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

Percentage Accurate: 99.8% → 99.9%

Time: 11.0s

Alternatives: 20

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 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 88.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+63}:\\ \;\;\;\;x + \left(y + t\_1\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\_1\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -1e+63)
     (+ x (+ y t_1))
     (if (<= t_1 5e+121)
       (+ (* z (- 1.0 (log t))) (+ x y))
       (- (+ z t_1) (* z (log t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+63) {
		tmp = x + (y + t_1);
	} else if (t_1 <= 5e+121) {
		tmp = (z * (1.0 - log(t))) + (x + y);
	} else {
		tmp = (z + t_1) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-1d+63)) then
        tmp = x + (y + t_1)
    else if (t_1 <= 5d+121) then
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    else
        tmp = (z + t_1) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+63) {
		tmp = x + (y + t_1);
	} else if (t_1 <= 5e+121) {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	} else {
		tmp = (z + t_1) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -1e+63:
		tmp = x + (y + t_1)
	elif t_1 <= 5e+121:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	else:
		tmp = (z + t_1) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -1e+63)
		tmp = Float64(x + Float64(y + t_1));
	elseif (t_1 <= 5e+121)
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	else
		tmp = Float64(Float64(z + t_1) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -1e+63)
		tmp = x + (y + t_1);
	elseif (t_1 <= 5e+121)
		tmp = (z * (1.0 - log(t))) + (x + y);
	else
		tmp = (z + t_1) - (z * log(t));
	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, -1e+63], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+121], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(z + t$95$1), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.00000000000000006e63

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. pow2 100.0%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 92.7%

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

   if -1.00000000000000006e63 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5.00000000000000007e121

   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-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 97.5%

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

   if 5.00000000000000007e121 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.5%

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

   4. Taylor expanded in y around 0 92.4%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+63}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + b \cdot \left(a - 0.5\right)\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+63}:\\ \;\;\;\;x + \left(y + t\_1\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(z - z \cdot \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -1e+63)
     (+ x (+ y t_1))
     (if (<= t_1 5e+121)
       (+ (* z (- 1.0 (log t))) (+ x y))
       (+ t_1 (- z (* z (log t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+63) {
		tmp = x + (y + t_1);
	} else if (t_1 <= 5e+121) {
		tmp = (z * (1.0 - log(t))) + (x + y);
	} else {
		tmp = t_1 + (z - (z * log(t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-1d+63)) then
        tmp = x + (y + t_1)
    else if (t_1 <= 5d+121) then
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    else
        tmp = t_1 + (z - (z * log(t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+63) {
		tmp = x + (y + t_1);
	} else if (t_1 <= 5e+121) {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	} else {
		tmp = t_1 + (z - (z * Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -1e+63:
		tmp = x + (y + t_1)
	elif t_1 <= 5e+121:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	else:
		tmp = t_1 + (z - (z * math.log(t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -1e+63)
		tmp = Float64(x + Float64(y + t_1));
	elseif (t_1 <= 5e+121)
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	else
		tmp = Float64(t_1 + Float64(z - Float64(z * log(t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -1e+63)
		tmp = x + (y + t_1);
	elseif (t_1 <= 5e+121)
		tmp = (z * (1.0 - log(t))) + (x + y);
	else
		tmp = t_1 + (z - (z * log(t)));
	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, -1e+63], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+121], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.00000000000000006e63

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. pow2 100.0%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 92.7%

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

   if -1.00000000000000006e63 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5.00000000000000007e121

   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-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 97.5%

