2 + \left(x + z\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{+31}:\\ \;\;\;\;t_2 - y \cdot z\\ \mathbf{elif}\;b \leq 3.3 \lor \neg \left(b \leq 7.8 \cdot 10^{+96}\right) \land b \leq 6 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (- (* y z) z) a)))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ t_2 (+ x z))))
   (if (<= b -1.2e+97)
     t_3
     (if (<= b -6.8e+87)
       t_1
       (if (<= b -3.3e+31)
         (- t_2 (* y z))
         (if (or (<= b 3.3) (and (not (<= b 7.8e+96)) (<= b 6e+133)))
           t_1
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y * z) - z) - a);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = t_2 + (x + z);
	double tmp;
	if (b <= -1.2e+97) {
		tmp = t_3;
	} else if (b <= -6.8e+87) {
		tmp = t_1;
	} else if (b <= -3.3e+31) {
		tmp = t_2 - (y * z);
	} else if ((b <= 3.3) || (!(b <= 7.8e+96) && (b <= 6e+133))) {
		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 - (((y * z) - z) - a)
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = t_2 + (x + z)
    if (b <= (-1.2d+97)) then
        tmp = t_3
    else if (b <= (-6.8d+87)) then
        tmp = t_1
    else if (b <= (-3.3d+31)) then
        tmp = t_2 - (y * z)
    else if ((b <= 3.3d0) .or. (.not. (b <= 7.8d+96)) .and. (b <= 6d+133)) 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 - (((y * z) - z) - a);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = t_2 + (x + z);
	double tmp;
	if (b <= -1.2e+97) {
		tmp = t_3;
	} else if (b <= -6.8e+87) {
		tmp = t_1;
	} else if (b <= -3.3e+31) {
		tmp = t_2 - (y * z);
	} else if ((b <= 3.3) || (!(b <= 7.8e+96) && (b <= 6e+133))) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (((y * z) - z) - a)
	t_2 = ((y + t) - 2.0) * b
	t_3 = t_2 + (x + z)
	tmp = 0
	if b <= -1.2e+97:
		tmp = t_3
	elif b <= -6.8e+87:
		tmp = t_1
	elif b <= -3.3e+31:
		tmp = t_2 - (y * z)
	elif (b <= 3.3) or (not (b <= 7.8e+96) and (b <= 6e+133)):
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(Float64(y * z) - z) - a))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(t_2 + Float64(x + z))
	tmp = 0.0
	if (b <= -1.2e+97)
		tmp = t_3;
	elseif (b <= -6.8e+87)
		tmp = t_1;
	elseif (b <= -3.3e+31)
		tmp = Float64(t_2 - Float64(y * z));
	elseif ((b <= 3.3) || (!(b <= 7.8e+96) && (b <= 6e+133)))
		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 - (((y * z) - z) - a);
	t_2 = ((y + t) - 2.0) * b;
	t_3 = t_2 + (x + z);
	tmp = 0.0;
	if (b <= -1.2e+97)
		tmp = t_3;
	elseif (b <= -6.8e+87)
		tmp = t_1;
	elseif (b <= -3.3e+31)
		tmp = t_2 - (y * z);
	elseif ((b <= 3.3) || (~((b <= 7.8e+96)) && (b <= 6e+133)))
		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[(N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+97], t$95$3, If[LessEqual[b, -6.8e+87], t$95$1, If[LessEqual[b, -3.3e+31], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 3.3], And[N[Not[LessEqual[b, 7.8e+96]], $MachinePrecision], LessEqual[b, 6e+133]]], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2e97 or 3.2999999999999998 < b < 7.8e96 or 6.00000000000000013e133 < b

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. associate--r+ 96.8%

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

      2. sub-neg 96.8%

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

      3. mul-1-neg 96.8%

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

      4. remove-double-neg 96.8%

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

      5. sub-neg 96.8%

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

      6. metadata-eval 96.8%

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

      7. distribute-lft-in 96.8%

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

      8. *-commutative 96.8%

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

      9. neg-mul-1 96.8%

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

      10. unsub-neg 96.8%

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

      11. *-commutative 96.8%

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

   4. Simplified 96.8%

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

   5. Taylor expanded in a around 0 88.4%

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

      1. +-commutative 88.4%

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

   7. Simplified 88.4%

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

   if -1.2e97 < b < -6.8000000000000004e87 or -3.29999999999999992e31 < b < 3.2999999999999998 or 7.8e96 < b < 6.00000000000000013e133

   1. Initial program 96.0%

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

   2. Taylor expanded in b around 0 90.2%

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

   3. Taylor expanded in t around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. sub-neg 77.3%

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

      3. metadata-eval 77.3%

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

      4. neg-mul-1 77.3%

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

      5. unsub-neg 77.3%

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

      6. distribute-rgt-in 77.3%

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

      7. mul-1-neg 77.3%

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

      8. unsub-neg 77.3%

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

   5. Simplified 77.3%

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

   if -6.8000000000000004e87 < b < -3.29999999999999992e31

   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 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-rgt-neg-in 82.0%

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

   4. Simplified 82.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+97}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+87}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{+31}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{elif}\;b \leq 3.3 \lor \neg \left(b \leq 7.8 \cdot 10^{+96}\right) \land b \leq 6 \cdot 10^{+133}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z\right)\\ \end{array} \]

Alternative 4: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(\left(y \cdot z - z\right) - a\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := t_2 + \left(x + z\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+41}:\\ \;\;\;\;t_2 - y \cdot z\\ \mathbf{elif}\;b \leq 5.8:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+96}:\\ \;\;\;\;\left(x + z\right) + \left(b \cdot \left(t - 2\right) + y \cdot b\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (- (* y z) z) a)))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ t_2 (+ x z))))
   (if (<= b -7e+95)
     t_3
     (if (<= b -3.5e+84)
       t_1
       (if (<= b -4e+41)
         (- t_2 (* y z))
         (if (<= b 5.8)
           t_1
           (if (<= b 8.4e+96)
             (+ (+ x z) (+ (* b (- t 2.0)) (* y b)))
             (if (<= b 6e+133) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y * z) - z) - a);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = t_2 + (x + z);
	double tmp;
	if (b <= -7e+95) {
		tmp = t_3;
	} else if (b <= -3.5e+84) {
		tmp = t_1;
	} else if (b <= -4e+41) {
		tmp = t_2 - (y * z);
	} else if (b <= 5.8) {
		tmp = t_1;
	} else if (b <= 8.4e+96) {
		tmp = (x + z) + ((b * (t - 2.0)) + (y * b));
	} else if (b <= 6e+133) {
		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 - (((y * z) - z) - a)
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = t_2 + (x + z)
    if (b <= (-7d+95)) then
        tmp = t_3
    else if (b <= (-3.5d+84)) then
        tmp = t_1
    else if (b <= (-4d+41)) then
        tmp = t_2 - (y * z)
    else if (b <= 5.8d0) then
        tmp = t_1
    else if (b <= 8.4d+96) then
        tmp = (x + z) + ((b * (t - 2.0d0)) + (y * b))
    else if (b <= 6d+133) 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 - (((y * z) - z) - a);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = t_2 + (x + z);
	double tmp;
	if (b <= -7e+95) {
		tmp = t_3;
	} else if (b <= -3.5e+84) {
		tmp = t_1;
	} else if (b <= -4e+41) {
		tmp = t_2 - (y * z);
	} else if (b <= 5.8) {
		tmp = t_1;
	} else if (b <= 8.4e+96) {
		tmp = (x + z) + ((b * (t - 2.0)) + (y * b));
	} else if (b <= 6e+133) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (((y * z) - z) - a)
	t_2 = ((y + t) - 2.0) * b
	t_3 = t_2 + (x + z)
	tmp = 0
	if b <= -7e+95:
		tmp = t_3
	elif b <= -3.5e+84:
		tmp = t_1
	elif b <= -4e+41:
		tmp = t_2 - (y * z)
	elif b <= 5.8:
		tmp = t_1
	elif b <= 8.4e+96:
		tmp = (x + z) + ((b * (t - 2.0)) + (y * b))
	elif b <= 6e+133:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(Float64(y * z) - z) - a))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(t_2 + Float64(x + z))
	tmp = 0.0
	if (b <= -7e+95)
		tmp = t_3;
	elseif (b <= -3.5e+84)
		tmp = t_1;
	elseif (b <= -4e+41)
		tmp = Float64(t_2 - Float64(y * z));
	elseif (b <= 5.8)
		tmp = t_1;
	elseif (b <= 8.4e+96)
		tmp = Float64(Float64(x + z) + Float64(Float64(b * Float64(t - 2.0)) + Float64(y * b)));
	elseif (b <= 6e+133)
		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 - (((y * z) - z) - a);
	t_2 = ((y + t) - 2.0) * b;
	t_3 = t_2 + (x + z);
	tmp = 0.0;
	if (b <= -7e+95)
		tmp = t_3;
	elseif (b <= -3.5e+84)
		tmp = t_1;
	elseif (b <= -4e+41)
		tmp = t_2 - (y * z);
	elseif (b <= 5.8)
		tmp = t_1;
	elseif (b <= 8.4e+96)
		tmp = (x + z) + ((b * (t - 2.0)) + (y * b));
	elseif (b <= 6e+133)
		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[(N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+95], t$95$3, If[LessEqual[b, -3.5e+84], t$95$1, If[LessEqual[b, -4e+41], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8], t$95$1, If[LessEqual[b, 8.4e+96], N[(N[(x + z), $MachinePrecision] + N[(N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+133], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.99999999999999999e95 or 6.00000000000000013e133 < b

