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

Percentage Accurate: 99.8% → 99.9%

Time: 15.1s

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: 99.8% 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-def 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. Final simplification 99.9%

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

Alternative 2: 93.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+85}:\\ \;\;\;\;x + \left(y + t\_1\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+120}:\\ \;\;\;\;\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+85)
     (+ x (+ y t_1))
     (if (<= t_1 4e+120)
       (+ (+ (+ x y) (- z (* z (log t)))) (* -0.5 b))
       (+ t_1 (+ x (+ 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 (t_1 <= -2e+85) {
		tmp = x + (y + t_1);
	} else if (t_1 <= 4e+120) {
		tmp = ((x + y) + (z - (z * log(t)))) + (-0.5 * b);
	} else {
		tmp = t_1 + (x + (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 (t_1 <= (-2d+85)) then
        tmp = x + (y + t_1)
    else if (t_1 <= 4d+120) then
        tmp = ((x + y) + (z - (z * log(t)))) + ((-0.5d0) * b)
    else
        tmp = t_1 + (x + (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 (t_1 <= -2e+85) {
		tmp = x + (y + t_1);
	} else if (t_1 <= 4e+120) {
		tmp = ((x + y) + (z - (z * Math.log(t)))) + (-0.5 * b);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -2e+85:
		tmp = x + (y + t_1)
	elif t_1 <= 4e+120:
		tmp = ((x + y) + (z - (z * math.log(t)))) + (-0.5 * b)
	else:
		tmp = t_1 + (x + (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 (t_1 <= -2e+85)
		tmp = Float64(x + Float64(y + t_1));
	elseif (t_1 <= 4e+120)
		tmp = Float64(Float64(Float64(x + y) + Float64(z - Float64(z * log(t)))) + Float64(-0.5 * b));
	else
		tmp = Float64(t_1 + Float64(x + 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 (t_1 <= -2e+85)
		tmp = x + (y + t_1);
	elseif (t_1 <= 4e+120)
		tmp = ((x + y) + (z - (z * log(t)))) + (-0.5 * b);
	else
		tmp = t_1 + (x + (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[t$95$1, -2e+85], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+120], N[(N[(N[(x + y), $MachinePrecision] + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -2e85

   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-def 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 z around 0 89.6%

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

   if -2e85 < (*.f64 (-.f64 a 1/2) b) < 3.9999999999999999e120

   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. Step-by-step derivation

      1. add-sqr-sqrt 54.8%

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

      2. pow2 54.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 54.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]
   5. Step-by-step derivation

      1. unpow2 54.8%

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

      2. add-sqr-sqrt 99.7%

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

      3. associate--l+ 99.7%

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

      4. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 94.2%

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

      1. *-commutative 94.2%

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

   9. Simplified 94.2%

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

   if 3.9999999999999999e120 < (*.f64 (-.f64 a 1/2) 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. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 52.6%

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

      2. pow2 52.6%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 52.6%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 93.7%

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

      1. +-commutative 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+85}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 4 \cdot 10^{+120}:\\ \;\;\;\;\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+82}:\\ \;\;\;\;x + \left(y + t\_1\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+82)
     (+ x (+ y t_1))
     (if (<= t_1 4e+120)
       (+ (* z (- 1.0 (log t))) (+ x y))
       (+ t_1 (+ x (+ 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 (t_1 <= -5e+82) {
		tmp = x + (y + t_1);
	} else if (t_1 <= 4e+120) {
		tmp = (z * (1.0 - log(t))) + (x + y);
	} else {
		tmp = t_1 + (x + (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 (t_1 <= (-5d+82)) then
        tmp = x + (y + t_1)
    else if (t_1 <= 4d+120) then
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    else
        tmp = t_1 + (x + (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 (t_1 <= -5e+82) {
		tmp = x + (y + t_1);
	} else if (t_1 <= 4e+120) {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	} else {
		tmp = t_1 + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -5e+82:
		tmp = x + (y + t_1)
	elif t_1 <= 4e+120:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	else:
		tmp = t_1 + (x + (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 (t_1 <= -5e+82)
		tmp = Float64(x + Float64(y + t_1));
	elseif (t_1 <= 4e+120)
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	else
		tmp = Float64(t_1 + Float64(x + 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 (t_1 <= -5e+82)
		tmp = x + (y + t_1);
	elseif (t_1 <= 4e+120)
		tmp = (z * (1.0 - log(t))) + (x + y);
	else
		tmp = t_1 + (x + (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[t$95$1, -5e+82], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+120], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -5.00000000000000015e82

