Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Percentage Accurate: 99.9% → 99.9%

Time: 11.6s

Alternatives: 17

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * 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) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * 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) + z) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (* z (- 1.0 (log t))) (fma (+ a -0.5) b (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (z * (1.0 - log(t))) + fma((a + -0.5), b, (x + y));
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(z * Float64(1.0 - log(t))) + fma(Float64(a + -0.5), b, Float64(x + y)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 99.8%

      \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

   2. associate--l+ 99.8%

      \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

   3. associate-+r+ 99.8%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

   4. +-commutative 99.8%

      \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

   5. *-lft-identity 99.8%

      \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   7. *-commutative 99.8%

      \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   8. distribute-rgt-out-- 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   9. metadata-eval 99.9%

      \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   10. fma-define 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

   11. sub-neg 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

   12. metadata-eval 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 72.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := z \cdot \left(1 - \log t\right)\\ t_3 := b \cdot \left(\left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right) - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t\_2 + x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+115}:\\ \;\;\;\;t\_2 + y\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))
        (t_2 (* z (- 1.0 (log t))))
        (t_3 (* b (- (+ a (+ (/ x b) (/ y b))) 0.5))))
   (if (<= t_1 -1e+106)
     t_3
     (if (<= t_1 -1e-59) (+ t_2 x) (if (<= t_1 5e+115) (+ t_2 y) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = z * (1.0 - log(t));
	double t_3 = b * ((a + ((x / b) + (y / b))) - 0.5);
	double tmp;
	if (t_1 <= -1e+106) {
		tmp = t_3;
	} else if (t_1 <= -1e-59) {
		tmp = t_2 + x;
	} else if (t_1 <= 5e+115) {
		tmp = t_2 + y;
	} 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 = b * (a - 0.5d0)
    t_2 = z * (1.0d0 - log(t))
    t_3 = b * ((a + ((x / b) + (y / b))) - 0.5d0)
    if (t_1 <= (-1d+106)) then
        tmp = t_3
    else if (t_1 <= (-1d-59)) then
        tmp = t_2 + x
    else if (t_1 <= 5d+115) then
        tmp = t_2 + y
    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 = b * (a - 0.5);
	double t_2 = z * (1.0 - Math.log(t));
	double t_3 = b * ((a + ((x / b) + (y / b))) - 0.5);
	double tmp;
	if (t_1 <= -1e+106) {
		tmp = t_3;
	} else if (t_1 <= -1e-59) {
		tmp = t_2 + x;
	} else if (t_1 <= 5e+115) {
		tmp = t_2 + y;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	t_2 = z * (1.0 - math.log(t))
	t_3 = b * ((a + ((x / b) + (y / b))) - 0.5)
	tmp = 0
	if t_1 <= -1e+106:
		tmp = t_3
	elif t_1 <= -1e-59:
		tmp = t_2 + x
	elif t_1 <= 5e+115:
		tmp = t_2 + y
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(z * Float64(1.0 - log(t)))
	t_3 = Float64(b * Float64(Float64(a + Float64(Float64(x / b) + Float64(y / b))) - 0.5))
	tmp = 0.0
	if (t_1 <= -1e+106)
		tmp = t_3;
	elseif (t_1 <= -1e-59)
		tmp = Float64(t_2 + x);
	elseif (t_1 <= 5e+115)
		tmp = Float64(t_2 + y);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	t_2 = z * (1.0 - log(t));
	t_3 = b * ((a + ((x / b) + (y / b))) - 0.5);
	tmp = 0.0;
	if (t_1 <= -1e+106)
		tmp = t_3;
	elseif (t_1 <= -1e-59)
		tmp = t_2 + x;
	elseif (t_1 <= 5e+115)
		tmp = t_2 + y;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a + N[(N[(x / b), $MachinePrecision] + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+106], t$95$3, If[LessEqual[t$95$1, -1e-59], N[(t$95$2 + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+115], N[(t$95$2 + y), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.00000000000000009e106 or 5.00000000000000008e115 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 100.0%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around -inf 97.5%

      \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \left(a - 0.5\right) + -1 \cdot \frac{x + y}{b}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 97.5%

         \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(-1 \cdot b\right) \cdot \left(-1 \cdot \left(a - 0.5\right) + -1 \cdot \frac{x + y}{b}\right)} \]

      2. mul-1-neg 97.5%

         \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(-b\right)} \cdot \left(-1 \cdot \left(a - 0.5\right) + -1 \cdot \frac{x + y}{b}\right) \]

      3. mul-1-neg 97.5%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(-1 \cdot \left(a - 0.5\right) + \color{blue}{\left(-\frac{x + y}{b}\right)}\right) \]