   1. Initial program 89.8%

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

   2. Taylor expanded in y around 0 97.1%

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

      1. associate--r+ 97.1%

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

      2. sub-neg 97.1%

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

      3. mul-1-neg 97.1%

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

      4. remove-double-neg 97.1%

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

      5. sub-neg 97.1%

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

      6. metadata-eval 97.1%

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

      7. distribute-lft-in 97.1%

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

      8. *-commutative 97.1%

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

      9. neg-mul-1 97.1%

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

      10. unsub-neg 97.1%

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

      11. *-commutative 97.1%

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

   4. Simplified 97.1%

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

   5. Taylor expanded in a around 0 90.4%

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

      1. +-commutative 90.4%

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

   7. Simplified 90.4%

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

   if -6.99999999999999999e95 < b < -3.4999999999999999e84 or -4.00000000000000002e41 < b < 5.79999999999999982 or 8.4000000000000005e96 < b < 6.00000000000000013e133

   1. Initial program 96.0%

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

   2. Taylor expanded in b around 0 90.2%

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

   3. Taylor expanded in t around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. sub-neg 77.3%

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

      3. metadata-eval 77.3%

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

      4. neg-mul-1 77.3%

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

      5. unsub-neg 77.3%

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

      6. distribute-rgt-in 77.3%

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

      7. mul-1-neg 77.3%

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

      8. unsub-neg 77.3%

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

   5. Simplified 77.3%

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

   if -3.4999999999999999e84 < b < -4.00000000000000002e41

   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 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-rgt-neg-in 82.0%

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

   4. Simplified 82.0%

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

   if 5.79999999999999982 < b < 8.4000000000000005e96

   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 0 96.1%

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

      1. associate--r+ 96.1%

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

      2. sub-neg 96.1%

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

      3. mul-1-neg 96.1%

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

      4. remove-double-neg 96.1%

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

      5. sub-neg 96.1%

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

      6. metadata-eval 96.1%

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

      7. distribute-lft-in 96.1%

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

      8. *-commutative 96.1%

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

      9. neg-mul-1 96.1%

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

      10. unsub-neg 96.1%

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

      11. *-commutative 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in a around 0 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in y around 0 83.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+95}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+84}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+41}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{elif}\;b \leq 5.8:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+96}:\\ \;\;\;\;\left(x + z\right) + \left(b \cdot \left(t - 2\right) + y \cdot b\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+133}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z\right)\\ \end{array} \]

Alternative 5: 83.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(\left(y \cdot z - z\right) - a\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := t_2 + \left(x + z\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+96}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{+42}:\\ \;\;\;\;t_2 - y \cdot z\\ \mathbf{elif}\;b \leq 6.2:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{+97}:\\ \;\;\;\;\left(x + z\right) + \left(b \cdot \left(t - 2\right) + y \cdot b\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (- (* y z) z) a)))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ t_2 (+ x z))))
   (if (<= b -2.5e+96)
     t_3
     (if (<= b -4.2e+87)
       t_1
       (if (<= b -3e+42)
         (- t_2 (* y z))
         (if (<= b 6.2)
           (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))
           (if (<= b 1.04e+97)
             (+ (+ x z) (+ (* b (- t 2.0)) (* y b)))
             (if (<= b 6e+133) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y * z) - z) - a);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = t_2 + (x + z);
	double tmp;
	if (b <= -2.5e+96) {
		tmp = t_3;
	} else if (b <= -4.2e+87) {
		tmp = t_1;
	} else if (b <= -3e+42) {
		tmp = t_2 - (y * z);
	} else if (b <= 6.2) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else if (b <= 1.04e+97) {
		tmp = (x + z) + ((b * (t - 2.0)) + (y * b));
	} else if (b <= 6e+133) {
		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 - (((y * z) - z) - a)
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = t_2 + (x + z)
    if (b <= (-2.5d+96)) then
        tmp = t_3
    else if (b <= (-4.2d+87)) then
        tmp = t_1
    else if (b <= (-3d+42)) then
        tmp = t_2 - (y * z)
    else if (b <= 6.2d0) then
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    else if (b <= 1.04d+97) then
        tmp = (x + z) + ((b * (t - 2.0d0)) + (y * b))
    else if (b <= 6d+133) 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 - (((y * z) - z) - a);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = t_2 + (x + z);
	double tmp;
	if (b <= -2.5e+96) {
		tmp = t_3;
	} else if (b <= -4.2e+87) {
		tmp = t_1;
	} else if (b <= -3e+42) {
		tmp = t_2 - (y * z);
	} else if (b <= 6.2) {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	} else if (b <= 1.04e+97) {
		tmp = (x + z) + ((b * (t - 2.0)) + (y * b));
	} else if (b <= 6e+133) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (((y * z) - z) - a)
	t_2 = ((y + t) - 2.0) * b
	t_3 = t_2 + (x + z)
	tmp = 0
	if b <= -2.5e+96:
		tmp = t_3
	elif b <= -4.2e+87:
		tmp = t_1
	elif b <= -3e+42:
		tmp = t_2 - (y * z)
	elif b <= 6.2:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	elif b <= 1.04e+97:
		tmp = (x + z) + ((b * (t - 2.0)) + (y * b))
	elif b <= 6e+133:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(Float64(y * z) - z) - a))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(t_2 + Float64(x + z))
	tmp = 0.0
	if (b <= -2.5e+96)
		tmp = t_3;
	elseif (b <= -4.2e+87)
		tmp = t_1;
	elseif (b <= -3e+42)
		tmp = Float64(t_2 - Float64(y * z));
	elseif (b <= 6.2)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	elseif (b <= 1.04e+97)
		tmp = Float64(Float64(x + z) + Float64(Float64(b * Float64(t - 2.0)) + Float64(y * b)));
	elseif (b <= 6e+133)
		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 - (((y * z) - z) - a);
	t_2 = ((y + t) - 2.0) * b;
	t_3 = t_2 + (x + z);
	tmp = 0.0;
	if (b <= -2.5e+96)
		tmp = t_3;
	elseif (b <= -4.2e+87)
		tmp = t_1;
	elseif (b <= -3e+42)
		tmp = t_2 - (y * z);
	elseif (b <= 6.2)
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	elseif (b <= 1.04e+97)
		tmp = (x + z) + ((b * (t - 2.0)) + (y * b));
	elseif (b <= 6e+133)
		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[(N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+96], t$95$3, If[LessEqual[b, -4.2e+87], t$95$1, If[LessEqual[b, -3e+42], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.04e+97], N[(N[(x + z), $MachinePrecision] + N[(N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+133], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.5000000000000002e96 or 6.00000000000000013e133 < b

   1. Initial program 89.8%

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

   2. Taylor expanded in y around 0 97.1%

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

      1. associate--r+ 97.1%

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

      2. sub-neg 97.1%

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

      3. mul-1-neg 97.1%

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

      4. remove-double-neg 97.1%

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

      5. sub-neg 97.1%

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

      6. metadata-eval 97.1%

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

      7. distribute-lft-in 97.1%

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

      8. *-commutative 97.1%

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

      9. neg-mul-1 97.1%

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

      10. unsub-neg 97.1%

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

      11. *-commutative 97.1%

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

   4. Simplified 97.1%

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

   5. Taylor expanded in a around 0 90.4%

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

      1. +-commutative 90.4%

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

   7. Simplified 90.4%

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

   if -2.5000000000000002e96 < b < -4.2e87 or 1.04e97 < b < 6.00000000000000013e133

   1. Initial program 66.7%

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

   2. Taylor expanded in b around 0 86.7%

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

   3. Taylor expanded in t around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. sub-neg 93.8%

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

      3. metadata-eval 93.8%

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

      4. neg-mul-1 93.8%

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

      5. unsub-neg 93.8%

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

      6. distribute-rgt-in 93.8%

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

      7. mul-1-neg 93.8%

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

      8. unsub-neg 93.8%

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

   5. Simplified 93.8%

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

   if -4.2e87 < b < -3.00000000000000029e42

   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 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-rgt-neg-in 82.0%

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

   4. Simplified 82.0%

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

   if -3.00000000000000029e42 < b < 6.20000000000000018

   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 90.5%

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

   if 6.20000000000000018 < b < 1.04e97

   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 0 96.1%

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

      1. associate--r+ 96.1%

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

      2. sub-neg 96.1%

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

      3. mul-1-neg 96.1%

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

      4. remove-double-neg 96.1%

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

      5. sub-neg 96.1%

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

      6. metadata-eval 96.1%

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

      7. distribute-lft-in 96.1%

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

      8. *-commutative 96.1%

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

      9. neg-mul-1 96.1%

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

      10. unsub-neg 96.1%

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

      11. *-commutative 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in a around 0 83.0%

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

      1. +-commutative 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in y around 0 83.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+96}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+87}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{+42}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{elif}\;b \leq 6.2:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{+97}:\\ \;\;\;\;\left(x + z\right) + \left(b \cdot \left(t - 2\right) + y \cdot b\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+133}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z\right)\\ \end{array} \]