   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-def 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 z around 0 89.8%

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

   if -5.00000000000000015e82 < (*.f64 (-.f64 a 1/2) b) < 3.9999999999999999e120

   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-def 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 92.8%

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

   if 3.9999999999999999e120 < (*.f64 (-.f64 a 1/2) 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. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 52.6%

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

      2. pow2 52.6%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 52.6%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 93.7%

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

      1. +-commutative 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+82}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 4 \cdot 10^{+120}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;x + y \leq -3 \cdot 10^{+46}:\\ \;\;\;\;\left(\left(x + y\right) + \left(z - t\_1\right)\right) + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + y\right) - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= (+ x y) -3e+46)
     (+ (+ (+ x y) (- z t_1)) (* -0.5 b))
     (+ (* b (- a 0.5)) (- (+ 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 tmp;
	if ((x + y) <= -3e+46) {
		tmp = ((x + y) + (z - t_1)) + (-0.5 * b);
	} else {
		tmp = (b * (a - 0.5)) + ((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) :: tmp
    t_1 = z * log(t)
    if ((x + y) <= (-3d+46)) then
        tmp = ((x + y) + (z - t_1)) + ((-0.5d0) * b)
    else
        tmp = (b * (a - 0.5d0)) + ((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 tmp;
	if ((x + y) <= -3e+46) {
		tmp = ((x + y) + (z - t_1)) + (-0.5 * b);
	} else {
		tmp = (b * (a - 0.5)) + ((z + y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if (x + y) <= -3e+46:
		tmp = ((x + y) + (z - t_1)) + (-0.5 * b)
	else:
		tmp = (b * (a - 0.5)) + ((z + y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (Float64(x + y) <= -3e+46)
		tmp = Float64(Float64(Float64(x + y) + Float64(z - t_1)) + Float64(-0.5 * b));
	else
		tmp = Float64(Float64(b * Float64(a - 0.5)) + 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);
	tmp = 0.0;
	if ((x + y) <= -3e+46)
		tmp = ((x + y) + (z - t_1)) + (-0.5 * b);
	else
		tmp = (b * (a - 0.5)) + ((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]}, If[LessEqual[N[(x + y), $MachinePrecision], -3e+46], N[(N[(N[(x + y), $MachinePrecision] + N[(z - t$95$1), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[(z + y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -3.00000000000000023e46

   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. add-sqr-sqrt 54.9%

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

      2. pow2 54.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 54.9%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]
   5. Step-by-step derivation

      1. unpow2 54.9%

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

      2. add-sqr-sqrt 99.8%

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

      3. associate--l+ 99.9%

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

      4. *-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in a around 0 88.7%

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

      1. *-commutative 88.7%

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

   9. Simplified 88.7%

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

   if -3.00000000000000023e46 < (+.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 84.7%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -3 \cdot 10^{+46}:\\ \;\;\;\;\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + y\right) - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+207} \lor \neg \left(z \leq 1.8 \cdot 10^{+205}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e+207) (not (<= z 1.8e+205)))
   (* z (- 1.0 (log t)))
   (+ (* b (- a 0.5)) (+ x (+ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e+207) || !(z <= 1.8e+205)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (b * (a - 0.5)) + (x + (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) :: tmp
    if ((z <= (-2.3d+207)) .or. (.not. (z <= 1.8d+205))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (b * (a - 0.5d0)) + (x + (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 tmp;
	if ((z <= -2.3e+207) || !(z <= 1.8e+205)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e+207) or not (z <= 1.8e+205):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (b * (a - 0.5)) + (x + (z + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e+207) || !(z <= 1.8e+205))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(b * Float64(a - 0.5)) + Float64(x + Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.3e+207) || ~((z <= 1.8e+205)))
		tmp = z * (1.0 - log(t));
	else
		tmp = (b * (a - 0.5)) + (x + (z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e+207], N[Not[LessEqual[z, 1.8e+205]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999995e207 or 1.80000000000000001e205 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 99.4%

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

   4. Taylor expanded in z around -inf 71.8%

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

   5. Taylor expanded in t around inf 71.8%

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

      1. log-rec 71.8%

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

      2. sub-neg 71.8%

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

   7. Simplified 71.8%

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

   if -2.29999999999999995e207 < z < 1.80000000000000001e205

   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. add-sqr-sqrt 52.6%

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

      2. pow2 52.6%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 52.6%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 87.9%