      4. unsub-neg 97.5%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \color{blue}{\left(-1 \cdot \left(a - 0.5\right) - \frac{x + y}{b}\right)} \]

      5. sub-neg 97.5%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(-1 \cdot \color{blue}{\left(a + \left(-0.5\right)\right)} - \frac{x + y}{b}\right) \]

      6. metadata-eval 97.5%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(-1 \cdot \left(a + \color{blue}{-0.5}\right) - \frac{x + y}{b}\right) \]

      7. mul-1-neg 97.5%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(\color{blue}{\left(-\left(a + -0.5\right)\right)} - \frac{x + y}{b}\right) \]

      8. +-commutative 97.5%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(\left(-\color{blue}{\left(-0.5 + a\right)}\right) - \frac{x + y}{b}\right) \]

   7. Simplified 97.5%

      \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(-b\right) \cdot \left(\left(-\left(-0.5 + a\right)\right) - \frac{x + y}{b}\right)} \]

   8. Taylor expanded in z around 0 88.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(0.5 - \left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 88.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(0.5 - \left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right)\right)} \]

      2. mul-1-neg 88.9%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(0.5 - \left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right)\right) \]

      3. +-commutative 88.9%

         \[\leadsto \left(-b\right) \cdot \left(0.5 - \color{blue}{\left(\left(\frac{x}{b} + \frac{y}{b}\right) + a\right)}\right) \]

   10. Simplified 88.9%

       \[\leadsto \color{blue}{\left(-b\right) \cdot \left(0.5 - \left(\left(\frac{x}{b} + \frac{y}{b}\right) + a\right)\right)} \]

   if -1.00000000000000009e106 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1e-59

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.7%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.7%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.7%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.7%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.7%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 73.3%

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

   if -1e-59 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5.00000000000000008e115

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.9%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 61.4%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(\left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right) - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right) - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+166} \lor \neg \left(t\_1 \leq 10^{+138}\right):\\ \;\;\;\;b \cdot \left(\left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right) - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -2e+166) (not (<= t_1 1e+138)))
     (* b (- (+ a (+ (/ x b) (/ y b))) 0.5))
     (+ (* z (- 1.0 (log t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -2e+166) || !(t_1 <= 1e+138)) {
		tmp = b * ((a + ((x / b) + (y / b))) - 0.5);
	} else {
		tmp = (z * (1.0 - log(t))) + (x + 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 = b * (a - 0.5d0)
    if ((t_1 <= (-2d+166)) .or. (.not. (t_1 <= 1d+138))) then
        tmp = b * ((a + ((x / b) + (y / b))) - 0.5d0)
    else
        tmp = (z * (1.0d0 - log(t))) + (x + 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 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -2e+166) || !(t_1 <= 1e+138)) {
		tmp = b * ((a + ((x / b) + (y / b))) - 0.5);
	} else {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -2e+166) or not (t_1 <= 1e+138):
		tmp = b * ((a + ((x / b) + (y / b))) - 0.5)
	else:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -2e+166) || !(t_1 <= 1e+138))
		tmp = Float64(b * Float64(Float64(a + Float64(Float64(x / b) + Float64(y / b))) - 0.5));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -2e+166) || ~((t_1 <= 1e+138)))
		tmp = b * ((a + ((x / b) + (y / b))) - 0.5);
	else
		tmp = (z * (1.0 - log(t))) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+166], N[Not[LessEqual[t$95$1, 1e+138]], $MachinePrecision]], N[(b * N[(N[(a + N[(N[(x / b), $MachinePrecision] + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.99999999999999988e166 or 1e138 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 100.0%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 100.0%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 100.0%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 100.0%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 100.0%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around -inf 98.9%

      \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \left(a - 0.5\right) + -1 \cdot \frac{x + y}{b}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 98.9%

         \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(-1 \cdot b\right) \cdot \left(-1 \cdot \left(a - 0.5\right) + -1 \cdot \frac{x + y}{b}\right)} \]

      2. mul-1-neg 98.9%

         \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(-b\right)} \cdot \left(-1 \cdot \left(a - 0.5\right) + -1 \cdot \frac{x + y}{b}\right) \]

      3. mul-1-neg 98.9%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(-1 \cdot \left(a - 0.5\right) + \color{blue}{\left(-\frac{x + y}{b}\right)}\right) \]

      4. unsub-neg 98.9%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \color{blue}{\left(-1 \cdot \left(a - 0.5\right) - \frac{x + y}{b}\right)} \]

      5. sub-neg 98.9%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(-1 \cdot \color{blue}{\left(a + \left(-0.5\right)\right)} - \frac{x + y}{b}\right) \]