Alternative 6: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(b \cdot -2 + \left(x + z\right)\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := \left(x + z\right) + t \cdot b\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-294}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ (* b -2.0) (+ x z))))
        (t_2 (* y (- b z)))
        (t_3 (+ (+ x z) (* t b))))
   (if (<= y -1.5e+88)
     t_2
     (if (<= y -6e-239)
       t_1
       (if (<= y 1e-294)
         t_3
         (if (<= y 4.2e-205)
           t_1
           (if (<= y 5.2e-15) t_3 (if (<= y 9e+70) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + ((b * -2.0) + (x + z));
	double t_2 = y * (b - z);
	double t_3 = (x + z) + (t * b);
	double tmp;
	if (y <= -1.5e+88) {
		tmp = t_2;
	} else if (y <= -6e-239) {
		tmp = t_1;
	} else if (y <= 1e-294) {
		tmp = t_3;
	} else if (y <= 4.2e-205) {
		tmp = t_1;
	} else if (y <= 5.2e-15) {
		tmp = t_3;
	} else if (y <= 9e+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) :: t_3
    real(8) :: tmp
    t_1 = a + ((b * (-2.0d0)) + (x + z))
    t_2 = y * (b - z)
    t_3 = (x + z) + (t * b)
    if (y <= (-1.5d+88)) then
        tmp = t_2
    else if (y <= (-6d-239)) then
        tmp = t_1
    else if (y <= 1d-294) then
        tmp = t_3
    else if (y <= 4.2d-205) then
        tmp = t_1
    else if (y <= 5.2d-15) then
        tmp = t_3
    else if (y <= 9d+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 = a + ((b * -2.0) + (x + z));
	double t_2 = y * (b - z);
	double t_3 = (x + z) + (t * b);
	double tmp;
	if (y <= -1.5e+88) {
		tmp = t_2;
	} else if (y <= -6e-239) {
		tmp = t_1;
	} else if (y <= 1e-294) {
		tmp = t_3;
	} else if (y <= 4.2e-205) {
		tmp = t_1;
	} else if (y <= 5.2e-15) {
		tmp = t_3;
	} else if (y <= 9e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + ((b * -2.0) + (x + z))
	t_2 = y * (b - z)
	t_3 = (x + z) + (t * b)
	tmp = 0
	if y <= -1.5e+88:
		tmp = t_2
	elif y <= -6e-239:
		tmp = t_1
	elif y <= 1e-294:
		tmp = t_3
	elif y <= 4.2e-205:
		tmp = t_1
	elif y <= 5.2e-15:
		tmp = t_3
	elif y <= 9e+70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(Float64(b * -2.0) + Float64(x + z)))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(Float64(x + z) + Float64(t * b))
	tmp = 0.0
	if (y <= -1.5e+88)
		tmp = t_2;
	elseif (y <= -6e-239)
		tmp = t_1;
	elseif (y <= 1e-294)
		tmp = t_3;
	elseif (y <= 4.2e-205)
		tmp = t_1;
	elseif (y <= 5.2e-15)
		tmp = t_3;
	elseif (y <= 9e+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 = a + ((b * -2.0) + (x + z));
	t_2 = y * (b - z);
	t_3 = (x + z) + (t * b);
	tmp = 0.0;
	if (y <= -1.5e+88)
		tmp = t_2;
	elseif (y <= -6e-239)
		tmp = t_1;
	elseif (y <= 1e-294)
		tmp = t_3;
	elseif (y <= 4.2e-205)
		tmp = t_1;
	elseif (y <= 5.2e-15)
		tmp = t_3;
	elseif (y <= 9e+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[(a + N[(N[(b * -2.0), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + z), $MachinePrecision] + N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+88], t$95$2, If[LessEqual[y, -6e-239], t$95$1, If[LessEqual[y, 1e-294], t$95$3, If[LessEqual[y, 4.2e-205], t$95$1, If[LessEqual[y, 5.2e-15], t$95$3, If[LessEqual[y, 9e+70], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.50000000000000003e88 or 8.9999999999999999e70 < y

   1. Initial program 89.2%

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

   2. Taylor expanded in y around inf 81.5%

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

   if -1.50000000000000003e88 < y < -5.9999999999999996e-239 or 1.00000000000000002e-294 < y < 4.19999999999999965e-205 or 5.20000000000000009e-15 < y < 8.9999999999999999e70

   1. Initial program 97.9%

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

   2. Taylor expanded in y around 0 89.8%

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

      1. associate--r+ 89.8%

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

      2. sub-neg 89.8%

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

      3. mul-1-neg 89.8%

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

      4. remove-double-neg 89.8%

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

      5. sub-neg 89.8%

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

      6. metadata-eval 89.8%

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

      7. distribute-lft-in 89.8%

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

      8. *-commutative 89.8%

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

      9. neg-mul-1 89.8%

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

      10. unsub-neg 89.8%

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

      11. *-commutative 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in t around 0 73.4%

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

      1. associate-+r+ 73.4%

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

      2. +-commutative 73.4%

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

      3. sub-neg 73.4%

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

      4. metadata-eval 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in y around 0 65.7%

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

      1. *-commutative 65.7%

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

   10. Simplified 65.7%

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

   if -5.9999999999999996e-239 < y < 1.00000000000000002e-294 or 4.19999999999999965e-205 < y < 5.20000000000000009e-15

   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 y around 0 98.5%

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

      1. associate--r+ 98.5%

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

      2. sub-neg 98.5%

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

      3. mul-1-neg 98.5%

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

      4. remove-double-neg 98.5%

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

      5. sub-neg 98.5%

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

      6. metadata-eval 98.5%

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

      7. distribute-lft-in 98.5%

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

      8. *-commutative 98.5%

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

      9. neg-mul-1 98.5%

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

      10. unsub-neg 98.5%

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

      11. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in a around 0 77.9%

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

      1. +-commutative 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in t around inf 74.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-239}:\\ \;\;\;\;a + \left(b \cdot -2 + \left(x + z\right)\right)\\ \mathbf{elif}\;y \leq 10^{-294}:\\ \;\;\;\;\left(x + z\right) + t \cdot b\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-205}:\\ \;\;\;\;a + \left(b \cdot -2 + \left(x + z\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-15}:\\ \;\;\;\;\left(x + z\right) + t \cdot b\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+70}:\\ \;\;\;\;a + \left(b \cdot -2 + \left(x + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 7: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(\left(y \cdot z - z\right) - a\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+154}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (- (* y z) z) a))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -3.3e+100)
     t_2
     (if (<= b 3.3e+17)
       t_1
       (if (<= b 7.2e+96)
         t_2
         (if (<= b 2.3e+118)
           t_1
           (if (<= b 3e+154) (+ a (+ (+ x z) (* b (+ y -2.0)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y * z) - z) - a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -3.3e+100) {
		tmp = t_2;
	} else if (b <= 3.3e+17) {
		tmp = t_1;
	} else if (b <= 7.2e+96) {
		tmp = t_2;
	} else if (b <= 2.3e+118) {
		tmp = t_1;
	} else if (b <= 3e+154) {
		tmp = a + ((x + z) + (b * (y + -2.0)));
	} 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 - (((y * z) - z) - a)
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-3.3d+100)) then
        tmp = t_2
    else if (b <= 3.3d+17) then
        tmp = t_1
    else if (b <= 7.2d+96) then
        tmp = t_2
    else if (b <= 2.3d+118) then
        tmp = t_1
    else if (b <= 3d+154) then
        tmp = a + ((x + z) + (b * (y + (-2.0d0))))
    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 - (((y * z) - z) - a);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -3.3e+100) {
		tmp = t_2;
	} else if (b <= 3.3e+17) {
		tmp = t_1;
	} else if (b <= 7.2e+96) {
		tmp = t_2;
	} else if (b <= 2.3e+118) {
		tmp = t_1;
	} else if (b <= 3e+154) {
		tmp = a + ((x + z) + (b * (y + -2.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (((y * z) - z) - a)
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -3.3e+100:
		tmp = t_2
	elif b <= 3.3e+17:
		tmp = t_1
	elif b <= 7.2e+96:
		tmp = t_2
	elif b <= 2.3e+118:
		tmp = t_1
	elif b <= 3e+154:
		tmp = a + ((x + z) + (b * (y + -2.0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(Float64(y * z) - z) - a))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -3.3e+100)
		tmp = t_2;
	elseif (b <= 3.3e+17)
		tmp = t_1;
	elseif (b <= 7.2e+96)
		tmp = t_2;
	elseif (b <= 2.3e+118)
		tmp = t_1;
	elseif (b <= 3e+154)
		tmp = Float64(a + Float64(Float64(x + z) + Float64(b * Float64(y + -2.0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (((y * z) - z) - a);
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -3.3e+100)
		tmp = t_2;
	elseif (b <= 3.3e+17)
		tmp = t_1;
	elseif (b <= 7.2e+96)
		tmp = t_2;
	elseif (b <= 2.3e+118)
		tmp = t_1;
	elseif (b <= 3e+154)
		tmp = a + ((x + z) + (b * (y + -2.0)));
	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[(N[(y * z), $MachinePrecision] - z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -3.3e+100], t$95$2, If[LessEqual[b, 3.3e+17], t$95$1, If[LessEqual[b, 7.2e+96], t$95$2, If[LessEqual[b, 2.3e+118], t$95$1, If[LessEqual[b, 3e+154], N[(a + N[(N[(x + z), $MachinePrecision] + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3000000000000001e100 or 3.3e17 < b < 7.20000000000000026e96 or 3.00000000000000026e154 < b

   1. Initial program 91.5%

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

   2. Taylor expanded in b around inf 82.8%

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

   if -3.3000000000000001e100 < b < 3.3e17 or 7.20000000000000026e96 < b < 2.30000000000000016e118