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

      1. +-commutative 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+207} \lor \neg \left(z \leq 1.8 \cdot 10^{+205}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.8% 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 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(z - N[(z * N[Log[t], $MachinePrecision]), $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. Step-by-step derivation

   1. add-sqr-sqrt 53.0%

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

   2. pow2 53.0%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

4. Applied egg-rr 53.0%

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]
5. Step-by-step derivation

   1. unpow2 53.0%

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

   2. add-sqr-sqrt 99.8%

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

   3. associate--l+ 99.8%

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

   4. *-commutative 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 8: 28.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-210} \lor \neg \left(x \leq 1.45 \cdot 10^{-77}\right) \land x \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.45e+23)
   x
   (if (or (<= x 9.4e-210) (and (not (<= x 1.45e-77)) (<= x 1.8e+25)))
     (* a b)
     y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.45e+23) {
		tmp = x;
	} else if ((x <= 9.4e-210) || (!(x <= 1.45e-77) && (x <= 1.8e+25))) {
		tmp = a * 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 (x <= (-2.45d+23)) then
        tmp = x
    else if ((x <= 9.4d-210) .or. (.not. (x <= 1.45d-77)) .and. (x <= 1.8d+25)) then
        tmp = a * 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 (x <= -2.45e+23) {
		tmp = x;
	} else if ((x <= 9.4e-210) || (!(x <= 1.45e-77) && (x <= 1.8e+25))) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.45e+23:
		tmp = x
	elif (x <= 9.4e-210) or (not (x <= 1.45e-77) and (x <= 1.8e+25)):
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.45e+23)
		tmp = x;
	elseif ((x <= 9.4e-210) || (!(x <= 1.45e-77) && (x <= 1.8e+25)))
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.45e+23)
		tmp = x;
	elseif ((x <= 9.4e-210) || (~((x <= 1.45e-77)) && (x <= 1.8e+25)))
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.45e+23], x, If[Or[LessEqual[x, 9.4e-210], And[N[Not[LessEqual[x, 1.45e-77]], $MachinePrecision], LessEqual[x, 1.8e+25]]], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4500000000000001e23

   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-- 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-def 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 x around inf 49.0%

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

   if -2.4500000000000001e23 < x < 9.39999999999999933e-210 or 1.4499999999999999e-77 < x < 1.80000000000000008e25

   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-def 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 a around inf 44.5%

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

      1. *-commutative 44.5%

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

   7. Simplified 44.5%

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

   if 9.39999999999999933e-210 < x < 1.4499999999999999e-77 or 1.80000000000000008e25 < x

   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-def 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 23.6%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-210} \lor \neg \left(x \leq 1.45 \cdot 10^{-77}\right) \land x \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.2% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x + y \leq 10^{+107}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -2e+42) x (if (<= (+ x y) 1e+107) (* a b) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -2e+42) {
		tmp = x;
	} else if ((x + y) <= 1e+107) {
		tmp = a * b;
	} else {
		tmp = 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) :: tmp
    if ((x + y) <= (-2d+42)) then
        tmp = x
    else if ((x + y) <= 1d+107) then
        tmp = a * b
    else
        tmp = 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 tmp;
	if ((x + y) <= -2e+42) {
		tmp = x;
	} else if ((x + y) <= 1e+107) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -2e+42:
		tmp = x
	elif (x + y) <= 1e+107:
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -2e+42)
		tmp = x;
	elseif (Float64(x + y) <= 1e+107)
		tmp = Float64(a * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -2e+42)
		tmp = x;
	elseif ((x + y) <= 1e+107)
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -2e+42], x, If[LessEqual[N[(x + y), $MachinePrecision], 1e+107], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -2.00000000000000009e42

   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-- 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-def 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 x around inf 34.2%

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

   if -2.00000000000000009e42 < (+.f64 x y) < 9.9999999999999997e106

   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-def 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 a around inf 44.7%

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

      1. *-commutative 44.7%

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

   7. Simplified 44.7%

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

   if 9.9999999999999997e106 < (+.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. 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+ 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-- 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-def 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 z around 0 89.2%