      6. metadata-eval 98.9%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(-1 \cdot \left(a + \color{blue}{-0.5}\right) - \frac{x + y}{b}\right) \]

      7. mul-1-neg 98.9%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(\color{blue}{\left(-\left(a + -0.5\right)\right)} - \frac{x + y}{b}\right) \]

      8. +-commutative 98.9%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(\left(-\color{blue}{\left(-0.5 + a\right)}\right) - \frac{x + y}{b}\right) \]

   7. Simplified 98.9%

      \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(-b\right) \cdot \left(\left(-\left(-0.5 + a\right)\right) - \frac{x + y}{b}\right)} \]

   8. Taylor expanded in z around 0 93.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(0.5 - \left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 93.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(0.5 - \left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right)\right)} \]

      2. mul-1-neg 93.9%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(0.5 - \left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right)\right) \]

      3. +-commutative 93.9%

         \[\leadsto \left(-b\right) \cdot \left(0.5 - \color{blue}{\left(\left(\frac{x}{b} + \frac{y}{b}\right) + a\right)}\right) \]

   10. Simplified 93.9%

       \[\leadsto \color{blue}{\left(-b\right) \cdot \left(0.5 - \left(\left(\frac{x}{b} + \frac{y}{b}\right) + a\right)\right)} \]

   if -1.99999999999999988e166 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1e138

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.8%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 88.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+166} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 10^{+138}\right):\\ \;\;\;\;b \cdot \left(\left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right) - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+106} \lor \neg \left(t\_1 \leq 3 \cdot 10^{+76}\right):\\ \;\;\;\;b \cdot \left(\left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right) - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+106) (not (<= t_1 3e+76)))
     (* b (- (+ a (+ (/ x b) (/ y b))) 0.5))
     (+ (* z (- 1.0 (log t))) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+106) || !(t_1 <= 3e+76)) {
		tmp = b * ((a + ((x / b) + (y / b))) - 0.5);
	} else {
		tmp = (z * (1.0 - log(t))) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+106)) .or. (.not. (t_1 <= 3d+76))) then
        tmp = b * ((a + ((x / b) + (y / b))) - 0.5d0)
    else
        tmp = (z * (1.0d0 - log(t))) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+106) || !(t_1 <= 3e+76)) {
		tmp = b * ((a + ((x / b) + (y / b))) - 0.5);
	} else {
		tmp = (z * (1.0 - Math.log(t))) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+106) or not (t_1 <= 3e+76):
		tmp = b * ((a + ((x / b) + (y / b))) - 0.5)
	else:
		tmp = (z * (1.0 - math.log(t))) + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+106) || !(t_1 <= 3e+76))
		tmp = Float64(b * Float64(Float64(a + Float64(Float64(x / b) + Float64(y / b))) - 0.5));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+106) || ~((t_1 <= 3e+76)))
		tmp = b * ((a + ((x / b) + (y / b))) - 0.5);
	else
		tmp = (z * (1.0 - log(t))) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+106], N[Not[LessEqual[t$95$1, 3e+76]], $MachinePrecision]], N[(b * N[(N[(a + N[(N[(x / b), $MachinePrecision] + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.00000000000000009e106 or 2.9999999999999998e76 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 100.0%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around -inf 97.1%

      \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \left(a - 0.5\right) + -1 \cdot \frac{x + y}{b}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 97.1%

         \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(-1 \cdot b\right) \cdot \left(-1 \cdot \left(a - 0.5\right) + -1 \cdot \frac{x + y}{b}\right)} \]

      2. mul-1-neg 97.1%

         \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(-b\right)} \cdot \left(-1 \cdot \left(a - 0.5\right) + -1 \cdot \frac{x + y}{b}\right) \]

      3. mul-1-neg 97.1%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(-1 \cdot \left(a - 0.5\right) + \color{blue}{\left(-\frac{x + y}{b}\right)}\right) \]

      4. unsub-neg 97.1%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \color{blue}{\left(-1 \cdot \left(a - 0.5\right) - \frac{x + y}{b}\right)} \]

      5. sub-neg 97.1%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(-1 \cdot \color{blue}{\left(a + \left(-0.5\right)\right)} - \frac{x + y}{b}\right) \]

      6. metadata-eval 97.1%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(-1 \cdot \left(a + \color{blue}{-0.5}\right) - \frac{x + y}{b}\right) \]

      7. mul-1-neg 97.1%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(\color{blue}{\left(-\left(a + -0.5\right)\right)} - \frac{x + y}{b}\right) \]

      8. +-commutative 97.1%

         \[\leadsto z \cdot \left(1 - \log t\right) + \left(-b\right) \cdot \left(\left(-\color{blue}{\left(-0.5 + a\right)}\right) - \frac{x + y}{b}\right) \]