   1. Initial program 96.3%

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

   2. Taylor expanded in b around 0 85.5%

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

   3. Taylor expanded in t around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. sub-neg 73.8%

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

      3. metadata-eval 73.8%

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

      4. neg-mul-1 73.8%

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

      5. unsub-neg 73.8%

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

      6. distribute-rgt-in 73.7%

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

      7. mul-1-neg 73.7%

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

      8. unsub-neg 73.7%

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

   5. Simplified 73.7%

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

   if 2.30000000000000016e118 < b < 3.00000000000000026e154

   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 y around 0 99.8%

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

      1. associate--r+ 99.8%

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

      2. sub-neg 99.8%

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

      3. mul-1-neg 99.8%

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

      4. remove-double-neg 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. distribute-lft-in 99.8%

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

      8. *-commutative 99.8%

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

      9. neg-mul-1 99.8%

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

      10. unsub-neg 99.8%

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

      11. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in t around 0 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+17}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+96}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+118}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+154}:\\ \;\;\;\;a + \left(\left(x + z\right) + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 8: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+70}:\\ \;\;\;\;\left(\left(x + z\right) - \left(t \cdot a - a\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + t_1\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= y -2.6e+107)
     (* y (- b z))
     (if (<= y 2.65e+70)
       (+ (- (+ x z) (- (* t a) a)) t_1)
       (+ (+ x t_1) (* z (- 1.0 y)))))))

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 (y <= -2.6e+107) {
		tmp = y * (b - z);
	} else if (y <= 2.65e+70) {
		tmp = ((x + z) - ((t * a) - a)) + t_1;
	} else {
		tmp = (x + t_1) + (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) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (y <= (-2.6d+107)) then
        tmp = y * (b - z)
    else if (y <= 2.65d+70) then
        tmp = ((x + z) - ((t * a) - a)) + t_1
    else
        tmp = (x + t_1) + (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 t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (y <= -2.6e+107) {
		tmp = y * (b - z);
	} else if (y <= 2.65e+70) {
		tmp = ((x + z) - ((t * a) - a)) + t_1;
	} else {
		tmp = (x + t_1) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if y <= -2.6e+107:
		tmp = y * (b - z)
	elif y <= 2.65e+70:
		tmp = ((x + z) - ((t * a) - a)) + t_1
	else:
		tmp = (x + t_1) + (z * (1.0 - y))
	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 (y <= -2.6e+107)
		tmp = Float64(y * Float64(b - z));
	elseif (y <= 2.65e+70)
		tmp = Float64(Float64(Float64(x + z) - Float64(Float64(t * a) - a)) + t_1);
	else
		tmp = Float64(Float64(x + t_1) + Float64(z * Float64(1.0 - y)));
	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 (y <= -2.6e+107)
		tmp = y * (b - z);
	elseif (y <= 2.65e+70)
		tmp = ((x + z) - ((t * a) - a)) + t_1;
	else
		tmp = (x + t_1) + (z * (1.0 - y));
	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[y, -2.6e+107], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e+70], N[(N[(N[(x + z), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(x + t$95$1), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6000000000000001e107

   1. Initial program 86.7%

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

   2. Taylor expanded in y around inf 89.0%

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

   if -2.6000000000000001e107 < y < 2.65e70

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 93.4%

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

      1. associate--r+ 93.4%

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

      2. sub-neg 93.4%

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

      3. mul-1-neg 93.4%

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

      4. remove-double-neg 93.4%

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

      5. sub-neg 93.4%

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

      6. metadata-eval 93.4%

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

      7. distribute-lft-in 93.4%

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

      8. *-commutative 93.4%

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

      9. neg-mul-1 93.4%

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

      10. unsub-neg 93.4%

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

      11. *-commutative 93.4%

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

   4. Simplified 93.4%

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

   if 2.65e70 < y

   1. Initial program 91.4%

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

   2. Taylor expanded in a around 0 85.4%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+70}:\\ \;\;\;\;\left(\left(x + z\right) - \left(t \cdot a - a\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 9: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+49}:\\ \;\;\;\;z + \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;\left(\left(x + z\right) - \left(t \cdot a - a\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + t_1\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= y -1.75e+49)
     (+ z (+ x (+ (* b (- t 2.0)) (* y (- b z)))))
     (if (<= y 2.5e+70)
       (+ (- (+ x z) (- (* t a) a)) t_1)
       (+ (+ x t_1) (* z (- 1.0 y)))))))

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 (y <= -1.75e+49) {
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	} else if (y <= 2.5e+70) {
		tmp = ((x + z) - ((t * a) - a)) + t_1;
	} else {
		tmp = (x + t_1) + (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) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (y <= (-1.75d+49)) then
        tmp = z + (x + ((b * (t - 2.0d0)) + (y * (b - z))))
    else if (y <= 2.5d+70) then
        tmp = ((x + z) - ((t * a) - a)) + t_1
    else
        tmp = (x + t_1) + (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 t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (y <= -1.75e+49) {
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	} else if (y <= 2.5e+70) {
		tmp = ((x + z) - ((t * a) - a)) + t_1;
	} else {
		tmp = (x + t_1) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if y <= -1.75e+49:
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))))
	elif y <= 2.5e+70:
		tmp = ((x + z) - ((t * a) - a)) + t_1
	else:
		tmp = (x + t_1) + (z * (1.0 - y))
	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 (y <= -1.75e+49)
		tmp = Float64(z + Float64(x + Float64(Float64(b * Float64(t - 2.0)) + Float64(y * Float64(b - z)))));
	elseif (y <= 2.5e+70)
		tmp = Float64(Float64(Float64(x + z) - Float64(Float64(t * a) - a)) + t_1);
	else
		tmp = Float64(Float64(x + t_1) + Float64(z * Float64(1.0 - y)));
	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 (y <= -1.75e+49)
		tmp = z + (x + ((b * (t - 2.0)) + (y * (b - z))));
	elseif (y <= 2.5e+70)
		tmp = ((x + z) - ((t * a) - a)) + t_1;
	else
		tmp = (x + t_1) + (z * (1.0 - y));
	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[y, -1.75e+49], N[(z + N[(x + N[(N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+70], N[(N[(N[(x + z), $MachinePrecision] - N[(N[(t * a), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(x + t$95$1), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999987e49

   1. Initial program 89.1%

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

   2. Taylor expanded in y around 0 92.7%

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

   3. Taylor expanded in a around 0 87.2%

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

   if -1.74999999999999987e49 < y < 2.5000000000000001e70

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0 94.8%

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

      1. associate--r+ 94.8%

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

      2. sub-neg 94.8%

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

      3. mul-1-neg 94.8%

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

      4. remove-double-neg 94.8%

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

      5. sub-neg 94.8%

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

      6. metadata-eval 94.8%

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

      7. distribute-lft-in 94.8%

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

      8. *-commutative 94.8%

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

      9. neg-mul-1 94.8%

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

      10. unsub-neg 94.8%

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

      11. *-commutative 94.8%

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

   4. Simplified 94.8%

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

   if 2.5000000000000001e70 < y

   1. Initial program 91.4%

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

   2. Taylor expanded in a around 0 85.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+49}:\\ \;\;\;\;z + \left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;\left(\left(x + z\right) - \left(t \cdot a - a\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 10: 46.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-187}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-130}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-120}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -9e+71)
     t_2
     (if (<= y -2.3e-187)
       (+ x a)
       (if (<= y 8.8e-269)
         t_1
         (if (<= y 3.2e-130)
           (+ x a)
           (if (<= y 4.2e-120)
             (+ x z)
             (if (<= y 4.5e-41) t_1 (if (<= y 2.5e+70) (+ x a) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -9e+71) {
		tmp = t_2;
	} else if (y <= -2.3e-187) {
		tmp = x + a;
	} else if (y <= 8.8e-269) {
		tmp = t_1;
	} else if (y <= 3.2e-130) {
		tmp = x + a;
	} else if (y <= 4.2e-120) {
		tmp = x + z;
	} else if (y <= 4.5e-41) {
		tmp = t_1;
	} else if (y <= 2.5e+70) {
		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 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-9d+71)) then
        tmp = t_2
    else if (y <= (-2.3d-187)) then
        tmp = x + a
    else if (y <= 8.8d-269) then
        tmp = t_1
    else if (y <= 3.2d-130) then
        tmp = x + a
    else if (y <= 4.2d-120) then
        tmp = x + z
    else if (y <= 4.5d-41) then
        tmp = t_1
    else if (y <= 2.5d+70) 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 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -9e+71) {
		tmp = t_2;
	} else if (y <= -2.3e-187) {
		tmp = x + a;
	} else if (y <= 8.8e-269) {
		tmp = t_1;
	} else if (y <= 3.2e-130) {
		tmp = x + a;
	} else if (y <= 4.2e-120) {
		tmp = x + z;
	} else if (y <= 4.5e-41) {
		tmp = t_1;
	} else if (y <= 2.5e+70) {
		tmp = x + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -9e+71:
		tmp = t_2
	elif y <= -2.3e-187:
		tmp = x + a
	elif y <= 8.8e-269:
		tmp = t_1
	elif y <= 3.2e-130:
		tmp = x + a
	elif y <= 4.2e-120:
		tmp = x + z
	elif y <= 4.5e-41:
		tmp = t_1
	elif y <= 2.5e+70:
		tmp = x + a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -9e+71)
		tmp = t_2;
	elseif (y <= -2.3e-187)
		tmp = Float64(x + a);
	elseif (y <= 8.8e-269)
		tmp = t_1;
	elseif (y <= 3.2e-130)
		tmp = Float64(x + a);
	elseif (y <= 4.2e-120)
		tmp = Float64(x + z);
	elseif (y <= 4.5e-41)
		tmp = t_1;
	elseif (y <= 2.5e+70)
		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 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -9e+71)
		tmp = t_2;
	elseif (y <= -2.3e-187)
		tmp = x + a;
	elseif (y <= 8.8e-269)
		tmp = t_1;
	elseif (y <= 3.2e-130)
		tmp = x + a;
	elseif (y <= 4.2e-120)
		tmp = x + z;
	elseif (y <= 4.5e-41)
		tmp = t_1;
	elseif (y <= 2.5e+70)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+71], t$95$2, If[LessEqual[y, -2.3e-187], N[(x + a), $MachinePrecision], If[LessEqual[y, 8.8e-269], t$95$1, If[LessEqual[y, 3.2e-130], N[(x + a), $MachinePrecision], If[LessEqual[y, 4.2e-120], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.5e-41], t$95$1, If[LessEqual[y, 2.5e+70], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.00000000000000087e71 or 2.5000000000000001e70 < y