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

   6. Taylor expanded in b around 0 54.3%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x + y \leq 10^{+107}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{+113} \lor \neg \left(b \leq 4.6 \cdot 10^{+37}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.1e+113) (not (<= b 4.6e+37))) (* b (- a 0.5)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.1e+113) || !(b <= 4.6e+37)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = 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) :: tmp
    if ((b <= (-6.1d+113)) .or. (.not. (b <= 4.6d+37))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = 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 tmp;
	if ((b <= -6.1e+113) || !(b <= 4.6e+37)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.1e+113) or not (b <= 4.6e+37):
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.1e+113) || !(b <= 4.6e+37))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.1e+113) || ~((b <= 4.6e+37)))
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.1e+113], N[Not[LessEqual[b, 4.6e+37]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.09999999999999996e113 or 4.60000000000000005e37 < 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-- 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-def 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 b around inf 73.0%

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

   if -6.09999999999999996e113 < b < 4.60000000000000005e37

   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-def 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 z around 0 69.9%

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

   6. Taylor expanded in b around 0 56.3%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{+113} \lor \neg \left(b \leq 4.6 \cdot 10^{+37}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.0% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+107}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 1e+107) (+ x (* b (- a 0.5))) (+ y (* -0.5 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e+107) {
		tmp = x + (b * (a - 0.5));
	} 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 ((x + y) <= 1d+107) then
        tmp = x + (b * (a - 0.5d0))
    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 ((x + y) <= 1e+107) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 1e+107:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 1e+107)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	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 ((x + y) <= 1e+107)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 1e+107], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 9.9999999999999997e106

   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+ 99.8%

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

      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-- 99.8%

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

      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-def 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 z around 0 76.2%

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

   6. Taylor expanded in y around 0 58.6%

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

   if 9.9999999999999997e106 < (+.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. 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+ 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-- 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-def 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 z around 0 89.2%

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

   6. Taylor expanded in x around 0 57.3%

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

   7. Taylor expanded in a around 0 33.4%

      \[\leadsto \color{blue}{y + -0.5 \cdot b} \]
   8. Step-by-step derivation

      1. *-commutative 33.4%

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

   9. Simplified 33.4%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+107}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.2% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -1 \cdot 10^{-150}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) -1e-150) (+ x t_1) (+ y t_1))))

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-150) {
		tmp = x + t_1;
	} else {
		tmp = 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) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= (-1d-150)) then
        tmp = x + t_1
    else
        tmp = 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 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -1e-150) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -1e-150:
		tmp = x + t_1
	else:
		tmp = y + t_1
	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-150)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	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-150)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	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-150], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000001e-150

   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-def 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 z around 0 79.6%

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

   6. Taylor expanded in y around 0 55.8%

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

   if -1.00000000000000001e-150 < (+.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. 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-- 99.8%

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

      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-def 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 z around 0 79.1%

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

   6. Taylor expanded in x around 0 63.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-150}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.4% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(y + N[(N[(-0.5 * b), $MachinePrecision] + N[(a * b), $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. 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-def 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 z around 0 79.3%

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

   1. sub-neg 79.3%

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

   2. metadata-eval 79.3%

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

   3. +-commutative 79.3%

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

   4. distribute-rgt-out 79.3%

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

   5. +-commutative 79.3%

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

7. Applied egg-rr 79.3%

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

8. Final simplification 79.3%

   \[\leadsto x + \left(y + \left(-0.5 \cdot b + a \cdot b\right)\right) \]
9. Add Preprocessing

Alternative 14: 79.2% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z + 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. Add Preprocessing
3. Step-by-step derivation

   1. add-sqr-sqrt 53.0%

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

   2. pow2 53.0%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

4. Applied egg-rr 53.0%

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

5. Taylor expanded in z around 0 79.6%

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

   1. +-commutative 79.6%

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

7. Simplified 79.6%

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

8. Final simplification 79.6%

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

Alternative 15: 78.4% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(y + N[(b * N[(a - 0.5), $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. 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-def 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 z around 0 79.3%

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

6. Final simplification 79.3%

   \[\leadsto x + \left(y + b \cdot \left(a - 0.5\right)\right) \]
7. Add Preprocessing

Alternative 16: 26.5% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -2.4e-51) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.4e-51) {
		tmp = x;
	} 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 (x <= (-2.4d-51)) then
        tmp = x
    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 (x <= -2.4e-51) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.4e-51:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.4e-51)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.4e-51)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.4e-51], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e-51

   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-- 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-def 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 x around inf 38.8%

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

   if -2.4e-51 < x

   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-def 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 21.3%

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

4. Final simplification 26.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.0% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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-def 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 x around inf 21.5%

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

6. Final simplification 21.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.5% 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 2024031 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

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