   7. Simplified 97.1%

      \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(-b\right) \cdot \left(\left(-\left(-0.5 + a\right)\right) - \frac{x + y}{b}\right)} \]

   8. Taylor expanded in z around 0 86.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(0.5 - \left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right)\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 86.2%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(0.5 - \left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right)\right)} \]

      2. mul-1-neg 86.2%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(0.5 - \left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right)\right) \]

      3. +-commutative 86.2%

         \[\leadsto \left(-b\right) \cdot \left(0.5 - \color{blue}{\left(\left(\frac{x}{b} + \frac{y}{b}\right) + a\right)}\right) \]

   10. Simplified 86.2%

       \[\leadsto \color{blue}{\left(-b\right) \cdot \left(0.5 - \left(\left(\frac{x}{b} + \frac{y}{b}\right) + a\right)\right)} \]

   if -1.00000000000000009e106 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.9999999999999998e76

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.8%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+106} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 3 \cdot 10^{+76}\right):\\ \;\;\;\;b \cdot \left(\left(a + \left(\frac{x}{b} + \frac{y}{b}\right)\right) - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{+18}:\\ \;\;\;\;t\_2 + \left(\left(z + x\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \left(\left(z + y\right) - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (* b (- a 0.5))))
   (if (<= (+ x y) -5e+18) (+ t_2 (- (+ z x) t_1)) (+ t_2 (- (+ z y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double t_2 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -5e+18) {
		tmp = t_2 + ((z + x) - t_1);
	} else {
		tmp = t_2 + ((z + y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = b * (a - 0.5d0)
    if ((x + y) <= (-5d+18)) then
        tmp = t_2 + ((z + x) - t_1)
    else
        tmp = t_2 + ((z + y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double t_2 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -5e+18) {
		tmp = t_2 + ((z + x) - t_1);
	} else {
		tmp = t_2 + ((z + y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -5e+18:
		tmp = t_2 + ((z + x) - t_1)
	else:
		tmp = t_2 + ((z + y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -5e+18)
		tmp = Float64(t_2 + Float64(Float64(z + x) - t_1));
	else
		tmp = Float64(t_2 + Float64(Float64(z + y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -5e+18)
		tmp = t_2 + ((z + x) - t_1);
	else
		tmp = t_2 + ((z + y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e+18], N[(t$95$2 + N[(N[(z + x), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(N[(z + y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5e18

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.8%

      \[\leadsto \left(\color{blue}{\left(x + z\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. +-commutative 77.8%

         \[\leadsto \left(\color{blue}{\left(z + x\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 77.8%

      \[\leadsto \left(\color{blue}{\left(z + x\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   if -5e18 < (+.f64 x y)

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.9%

      \[\leadsto \left(\color{blue}{\left(y + z\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. +-commutative 81.9%

         \[\leadsto \left(\color{blue}{\left(z + y\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 81.9%

      \[\leadsto \left(\color{blue}{\left(z + y\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + y\right) - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq 10^{+154}:\\ \;\;\;\;t\_1 + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= (+ x y) 1e+154) (+ t_1 (- (+ z x) (* z (log t)))) (+ t_1 (+ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 1e+154) {
		tmp = t_1 + ((z + x) - (z * log(t)));
	} else {
		tmp = t_1 + (z + 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 = b * (a - 0.5d0)
    if ((x + y) <= 1d+154) then
        tmp = t_1 + ((z + x) - (z * log(t)))
    else
        tmp = t_1 + (z + 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 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 1e+154) {
		tmp = t_1 + ((z + x) - (z * Math.log(t)));
	} else {
		tmp = t_1 + (z + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= 1e+154:
		tmp = t_1 + ((z + x) - (z * math.log(t)))
	else:
		tmp = t_1 + (z + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= 1e+154)
		tmp = Float64(t_1 + Float64(Float64(z + x) - Float64(z * log(t))));
	else
		tmp = Float64(t_1 + Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= 1e+154)
		tmp = t_1 + ((z + x) - (z * log(t)));
	else
		tmp = t_1 + (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 1e+154], N[(t$95$1 + N[(N[(z + x), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1.00000000000000004e154

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.5%

      \[\leadsto \left(\color{blue}{\left(x + z\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   4. Step-by-step derivation

      1. +-commutative 85.5%

         \[\leadsto \left(\color{blue}{\left(z + x\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   5. Simplified 85.5%

      \[\leadsto \left(\color{blue}{\left(z + x\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   if 1.00000000000000004e154 < (+.f64 x y)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 56.9%

      \[\leadsto \left(z + \color{blue}{y}\right) + \left(a - 0.5\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+154}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + b \cdot \left(a - 0.5\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ z (+ x y)) (* z (log t))) (* b (- a 0.5))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((z + (x + y)) - (z * Math.log(t))) + (b * (a - 0.5));
}