   1. Initial program 89.7%

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

   2. Taylor expanded in y around inf 80.3%

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

   if -9.00000000000000087e71 < y < -2.29999999999999998e-187 or 8.79999999999999936e-269 < y < 3.2e-130 or 4.5e-41 < y < 2.5000000000000001e70

   1. Initial program 98.0%

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

   2. Taylor expanded in b around 0 72.4%

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

   3. Taylor expanded in z around 0 58.1%

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

      1. sub-neg 58.1%

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

      2. metadata-eval 58.1%

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

      3. distribute-rgt-in 58.1%

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

      4. neg-mul-1 58.1%

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

      5. sub-neg 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in t around 0 47.8%

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

   if -2.29999999999999998e-187 < y < 8.79999999999999936e-269 or 4.2000000000000001e-120 < y < 4.5e-41

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 54.0%

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

   if 3.2e-130 < y < 4.2000000000000001e-120

   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. Taylor expanded in a around 0 69.0%

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

      1. sub-neg 69.0%

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

      2. metadata-eval 69.0%

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

      3. distribute-rgt-in 69.0%

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

      4. mul-1-neg 69.0%

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

      5. unsub-neg 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in y around 0 69.0%

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

      1. +-commutative 69.0%

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

   8. Simplified 69.0%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-187}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-130}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-120}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 11: 72.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+95} \lor \neg \left(b \leq 3.8\right) \land \left(b \leq 9.8 \cdot 10^{+96} \lor \neg \left(b \leq 6 \cdot 10^{+133}\right)\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.6e+95)
         (and (not (<= b 3.8)) (or (<= b 9.8e+96) (not (<= b 6e+133)))))
   (+ (* (- (+ y t) 2.0) b) (+ x z))
   (- x (- (- (* y z) z) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.6e+95) || (!(b <= 3.8) && ((b <= 9.8e+96) || !(b <= 6e+133)))) {
		tmp = (((y + t) - 2.0) * b) + (x + z);
	} else {
		tmp = x - (((y * z) - z) - a);
	}
	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+95)) .or. (.not. (b <= 3.8d0)) .and. (b <= 9.8d+96) .or. (.not. (b <= 6d+133))) then
        tmp = (((y + t) - 2.0d0) * b) + (x + z)
    else
        tmp = x - (((y * z) - z) - a)
    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+95) || (!(b <= 3.8) && ((b <= 9.8e+96) || !(b <= 6e+133)))) {
		tmp = (((y + t) - 2.0) * b) + (x + z);
	} else {
		tmp = x - (((y * z) - z) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.6e+95) or (not (b <= 3.8) and ((b <= 9.8e+96) or not (b <= 6e+133))):
		tmp = (((y + t) - 2.0) * b) + (x + z)
	else:
		tmp = x - (((y * z) - z) - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.6e+95) || (!(b <= 3.8) && ((b <= 9.8e+96) || !(b <= 6e+133))))
		tmp = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) + Float64(x + z));
	else
		tmp = Float64(x - Float64(Float64(Float64(y * z) - z) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.6e+95) || (~((b <= 3.8)) && ((b <= 9.8e+96) || ~((b <= 6e+133)))))
		tmp = (((y + t) - 2.0) * b) + (x + z);
	else
		tmp = x - (((y * z) - z) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.6e+95], And[N[Not[LessEqual[b, 3.8]], $MachinePrecision], Or[LessEqual[b, 9.8e+96], N[Not[LessEqual[b, 6e+133]], $MachinePrecision]]]], N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5999999999999997e95 or 3.7999999999999998 < b < 9.7999999999999993e96 or 6.00000000000000013e133 < b

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 96.8%

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

      1. associate--r+ 96.8%

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

      2. sub-neg 96.8%

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

      3. mul-1-neg 96.8%

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

      4. remove-double-neg 96.8%

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

      5. sub-neg 96.8%

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

      6. metadata-eval 96.8%

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

      7. distribute-lft-in 96.8%

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

      8. *-commutative 96.8%

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

      9. neg-mul-1 96.8%

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

      10. unsub-neg 96.8%

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

      11. *-commutative 96.8%

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

   4. Simplified 96.8%

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

   5. Taylor expanded in a around 0 88.4%

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

      1. +-commutative 88.4%

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

   7. Simplified 88.4%

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

   if -6.5999999999999997e95 < b < 3.7999999999999998 or 9.7999999999999993e96 < b < 6.00000000000000013e133

   1. Initial program 96.2%

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

   2. Taylor expanded in b around 0 87.1%

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

   3. Taylor expanded in t around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. sub-neg 75.1%

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

      3. metadata-eval 75.1%

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

      4. neg-mul-1 75.1%

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

      5. unsub-neg 75.1%

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

      6. distribute-rgt-in 75.1%

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

      7. mul-1-neg 75.1%

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

      8. unsub-neg 75.1%

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

   5. Simplified 75.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+95} \lor \neg \left(b \leq 3.8\right) \land \left(b \leq 9.8 \cdot 10^{+96} \lor \neg \left(b \leq 6 \cdot 10^{+133}\right)\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \end{array} \]

Alternative 12: 86.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-10} \lor \neg \left(b \leq 9.2 \cdot 10^{-60}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.6e-10) (not (<= b 9.2e-60)))
   (+ (+ x (* (- (+ y t) 2.0) b)) (* a (- 1.0 t)))
   (+ x (- (* z (- 1.0 y)) (* (+ t -1.0) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e-10) || !(b <= 9.2e-60)) {
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	}
	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 <= (-3.6d-10)) .or. (.not. (b <= 9.2d-60))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + (a * (1.0d0 - t))
    else
        tmp = x + ((z * (1.0d0 - y)) - ((t + (-1.0d0)) * a))
    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 <= -3.6e-10) || !(b <= 9.2e-60)) {
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	} else {
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.6e-10) or not (b <= 9.2e-60):
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t))
	else:
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.6e-10) || !(b <= 9.2e-60))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(t + -1.0) * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.6e-10) || ~((b <= 9.2e-60)))
		tmp = (x + (((y + t) - 2.0) * b)) + (a * (1.0 - t));
	else
		tmp = x + ((z * (1.0 - y)) - ((t + -1.0) * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.6e-10], N[Not[LessEqual[b, 9.2e-60]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.6e-10 or 9.2000000000000005e-60 < b

   1. Initial program 91.6%

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

   2. Taylor expanded in z around 0 85.0%

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

   if -3.6e-10 < b < 9.2000000000000005e-60

   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 92.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-10} \lor \neg \left(b \leq 9.2 \cdot 10^{-60}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \end{array} \]

Alternative 13: 85.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{+66}:\\ \;\;\;\;x + \left(t_2 - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+105}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))) (t_2 (* z (- 1.0 y))))
   (if (<= a -1.12e+66)
     (+ x (- t_2 (* (+ t -1.0) a)))
     (if (<= a 8e+105) (+ t_1 t_2) (+ t_1 (* a (- 1.0 t)))))))

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 t_2 = z * (1.0 - y);
	double tmp;
	if (a <= -1.12e+66) {
		tmp = x + (t_2 - ((t + -1.0) * a));
	} else if (a <= 8e+105) {
		tmp = t_1 + t_2;
	} else {
		tmp = t_1 + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (((y + t) - 2.0d0) * b)
    t_2 = z * (1.0d0 - y)
    if (a <= (-1.12d+66)) then
        tmp = x + (t_2 - ((t + (-1.0d0)) * a))
    else if (a <= 8d+105) then
        tmp = t_1 + t_2
    else
        tmp = t_1 + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (a <= -1.12e+66) {
		tmp = x + (t_2 - ((t + -1.0) * a));
	} else if (a <= 8e+105) {
		tmp = t_1 + t_2;
	} else {
		tmp = t_1 + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	t_2 = z * (1.0 - y)
	tmp = 0
	if a <= -1.12e+66:
		tmp = x + (t_2 - ((t + -1.0) * a))
	elif a <= 8e+105:
		tmp = t_1 + t_2
	else:
		tmp = t_1 + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	t_2 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (a <= -1.12e+66)
		tmp = Float64(x + Float64(t_2 - Float64(Float64(t + -1.0) * a)));
	elseif (a <= 8e+105)
		tmp = Float64(t_1 + t_2);
	else
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	t_2 = z * (1.0 - y);
	tmp = 0.0;
	if (a <= -1.12e+66)
		tmp = x + (t_2 - ((t + -1.0) * a));
	elseif (a <= 8e+105)
		tmp = t_1 + t_2;
	else
		tmp = t_1 + (a * (1.0 - t));
	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]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.12e+66], N[(x + N[(t$95$2 - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+105], N[(t$95$1 + t$95$2), $MachinePrecision], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12e66