Python

def code(x, y, z, t, a, b):
	return ((z + (x + y)) - (z * math.log(t))) + (b * (a - 0.5))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(z + Float64(x + y)) - Float64(z * log(t))) + Float64(b * Float64(a - 0.5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((z + (x + y)) - (z * log(t))) + (b * (a - 0.5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto \left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + b \cdot \left(a - 0.5\right) \]
4. Add Preprocessing

Alternative 8: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a - 0.5\right) + \left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (* b (- a 0.5)) (+ z (- (+ x y) (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a - 0.5)) + (z + ((x + y) - (z * log(t))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (b * (a - 0.5d0)) + (z + ((x + y) - (z * log(t))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a - 0.5)) + (z + ((x + y) - (z * Math.log(t))));
}

Python

def code(x, y, z, t, a, b):
	return (b * (a - 0.5)) + (z + ((x + y) - (z * math.log(t))))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(b * Float64(a - 0.5)) + Float64(z + Float64(Float64(x + y) - Float64(z * log(t)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (b * (a - 0.5)) + (z + ((x + y) - (z * log(t))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z + N[(N[(x + y), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.8%

      \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. associate--l+ 99.8%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

5. Final simplification 99.8%

   \[\leadsto b \cdot \left(a - 0.5\right) + \left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right) \]
6. Add Preprocessing

Alternative 9: 72.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+166} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+185}\right):\\ \;\;\;\;t\_1 + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -2e+166) (not (<= t_1 5e+185)))
     (+ t_1 (+ z x))
     (+ x (+ y (* -0.5 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -2e+166) || !(t_1 <= 5e+185)) {
		tmp = t_1 + (z + x);
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-2d+166)) .or. (.not. (t_1 <= 5d+185))) then
        tmp = t_1 + (z + x)
    else
        tmp = x + (y + ((-0.5d0) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -2e+166) || !(t_1 <= 5e+185)) {
		tmp = t_1 + (z + x);
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -2e+166) or not (t_1 <= 5e+185):
		tmp = t_1 + (z + x)
	else:
		tmp = x + (y + (-0.5 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -2e+166) || !(t_1 <= 5e+185))
		tmp = Float64(t_1 + Float64(z + x));
	else
		tmp = Float64(x + Float64(y + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -2e+166) || ~((t_1 <= 5e+185)))
		tmp = t_1 + (z + x);
	else
		tmp = x + (y + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+166], N[Not[LessEqual[t$95$1, 5e+185]], $MachinePrecision]], N[(t$95$1 + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.99999999999999988e166 or 4.9999999999999999e185 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 100.0%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in x around inf 83.3%

      \[\leadsto \left(z + \color{blue}{x}\right) + \left(a - 0.5\right) \cdot b \]

   if -1.99999999999999988e166 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.9999999999999999e185

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 94.7%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{-0.5 \cdot b} \]

   4. Taylor expanded in z around 0 58.4%

      \[\leadsto \color{blue}{x + \left(y + -0.5 \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+166} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+185}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.8% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+77}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-238}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-24}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.3e+77)
   (* a b)
   (if (<= a 1.45e-238) y (if (<= a 1.05e-24) (* -0.5 b) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.3e+77) {
		tmp = a * b;
	} else if (a <= 1.45e-238) {
		tmp = y;
	} else if (a <= 1.05e-24) {
		tmp = -0.5 * b;
	} else {
		tmp = a * 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 (a <= (-4.3d+77)) then
        tmp = a * b
    else if (a <= 1.45d-238) then
        tmp = y
    else if (a <= 1.05d-24) then
        tmp = (-0.5d0) * b
    else
        tmp = a * 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 (a <= -4.3e+77) {
		tmp = a * b;
	} else if (a <= 1.45e-238) {
		tmp = y;
	} else if (a <= 1.05e-24) {
		tmp = -0.5 * b;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.3e+77:
		tmp = a * b
	elif a <= 1.45e-238:
		tmp = y
	elif a <= 1.05e-24:
		tmp = -0.5 * b
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.3e+77)
		tmp = Float64(a * b);
	elseif (a <= 1.45e-238)
		tmp = y;
	elseif (a <= 1.05e-24)
		tmp = Float64(-0.5 * b);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.3e+77)
		tmp = a * b;
	elseif (a <= 1.45e-238)
		tmp = y;
	elseif (a <= 1.05e-24)
		tmp = -0.5 * b;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.3e+77], N[(a * b), $MachinePrecision], If[LessEqual[a, 1.45e-238], y, If[LessEqual[a, 1.05e-24], N[(-0.5 * b), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.29999999999999991e77 or 1.05e-24 < a

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in b around inf 47.4%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   6. Taylor expanded in a around inf 47.2%

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

   if -4.29999999999999991e77 < a < 1.4499999999999999e-238

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.7%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.7%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.7%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.7%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.8%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 99.8%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 57.1%

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

   6. Taylor expanded in z around 0 28.9%

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

   if 1.4499999999999999e-238 < a < 1.05e-24

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in b around inf 31.7%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   6. Taylor expanded in a around 0 31.7%

      \[\leadsto b \cdot \color{blue}{-0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+77}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-238}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-24}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+23} \lor \neg \left(a \leq 3.1 \cdot 10^{+14}\right):\\ \;\;\;\;\left(z + x\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.46e+23) (not (<= a 3.1e+14)))
   (+ (+ z x) (* a b))
   (+ x (+ y (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.46e+23) || !(a <= 3.1e+14)) {
		tmp = (z + x) + (a * b);
	} else {
		tmp = x + (y + (-0.5 * 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 ((a <= (-1.46d+23)) .or. (.not. (a <= 3.1d+14))) then
        tmp = (z + x) + (a * b)
    else
        tmp = x + (y + ((-0.5d0) * 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 ((a <= -1.46e+23) || !(a <= 3.1e+14)) {
		tmp = (z + x) + (a * b);
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.46e+23) or not (a <= 3.1e+14):
		tmp = (z + x) + (a * b)
	else:
		tmp = x + (y + (-0.5 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.46e+23) || !(a <= 3.1e+14))
		tmp = Float64(Float64(z + x) + Float64(a * b));
	else
		tmp = Float64(x + Float64(y + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.46e+23) || ~((a <= 3.1e+14)))
		tmp = (z + x) + (a * b);
	else
		tmp = x + (y + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.46e+23], N[Not[LessEqual[a, 3.1e+14]], $MachinePrecision]], N[(N[(z + x), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.45999999999999996e23 or 3.1e14 < a

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in x around inf 68.4%

      \[\leadsto \left(z + \color{blue}{x}\right) + \left(a - 0.5\right) \cdot b \]

   6. Taylor expanded in a around inf 68.4%

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

   if -1.45999999999999996e23 < a < 3.1e14

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 98.9%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{-0.5 \cdot b} \]

   4. Taylor expanded in z around 0 66.3%

      \[\leadsto \color{blue}{x + \left(y + -0.5 \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+23} \lor \neg \left(a \leq 3.1 \cdot 10^{+14}\right):\\ \;\;\;\;\left(z + x\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.8% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+158} \lor \neg \left(a \leq 1.7 \cdot 10^{+16}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.9e+158) (not (<= a 1.7e+16)))
   (* a b)
   (+ x (+ y (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.9e+158) || !(a <= 1.7e+16)) {
		tmp = a * b;
	} else {
		tmp = x + (y + (-0.5 * 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 ((a <= (-2.9d+158)) .or. (.not. (a <= 1.7d+16))) then
        tmp = a * b
    else
        tmp = x + (y + ((-0.5d0) * 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 ((a <= -2.9e+158) || !(a <= 1.7e+16)) {
		tmp = a * b;
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.9e+158) or not (a <= 1.7e+16):
		tmp = a * b
	else:
		tmp = x + (y + (-0.5 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.9e+158) || !(a <= 1.7e+16))
		tmp = Float64(a * b);
	else
		tmp = Float64(x + Float64(y + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.9e+158) || ~((a <= 1.7e+16)))
		tmp = a * b;
	else
		tmp = x + (y + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.9e+158], N[Not[LessEqual[a, 1.7e+16]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x + N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.90000000000000024e158 or 1.7e16 < a

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in b around inf 54.4%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   6. Taylor expanded in a around inf 54.4%

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

   if -2.90000000000000024e158 < a < 1.7e16

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 94.5%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{-0.5 \cdot b} \]

   4. Taylor expanded in z around 0 63.7%

      \[\leadsto \color{blue}{x + \left(y + -0.5 \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+158} \lor \neg \left(a \leq 1.7 \cdot 10^{+16}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.8% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+77} \lor \neg \left(a \leq 1.7 \cdot 10^{+16}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.65e+77) (not (<= a 1.7e+16))) (* a b) (+ y (* -0.5 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.65e+77) || !(a <= 1.7e+16)) {
		tmp = a * b;
	} else {
		tmp = y + (-0.5 * 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 ((a <= (-1.65d+77)) .or. (.not. (a <= 1.7d+16))) then
        tmp = a * b
    else
        tmp = y + ((-0.5d0) * 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 ((a <= -1.65e+77) || !(a <= 1.7e+16)) {
		tmp = a * b;
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.65e+77) or not (a <= 1.7e+16):
		tmp = a * b
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.65e+77) || !(a <= 1.7e+16))
		tmp = Float64(a * b);
	else
		tmp = Float64(y + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.65e+77) || ~((a <= 1.7e+16)))
		tmp = a * b;
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.65e+77], N[Not[LessEqual[a, 1.7e+16]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6499999999999999e77 or 1.7e16 < a