   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 b around 0 87.2%

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

   if -1.12e66 < a < 7.9999999999999995e105

   1. Initial program 96.3%

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

   2. Taylor expanded in a around 0 92.0%

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

   if 7.9999999999999995e105 < a

   1. Initial program 92.6%

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

   2. Taylor expanded in z around 0 80.5%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+66}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) - \left(t + -1\right) \cdot a\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+105}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 14: 68.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+96} \lor \neg \left(b \leq 9.2 \cdot 10^{+16}\right) \land \left(b \leq 10^{+97} \lor \neg \left(b \leq 2 \cdot 10^{+152}\right)\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.6e+96)
         (and (not (<= b 9.2e+16)) (or (<= b 1e+97) (not (<= b 2e+152)))))
   (* (- (+ y t) 2.0) b)
   (- x (- (- (* y z) z) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+96) || (!(b <= 9.2e+16) && ((b <= 1e+97) || !(b <= 2e+152)))) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x - (((y * z) - z) - a);
	}
	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 <= (-3.6d+96)) .or. (.not. (b <= 9.2d+16)) .and. (b <= 1d+97) .or. (.not. (b <= 2d+152))) then
        tmp = ((y + t) - 2.0d0) * b
    else
        tmp = x - (((y * z) - z) - a)
    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 <= -3.6e+96) || (!(b <= 9.2e+16) && ((b <= 1e+97) || !(b <= 2e+152)))) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x - (((y * z) - z) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.6e+96) or (not (b <= 9.2e+16) and ((b <= 1e+97) or not (b <= 2e+152))):
		tmp = ((y + t) - 2.0) * b
	else:
		tmp = x - (((y * z) - z) - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.6e+96) || (!(b <= 9.2e+16) && ((b <= 1e+97) || !(b <= 2e+152))))
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	else
		tmp = Float64(x - Float64(Float64(Float64(y * z) - z) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.6e+96) || (~((b <= 9.2e+16)) && ((b <= 1e+97) || ~((b <= 2e+152)))))
		tmp = ((y + t) - 2.0) * b;
	else
		tmp = x - (((y * z) - z) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.6e+96], And[N[Not[LessEqual[b, 9.2e+16]], $MachinePrecision], Or[LessEqual[b, 1e+97], N[Not[LessEqual[b, 2e+152]], $MachinePrecision]]]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(x - N[(N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.60000000000000013e96 or 9.2e16 < b < 1.0000000000000001e97 or 2.0000000000000001e152 < b

   1. Initial program 91.5%

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

   2. Taylor expanded in b around inf 82.8%

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

   if -3.60000000000000013e96 < b < 9.2e16 or 1.0000000000000001e97 < b < 2.0000000000000001e152

   1. Initial program 96.5%

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

   2. Taylor expanded in b around 0 85.0%

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

   3. Taylor expanded in t around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. sub-neg 73.8%

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

      3. metadata-eval 73.8%

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

      4. neg-mul-1 73.8%

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

      5. unsub-neg 73.8%

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

      6. distribute-rgt-in 73.8%

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

      7. mul-1-neg 73.8%

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

      8. unsub-neg 73.8%

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

   5. Simplified 73.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+96} \lor \neg \left(b \leq 9.2 \cdot 10^{+16}\right) \land \left(b \leq 10^{+97} \lor \neg \left(b \leq 2 \cdot 10^{+152}\right)\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(y \cdot z - z\right) - a\right)\\ \end{array} \]

Alternative 15: 53.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+16}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 10^{+97} \lor \neg \left(b \leq 2 \cdot 10^{+152}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -4.5e+32)
     t_1
     (if (<= b 3e+16)
       (- x (* y z))
       (if (or (<= b 1e+97) (not (<= b 2e+152))) t_1 (+ x a))))))

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+32) {
		tmp = t_1;
	} else if (b <= 3e+16) {
		tmp = x - (y * z);
	} else if ((b <= 1e+97) || !(b <= 2e+152)) {
		tmp = t_1;
	} else {
		tmp = x + a;
	}
	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+32)) then
        tmp = t_1
    else if (b <= 3d+16) then
        tmp = x - (y * z)
    else if ((b <= 1d+97) .or. (.not. (b <= 2d+152))) then
        tmp = t_1
    else
        tmp = x + a
    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+32) {
		tmp = t_1;
	} else if (b <= 3e+16) {
		tmp = x - (y * z);
	} else if ((b <= 1e+97) || !(b <= 2e+152)) {
		tmp = t_1;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -4.5e+32:
		tmp = t_1
	elif b <= 3e+16:
		tmp = x - (y * z)
	elif (b <= 1e+97) or not (b <= 2e+152):
		tmp = t_1
	else:
		tmp = x + a
	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+32)
		tmp = t_1;
	elseif (b <= 3e+16)
		tmp = Float64(x - Float64(y * z));
	elseif ((b <= 1e+97) || !(b <= 2e+152))
		tmp = t_1;
	else
		tmp = Float64(x + a);
	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+32)
		tmp = t_1;
	elseif (b <= 3e+16)
		tmp = x - (y * z);
	elseif ((b <= 1e+97) || ~((b <= 2e+152)))
		tmp = t_1;
	else
		tmp = x + a;
	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+32], t$95$1, If[LessEqual[b, 3e+16], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1e+97], N[Not[LessEqual[b, 2e+152]], $MachinePrecision]], t$95$1, N[(x + a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.5000000000000003e32 or 3e16 < b < 1.0000000000000001e97 or 2.0000000000000001e152 < b

   1. Initial program 90.8%

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

   2. Taylor expanded in b around inf 76.9%

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

   if -4.5000000000000003e32 < b < 3e16

   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. Taylor expanded in b around 0 88.8%

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

   3. Taylor expanded in y around inf 53.2%

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

   if 1.0000000000000001e97 < b < 2.0000000000000001e152

   1. Initial program 79.9%

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

   2. Taylor expanded in b around 0 80.1%

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

   3. Taylor expanded in z around 0 48.2%

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

      1. sub-neg 48.2%

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

      2. metadata-eval 48.2%

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

      3. distribute-rgt-in 48.2%

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

      4. neg-mul-1 48.2%

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

      5. sub-neg 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in t around 0 48.7%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+32}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+16}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 10^{+97} \lor \neg \left(b \leq 2 \cdot 10^{+152}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]

Alternative 16: 58.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) + t \cdot b\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-192}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x z) (* t b))) (t_2 (* y (- b z))))
   (if (<= y -6.5e+20)
     t_2
     (if (<= y -1.35e-141)
       t_1
       (if (<= y -2.2e-192) (* a (- 1.0 t)) (if (<= y 8.6e+38) 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 = y * (b - z);
	double tmp;
	if (y <= -6.5e+20) {
		tmp = t_2;
	} else if (y <= -1.35e-141) {
		tmp = t_1;
	} else if (y <= -2.2e-192) {
		tmp = a * (1.0 - t);
	} else if (y <= 8.6e+38) {
		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 = y * (b - z)
    if (y <= (-6.5d+20)) then
        tmp = t_2
    else if (y <= (-1.35d-141)) then
        tmp = t_1
    else if (y <= (-2.2d-192)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 8.6d+38) 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 = y * (b - z);
	double tmp;
	if (y <= -6.5e+20) {
		tmp = t_2;
	} else if (y <= -1.35e-141) {
		tmp = t_1;
	} else if (y <= -2.2e-192) {
		tmp = a * (1.0 - t);
	} else if (y <= 8.6e+38) {
		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 = y * (b - z)
	tmp = 0
	if y <= -6.5e+20:
		tmp = t_2
	elif y <= -1.35e-141:
		tmp = t_1
	elif y <= -2.2e-192:
		tmp = a * (1.0 - t)
	elif y <= 8.6e+38:
		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(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6.5e+20)
		tmp = t_2;
	elseif (y <= -1.35e-141)
		tmp = t_1;
	elseif (y <= -2.2e-192)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 8.6e+38)
		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 = y * (b - z);
	tmp = 0.0;
	if (y <= -6.5e+20)
		tmp = t_2;
	elseif (y <= -1.35e-141)
		tmp = t_1;
	elseif (y <= -2.2e-192)
		tmp = a * (1.0 - t);
	elseif (y <= 8.6e+38)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+20], t$95$2, If[LessEqual[y, -1.35e-141], t$95$1, If[LessEqual[y, -2.2e-192], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e+38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e20 or 8.5999999999999994e38 < y

   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 y around inf 75.7%

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

   if -6.5e20 < y < -1.3500000000000001e-141 or -2.20000000000000006e-192 < y < 8.5999999999999994e38

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 95.5%

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

      1. associate--r+ 95.5%

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

      2. sub-neg 95.5%

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

      3. mul-1-neg 95.5%

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

      4. remove-double-neg 95.5%

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

      5. sub-neg 95.5%

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

      6. metadata-eval 95.5%

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

      7. distribute-lft-in 95.5%

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

      8. *-commutative 95.5%

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

      9. neg-mul-1 95.5%

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

      10. unsub-neg 95.5%

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

      11. *-commutative 95.5%

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

   4. Simplified 95.5%

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

   5. Taylor expanded in a around 0 73.4%

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

      1. +-commutative 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in t around inf 60.0%