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in b around inf 50.2%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   6. Taylor expanded in a around inf 50.2%

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

   if -1.6499999999999999e77 < a < 1.7e16

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 97.2%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{-0.5 \cdot b} \]

   4. Taylor expanded in z around -inf 77.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot \frac{x + y}{z} - \left(1 + -1 \cdot \log t\right)\right)\right)} + -0.5 \cdot b \]
   5. Step-by-step derivation

      1. associate-*r* 77.4%

         \[\leadsto \color{blue}{\left(-1 \cdot z\right) \cdot \left(-1 \cdot \frac{x + y}{z} - \left(1 + -1 \cdot \log t\right)\right)} + -0.5 \cdot b \]

      2. neg-mul-1 77.4%

         \[\leadsto \color{blue}{\left(-z\right)} \cdot \left(-1 \cdot \frac{x + y}{z} - \left(1 + -1 \cdot \log t\right)\right) + -0.5 \cdot b \]

      3. mul-1-neg 77.4%

         \[\leadsto \left(-z\right) \cdot \left(\color{blue}{\left(-\frac{x + y}{z}\right)} - \left(1 + -1 \cdot \log t\right)\right) + -0.5 \cdot b \]

      4. neg-mul-1 77.4%

         \[\leadsto \left(-z\right) \cdot \left(\left(-\frac{x + y}{z}\right) - \left(1 + \color{blue}{\left(-\log t\right)}\right)\right) + -0.5 \cdot b \]

      5. sub-neg 77.4%

         \[\leadsto \left(-z\right) \cdot \left(\left(-\frac{x + y}{z}\right) - \color{blue}{\left(1 - \log t\right)}\right) + -0.5 \cdot b \]

   6. Simplified 77.4%

      \[\leadsto \color{blue}{\left(-z\right) \cdot \left(\left(-\frac{x + y}{z}\right) - \left(1 - \log t\right)\right)} + -0.5 \cdot b \]

   7. Taylor expanded in x around 0 63.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\log t - \left(1 + \frac{y}{z}\right)\right)\right)} + -0.5 \cdot b \]
   8. Step-by-step derivation

      1. mul-1-neg 63.0%

         \[\leadsto \color{blue}{\left(-z \cdot \left(\log t - \left(1 + \frac{y}{z}\right)\right)\right)} + -0.5 \cdot b \]

      2. *-commutative 63.0%

         \[\leadsto \left(-\color{blue}{\left(\log t - \left(1 + \frac{y}{z}\right)\right) \cdot z}\right) + -0.5 \cdot b \]

      3. distribute-rgt-neg-in 63.0%

         \[\leadsto \color{blue}{\left(\log t - \left(1 + \frac{y}{z}\right)\right) \cdot \left(-z\right)} + -0.5 \cdot b \]

   9. Simplified 63.0%

      \[\leadsto \color{blue}{\left(\log t - \left(1 + \frac{y}{z}\right)\right) \cdot \left(-z\right)} + -0.5 \cdot b \]

   10. Taylor expanded in z around 0 42.5%

       \[\leadsto \color{blue}{y + -0.5 \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+77} \lor \neg \left(a \leq 1.7 \cdot 10^{+16}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.9% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;y \leq 1.28 \cdot 10^{+26}:\\ \;\;\;\;t\_1 + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= y 1.28e+26) (+ t_1 (+ z x)) (+ t_1 (+ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (y <= 1.28e+26) {
		tmp = t_1 + (z + x);
	} else {
		tmp = t_1 + (z + 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 = b * (a - 0.5d0)
    if (y <= 1.28d+26) then
        tmp = t_1 + (z + x)
    else
        tmp = t_1 + (z + 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 = b * (a - 0.5);
	double tmp;
	if (y <= 1.28e+26) {
		tmp = t_1 + (z + x);
	} else {
		tmp = t_1 + (z + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if y <= 1.28e+26:
		tmp = t_1 + (z + x)
	else:
		tmp = t_1 + (z + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (y <= 1.28e+26)
		tmp = Float64(t_1 + Float64(z + x));
	else
		tmp = Float64(t_1 + Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (y <= 1.28e+26)
		tmp = t_1 + (z + x);
	else
		tmp = t_1 + (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.28e+26], N[(t$95$1 + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 1.28e26

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in x around inf 60.2%

      \[\leadsto \left(z + \color{blue}{x}\right) + \left(a - 0.5\right) \cdot b \]

   if 1.28e26 < y

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in y around inf 70.1%

      \[\leadsto \left(z + \color{blue}{y}\right) + \left(a - 0.5\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.28 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.8% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.8 \cdot 10^{+172}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 5.8e+172) (* b (- a 0.5)) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.8e+172) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 5.8d+172) then
        tmp = b * (a - 0.5d0)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.8e+172) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 5.8e+172:
		tmp = b * (a - 0.5)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 5.8e+172)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 5.8e+172)
		tmp = b * (a - 0.5);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 5.8e+172], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if y < 5.7999999999999999e172

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in b around inf 36.6%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   if 5.7999999999999999e172 < y

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 100.0%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 62.3%

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

   6. Taylor expanded in z around 0 53.6%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 22.1% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{+50}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 9.5e+50) (* -0.5 b) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 9.5e+50) {
		tmp = -0.5 * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 9.5d+50) then
        tmp = (-0.5d0) * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 9.5e+50) {
		tmp = -0.5 * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 9.5e+50:
		tmp = -0.5 * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 9.5e+50)
		tmp = Float64(-0.5 * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 9.5e+50)
		tmp = -0.5 * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 9.5e+50], N[(-0.5 * b), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if y < 9.4999999999999993e50

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(z + \left(x + y\right)\right)} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\left(z + \left(\left(x + y\right) - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in b around inf 37.0%

      \[\leadsto \color{blue}{b \cdot \left(a - 0.5\right)} \]

   6. Taylor expanded in a around 0 16.2%

      \[\leadsto b \cdot \color{blue}{-0.5} \]

   if 9.4999999999999993e50 < y

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

      2. associate--l+ 99.9%

         \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

      3. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

      5. *-lft-identity 99.9%

         \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      8. distribute-rgt-out-- 99.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      9. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

      10. fma-define 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

      11. sub-neg 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

      12. metadata-eval 100.0%

          \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 52.8%

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

   6. Taylor expanded in z around 0 37.3%

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

4. Final simplification 21.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{+50}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.3% accurate, 115.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 y)

C

double code(double x, double y, double z, double t, double a, double b) {
	return y;
}

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 = y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return y;
}

Python

def code(x, y, z, t, a, b):
	return y

Julia

function code(x, y, z, t, a, b)
	return y
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := y

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 99.8%

      \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right)} \]

   2. associate--l+ 99.8%

      \[\leadsto \left(a - 0.5\right) \cdot b + \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} \]

   3. associate-+r+ 99.8%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) + \left(z - z \cdot \log t\right)} \]

   4. +-commutative 99.8%

      \[\leadsto \color{blue}{\left(z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right)} \]

   5. *-lft-identity 99.8%

      \[\leadsto \left(\color{blue}{1 \cdot z} - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \left(\color{blue}{\left(--1\right)} \cdot z - z \cdot \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   7. *-commutative 99.8%

      \[\leadsto \left(\left(--1\right) \cdot z - \color{blue}{\log t \cdot z}\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   8. distribute-rgt-out-- 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(--1\right) - \log t\right)} + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   9. metadata-eval 99.9%

      \[\leadsto z \cdot \left(\color{blue}{1} - \log t\right) + \left(\left(a - 0.5\right) \cdot b + \left(x + y\right)\right) \]

   10. fma-define 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\mathsf{fma}\left(a - 0.5, b, x + y\right)} \]

   11. sub-neg 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(\color{blue}{a + \left(-0.5\right)}, b, x + y\right) \]

   12. metadata-eval 99.9%

       \[\leadsto z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + \color{blue}{-0.5}, b, x + y\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 41.8%

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

6. Taylor expanded in z around 0 17.9%

   \[\leadsto \color{blue}{y} \]
7. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t))))
  (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - pow(log(t), 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * 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 - (log(t) ** 2.0d0)) * z) / (1.0d0 + log(t)))) + ((a - 0.5d0) * 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 - Math.pow(Math.log(t), 2.0)) * z) / (1.0 + Math.log(t)))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + y) + (((1.0 - math.pow(math.log(t), 2.0)) * z) / (1.0 + math.log(t)))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + y) + Float64(Float64(Float64(1.0 - (log(t) ^ 2.0)) * z) / Float64(1.0 + log(t)))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + y) + (((1.0 - (log(t) ^ 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(N[(N[(1.0 - N[Power[N[Log[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] / N[(1.0 + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 1/2) b)))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))