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

   if -1.3500000000000001e-141 < y < -2.20000000000000006e-192

   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 a around inf 64.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-141}:\\ \;\;\;\;\left(x + z\right) + t \cdot b\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-192}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+38}:\\ \;\;\;\;\left(x + z\right) + t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 17: 59.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a - t \cdot a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-56}:\\ \;\;\;\;\left(x + z\right) + t \cdot b\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- a (* t a)))) (t_2 (* y (- b z))))
   (if (<= y -9.6e+71)
     t_2
     (if (<= y -1.9e-192)
       t_1
       (if (<= y 6.4e-56) (+ (+ x z) (* t b)) (if (<= y 5.2e+71) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a - (t * a));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -9.6e+71) {
		tmp = t_2;
	} else if (y <= -1.9e-192) {
		tmp = t_1;
	} else if (y <= 6.4e-56) {
		tmp = (x + z) + (t * b);
	} else if (y <= 5.2e+71) {
		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 - (t * a))
    t_2 = y * (b - z)
    if (y <= (-9.6d+71)) then
        tmp = t_2
    else if (y <= (-1.9d-192)) then
        tmp = t_1
    else if (y <= 6.4d-56) then
        tmp = (x + z) + (t * b)
    else if (y <= 5.2d+71) 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 - (t * a));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -9.6e+71) {
		tmp = t_2;
	} else if (y <= -1.9e-192) {
		tmp = t_1;
	} else if (y <= 6.4e-56) {
		tmp = (x + z) + (t * b);
	} else if (y <= 5.2e+71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a - (t * a))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -9.6e+71:
		tmp = t_2
	elif y <= -1.9e-192:
		tmp = t_1
	elif y <= 6.4e-56:
		tmp = (x + z) + (t * b)
	elif y <= 5.2e+71:
		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(t * a)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -9.6e+71)
		tmp = t_2;
	elseif (y <= -1.9e-192)
		tmp = t_1;
	elseif (y <= 6.4e-56)
		tmp = Float64(Float64(x + z) + Float64(t * b));
	elseif (y <= 5.2e+71)
		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 - (t * a));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -9.6e+71)
		tmp = t_2;
	elseif (y <= -1.9e-192)
		tmp = t_1;
	elseif (y <= 6.4e-56)
		tmp = (x + z) + (t * b);
	elseif (y <= 5.2e+71)
		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[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+71], t$95$2, If[LessEqual[y, -1.9e-192], t$95$1, If[LessEqual[y, 6.4e-56], N[(N[(x + z), $MachinePrecision] + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+71], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.59999999999999923e71 or 5.19999999999999983e71 < y

   1. Initial program 89.7%

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

   2. Taylor expanded in y around inf 80.3%

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

   if -9.59999999999999923e71 < y < -1.9000000000000001e-192 or 6.39999999999999971e-56 < y < 5.19999999999999983e71

   1. Initial program 97.4%

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

   2. Taylor expanded in b around 0 73.5%

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

   3. Taylor expanded in z around 0 55.9%

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

      1. sub-neg 55.9%

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

      2. metadata-eval 55.9%

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

      3. distribute-rgt-in 55.9%

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

      4. neg-mul-1 55.9%

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

      5. sub-neg 55.9%

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

   5. Simplified 55.9%

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

   if -1.9000000000000001e-192 < y < 6.39999999999999971e-56

   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. Taylor expanded in y around 0 98.7%

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

      1. associate--r+ 98.7%

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

      2. sub-neg 98.7%

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

      3. mul-1-neg 98.7%

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

      4. remove-double-neg 98.7%

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

      5. sub-neg 98.7%

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

      6. metadata-eval 98.7%

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

      7. distribute-lft-in 98.8%

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

      8. *-commutative 98.8%

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

      9. neg-mul-1 98.8%

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

      10. unsub-neg 98.8%

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

      11. *-commutative 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in a around 0 79.2%

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

      1. +-commutative 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in t around inf 67.8%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-192}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-56}:\\ \;\;\;\;\left(x + z\right) + t \cdot b\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;x + \left(a - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 18: 49.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.18 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-206}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.18e+33)
     t_1
     (if (<= t -2.4e-296)
       (+ x a)
       (if (<= t 1.85e-206) (+ x z) (if (<= t 5.2e+33) (+ 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 <= -1.18e+33) {
		tmp = t_1;
	} else if (t <= -2.4e-296) {
		tmp = x + a;
	} else if (t <= 1.85e-206) {
		tmp = x + z;
	} else if (t <= 5.2e+33) {
		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 <= (-1.18d+33)) then
        tmp = t_1
    else if (t <= (-2.4d-296)) then
        tmp = x + a
    else if (t <= 1.85d-206) then
        tmp = x + z
    else if (t <= 5.2d+33) 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 <= -1.18e+33) {
		tmp = t_1;
	} else if (t <= -2.4e-296) {
		tmp = x + a;
	} else if (t <= 1.85e-206) {
		tmp = x + z;
	} else if (t <= 5.2e+33) {
		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 <= -1.18e+33:
		tmp = t_1
	elif t <= -2.4e-296:
		tmp = x + a
	elif t <= 1.85e-206:
		tmp = x + z
	elif t <= 5.2e+33:
		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 <= -1.18e+33)
		tmp = t_1;
	elseif (t <= -2.4e-296)
		tmp = Float64(x + a);
	elseif (t <= 1.85e-206)
		tmp = Float64(x + z);
	elseif (t <= 5.2e+33)
		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 <= -1.18e+33)
		tmp = t_1;
	elseif (t <= -2.4e-296)
		tmp = x + a;
	elseif (t <= 1.85e-206)
		tmp = x + z;
	elseif (t <= 5.2e+33)
		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, -1.18e+33], t$95$1, If[LessEqual[t, -2.4e-296], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.85e-206], N[(x + z), $MachinePrecision], If[LessEqual[t, 5.2e+33], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.17999999999999993e33 or 5.1999999999999995e33 < t

   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 t around inf 58.1%

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

   if -1.17999999999999993e33 < t < -2.39999999999999996e-296 or 1.84999999999999999e-206 < t < 5.1999999999999995e33

   1. Initial program 98.2%

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

   2. Taylor expanded in b around 0 68.4%

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

   3. Taylor expanded in z around 0 40.7%

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

      1. sub-neg 40.7%

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

      2. metadata-eval 40.7%

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

      3. distribute-rgt-in 40.7%

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

      4. neg-mul-1 40.7%

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

      5. sub-neg 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in t around 0 39.7%

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

   if -2.39999999999999996e-296 < t < 1.84999999999999999e-206

   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 77.4%

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

   3. Taylor expanded in a around 0 70.4%

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

      1. sub-neg 70.4%

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

      2. metadata-eval 70.4%

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

      3. distribute-rgt-in 70.4%

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

      4. mul-1-neg 70.4%

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

      5. unsub-neg 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around 0 47.6%

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

      1. +-commutative 47.6%

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

   8. Simplified 47.6%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-206}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 19: 36.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+92}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-57}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-56}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+76}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.6e+92)
   (* y b)
   (if (<= y -3.5e-57)
     (+ x a)
     (if (<= y 1.2e-56) (+ x z) (if (<= y 8e+76) (+ x a) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.6e+92) {
		tmp = y * b;
	} else if (y <= -3.5e-57) {
		tmp = x + a;
	} else if (y <= 1.2e-56) {
		tmp = x + z;
	} else if (y <= 8e+76) {
		tmp = x + a;
	} 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 (y <= (-4.6d+92)) then
        tmp = y * b
    else if (y <= (-3.5d-57)) then
        tmp = x + a
    else if (y <= 1.2d-56) then
        tmp = x + z
    else if (y <= 8d+76) then
        tmp = x + a
    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 (y <= -4.6e+92) {
		tmp = y * b;
	} else if (y <= -3.5e-57) {
		tmp = x + a;
	} else if (y <= 1.2e-56) {
		tmp = x + z;
	} else if (y <= 8e+76) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.6e+92:
		tmp = y * b
	elif y <= -3.5e-57:
		tmp = x + a
	elif y <= 1.2e-56:
		tmp = x + z
	elif y <= 8e+76:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.6e+92)
		tmp = Float64(y * b);
	elseif (y <= -3.5e-57)
		tmp = Float64(x + a);
	elseif (y <= 1.2e-56)
		tmp = Float64(x + z);
	elseif (y <= 8e+76)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.6e+92)
		tmp = y * b;
	elseif (y <= -3.5e-57)
		tmp = x + a;
	elseif (y <= 1.2e-56)
		tmp = x + z;
	elseif (y <= 8e+76)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.6e+92], N[(y * b), $MachinePrecision], If[LessEqual[y, -3.5e-57], N[(x + a), $MachinePrecision], If[LessEqual[y, 1.2e-56], N[(x + z), $MachinePrecision], If[LessEqual[y, 8e+76], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.59999999999999997e92 or 8.0000000000000004e76 < y

   1. Initial program 89.1%

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

   2. Taylor expanded in y around 0 57.2%

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

      1. associate--r+ 57.2%

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

      2. sub-neg 57.2%

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

      3. mul-1-neg 57.2%

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

      4. remove-double-neg 57.2%

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

      5. sub-neg 57.2%

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

      6. metadata-eval 57.2%

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

      7. distribute-lft-in 57.2%

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

      8. *-commutative 57.2%

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

      9. neg-mul-1 57.2%

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

      10. unsub-neg 57.2%

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

      11. *-commutative 57.2%

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

   4. Simplified 57.2%

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

   5. Taylor expanded in y around inf 39.0%

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

      1. *-commutative 39.0%

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

   7. Simplified 39.0%

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

   if -4.59999999999999997e92 < y < -3.49999999999999991e-57 or 1.2e-56 < y < 8.0000000000000004e76

   1. Initial program 98.2%

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

   2. Taylor expanded in b around 0 69.8%

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

   3. Taylor expanded in z around 0 51.3%

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

      1. sub-neg 51.3%

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

      2. metadata-eval 51.3%

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

      3. distribute-rgt-in 51.3%

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

      4. neg-mul-1 51.3%

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

      5. sub-neg 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in t around 0 44.7%

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

   if -3.49999999999999991e-57 < y < 1.2e-56

   1. Initial program 98.1%

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

   2. Taylor expanded in b around 0 67.1%

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

   3. Taylor expanded in a around 0 40.8%

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

      1. sub-neg 40.8%

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

      2. metadata-eval 40.8%

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

      3. distribute-rgt-in 40.8%

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

      4. mul-1-neg 40.8%

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

      5. unsub-neg 40.8%

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

   5. Simplified 40.8%

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

   6. Taylor expanded in y around 0 40.8%

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

      1. +-commutative 40.8%

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

   8. Simplified 40.8%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+92}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-57}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-56}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+76}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 20: 40.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-155}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.3e+56)
     t_1
     (if (<= a 1.1e-155) (+ x z) (if (<= a 5.2e+105) (* y b) 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 <= -1.3e+56) {
		tmp = t_1;
	} else if (a <= 1.1e-155) {
		tmp = x + z;
	} else if (a <= 5.2e+105) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1.3d+56)) then
        tmp = t_1
    else if (a <= 1.1d-155) then
        tmp = x + z
    else if (a <= 5.2d+105) then
        tmp = y * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.3e+56) {
		tmp = t_1;
	} else if (a <= 1.1e-155) {
		tmp = x + z;
	} else if (a <= 5.2e+105) {
		tmp = y * b;
	} 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 <= -1.3e+56:
		tmp = t_1
	elif a <= 1.1e-155:
		tmp = x + z
	elif a <= 5.2e+105:
		tmp = y * b
	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 <= -1.3e+56)
		tmp = t_1;
	elseif (a <= 1.1e-155)
		tmp = Float64(x + z);
	elseif (a <= 5.2e+105)
		tmp = Float64(y * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.3e+56)
		tmp = t_1;
	elseif (a <= 1.1e-155)
		tmp = x + z;
	elseif (a <= 5.2e+105)
		tmp = y * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+56], t$95$1, If[LessEqual[a, 1.1e-155], N[(x + z), $MachinePrecision], If[LessEqual[a, 5.2e+105], N[(y * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.30000000000000005e56 or 5.2000000000000004e105 < a

   1. Initial program 92.7%

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

   2. Taylor expanded in a around inf 52.1%

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

   if -1.30000000000000005e56 < a < 1.1e-155

   1. Initial program 96.1%

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

   2. Taylor expanded in b around 0 63.5%

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

   3. Taylor expanded in a around 0 60.4%

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

      1. sub-neg 60.4%

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

      2. metadata-eval 60.4%

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

      3. distribute-rgt-in 60.4%

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

      4. mul-1-neg 60.4%

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

      5. unsub-neg 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in y around 0 40.7%

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

      1. +-commutative 40.7%

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

   8. Simplified 40.7%

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

   if 1.1e-155 < a < 5.2000000000000004e105

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 75.9%

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

      1. associate--r+ 75.9%

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

      2. sub-neg 75.9%

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

      3. mul-1-neg 75.9%

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

      4. remove-double-neg 75.9%

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

      5. sub-neg 75.9%

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

      6. metadata-eval 75.9%

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

      7. distribute-lft-in 75.8%

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

      8. *-commutative 75.8%

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

      9. neg-mul-1 75.8%

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

      10. unsub-neg 75.8%

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

      11. *-commutative 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in y around inf 35.6%

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

      1. *-commutative 35.6%

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

   7. Simplified 35.6%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-155}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 21: 21.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+169}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+202}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.05e+169)
   a
   (if (<= a 1.05e-155) x (if (<= a 1.35e+202) (* y b) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.05e+169) {
		tmp = a;
	} else if (a <= 1.05e-155) {
		tmp = x;
	} else if (a <= 1.35e+202) {
		tmp = y * b;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.05d+169)) then
        tmp = a
    else if (a <= 1.05d-155) then
        tmp = x
    else if (a <= 1.35d+202) then
        tmp = y * b
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.05e+169) {
		tmp = a;
	} else if (a <= 1.05e-155) {
		tmp = x;
	} else if (a <= 1.35e+202) {
		tmp = y * b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.05e+169:
		tmp = a
	elif a <= 1.05e-155:
		tmp = x
	elif a <= 1.35e+202:
		tmp = y * b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.05e+169)
		tmp = a;
	elseif (a <= 1.05e-155)
		tmp = x;
	elseif (a <= 1.35e+202)
		tmp = Float64(y * b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.05e+169)
		tmp = a;
	elseif (a <= 1.05e-155)
		tmp = x;
	elseif (a <= 1.35e+202)
		tmp = y * b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.05e+169], a, If[LessEqual[a, 1.05e-155], x, If[LessEqual[a, 1.35e+202], N[(y * b), $MachinePrecision], a]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.0500000000000002e169 or 1.34999999999999998e202 < a

   1. Initial program 92.6%

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

   2. Taylor expanded in a around inf 70.9%

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

   3. Taylor expanded in t around 0 46.9%

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

   if -2.0500000000000002e169 < a < 1.0500000000000001e-155

   1. Initial program 94.9%

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

   2. Taylor expanded in x around inf 24.3%

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

   if 1.0500000000000001e-155 < a < 1.34999999999999998e202

   1. Initial program 96.0%

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

   2. Taylor expanded in y around 0 77.9%

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

      1. associate--r+ 77.9%

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

      2. sub-neg 77.9%

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

      3. mul-1-neg 77.9%

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

      4. remove-double-neg 77.9%

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

      5. sub-neg 77.9%

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

      6. metadata-eval 77.9%

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

      7. distribute-lft-in 77.9%

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

      8. *-commutative 77.9%

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

      9. neg-mul-1 77.9%

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

      10. unsub-neg 77.9%

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

      11. *-commutative 77.9%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in y around inf 32.6%

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

      1. *-commutative 32.6%

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

   7. Simplified 32.6%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+169}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+202}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 22: 33.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+76}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.2e+95) (* y b) (if (<= y 8.2e+76) (+ x a) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e+95) {
		tmp = y * b;
	} else if (y <= 8.2e+76) {
		tmp = x + a;
	} 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 (y <= (-2.2d+95)) then
        tmp = y * b
    else if (y <= 8.2d+76) then
        tmp = x + a
    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 (y <= -2.2e+95) {
		tmp = y * b;
	} else if (y <= 8.2e+76) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.2e+95:
		tmp = y * b
	elif y <= 8.2e+76:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.2e+95)
		tmp = Float64(y * b);
	elseif (y <= 8.2e+76)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.2e+95)
		tmp = y * b;
	elseif (y <= 8.2e+76)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.2e+95], N[(y * b), $MachinePrecision], If[LessEqual[y, 8.2e+76], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1999999999999999e95 or 8.1999999999999997e76 < y

   1. Initial program 89.1%

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

   2. Taylor expanded in y around 0 57.2%

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

      1. associate--r+ 57.2%

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

      2. sub-neg 57.2%

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

      3. mul-1-neg 57.2%

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

      4. remove-double-neg 57.2%

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

      5. sub-neg 57.2%

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

      6. metadata-eval 57.2%

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

      7. distribute-lft-in 57.2%

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

      8. *-commutative 57.2%

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

      9. neg-mul-1 57.2%

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

      10. unsub-neg 57.2%

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

      11. *-commutative 57.2%

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

   4. Simplified 57.2%

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

   5. Taylor expanded in y around inf 39.0%

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

      1. *-commutative 39.0%

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

   7. Simplified 39.0%

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

   if -2.1999999999999999e95 < y < 8.1999999999999997e76

   1. Initial program 98.1%

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

   2. Taylor expanded in b around 0 68.0%

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

   3. Taylor expanded in z around 0 50.4%

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

      1. sub-neg 50.4%

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

      2. metadata-eval 50.4%

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

      3. distribute-rgt-in 50.4%

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

      4. neg-mul-1 50.4%

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

      5. sub-neg 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in t around 0 37.1%

      \[\leadsto \color{blue}{a + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+76}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 23: 21.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+169}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2e+169) a (if (<= a 5e+94) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2e+169) {
		tmp = a;
	} else if (a <= 5e+94) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2d+169)) then
        tmp = a
    else if (a <= 5d+94) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2e+169) {
		tmp = a;
	} else if (a <= 5e+94) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2e+169:
		tmp = a
	elif a <= 5e+94:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2e+169)
		tmp = a;
	elseif (a <= 5e+94)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2e+169)
		tmp = a;
	elseif (a <= 5e+94)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2e+169], a, If[LessEqual[a, 5e+94], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -1.99999999999999987e169 or 5.0000000000000001e94 < a

   1. Initial program 92.3%

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

   2. Taylor expanded in a around inf 57.5%

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

   3. Taylor expanded in t around 0 35.3%

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

   if -1.99999999999999987e169 < a < 5.0000000000000001e94

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 21.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+169}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 24: 11.7% 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 94.9%

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

2. Taylor expanded in a around inf 24.1%

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

3. Taylor expanded in t around 0 12.0%

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

4. Final simplification 12.0%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023290 
(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)))