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

   if 5.00000000000000007e121 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 92.4%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+63}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+63} \lor \neg \left(t\_1 \leq 10^{+125}\right):\\ \;\;\;\;x + \left(y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+63) (not (<= t_1 1e+125)))
     (+ x (+ y t_1))
     (+ (* z (- 1.0 (log t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+63) || !(t_1 <= 1e+125)) {
		tmp = x + (y + t_1);
	} else {
		tmp = (z * (1.0 - log(t))) + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+63)) .or. (.not. (t_1 <= 1d+125))) then
        tmp = x + (y + t_1)
    else
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+63) || !(t_1 <= 1e+125)) {
		tmp = x + (y + t_1);
	} else {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+63) or not (t_1 <= 1e+125):
		tmp = x + (y + t_1)
	else:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+63) || !(t_1 <= 1e+125))
		tmp = Float64(x + Float64(y + t_1));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+63) || ~((t_1 <= 1e+125)))
		tmp = x + (y + t_1);
	else
		tmp = (z * (1.0 - log(t))) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+63], N[Not[LessEqual[t$95$1, 1e+125]], $MachinePrecision]], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.00000000000000006e63 or 9.9999999999999992e124 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 99.9%

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

      3. associate-*l/ 99.3%

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

      4. metadata-eval 99.3%

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

      5. pow2 99.3%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 89.2%

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

   if -1.00000000000000006e63 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 9.9999999999999992e124

   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-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 97.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+63} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 10^{+125}\right):\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := z + b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -4 \cdot 10^{-123}:\\ \;\;\;\;\left(x + t\_2\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\_2\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (+ z (* b (- a 0.5)))))
   (if (<= (+ x y) -4e-123) (- (+ x t_2) t_1) (- (+ y t_2) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double t_2 = z + (b * (a - 0.5));
	double tmp;
	if ((x + y) <= -4e-123) {
		tmp = (x + t_2) - t_1;
	} else {
		tmp = (y + t_2) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = z + (b * (a - 0.5d0))
    if ((x + y) <= (-4d-123)) then
        tmp = (x + t_2) - t_1
    else
        tmp = (y + t_2) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double t_2 = z + (b * (a - 0.5));
	double tmp;
	if ((x + y) <= -4e-123) {
		tmp = (x + t_2) - t_1;
	} else {
		tmp = (y + t_2) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = z + (b * (a - 0.5))
	tmp = 0
	if (x + y) <= -4e-123:
		tmp = (x + t_2) - t_1
	else:
		tmp = (y + t_2) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(z + Float64(b * Float64(a - 0.5)))
	tmp = 0.0
	if (Float64(x + y) <= -4e-123)
		tmp = Float64(Float64(x + t_2) - t_1);
	else
		tmp = Float64(Float64(y + t_2) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = z + (b * (a - 0.5));
	tmp = 0.0;
	if ((x + y) <= -4e-123)
		tmp = (x + t_2) - t_1;
	else
		tmp = (y + t_2) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -4e-123], N[(N[(x + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(y + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.0000000000000002e-123

   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. Taylor expanded in y around 0 82.7%

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

   if -4.0000000000000002e-123 < (+.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.2%

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

Alternative 6: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq 5 \cdot 10^{+64}:\\ \;\;\;\;\left(x + \left(z + t\_1\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= (+ x y) 5e+64) (- (+ x (+ z t_1)) (* z (log t))) (+ x (+ 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) <= 5e+64) {
		tmp = (x + (z + t_1)) - (z * log(t));
	} else {
		tmp = x + (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) <= 5d+64) then
        tmp = (x + (z + t_1)) - (z * log(t))
    else
        tmp = x + (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) <= 5e+64) {
		tmp = (x + (z + t_1)) - (z * Math.log(t));
	} else {
		tmp = x + (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) <= 5e+64:
		tmp = (x + (z + t_1)) - (z * math.log(t))
	else:
		tmp = x + (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) <= 5e+64)
		tmp = Float64(Float64(x + Float64(z + t_1)) - Float64(z * log(t)));
	else
		tmp = Float64(x + 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) <= 5e+64)
		tmp = (x + (z + t_1)) - (z * log(t));
	else
		tmp = x + (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], 5e+64], N[(N[(x + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5e64

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 84.5%

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

   if 5e64 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. pow2 99.9%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 93.3%

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

Alternative 7: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+112} \lor \neg \left(z \leq 2.85 \cdot 10^{+113}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e+112) (not (<= z 2.85e+113)))
   (+ (* z (- 1.0 (log t))) (* a b))
   (+ x (+ y (* b (- a 0.5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e+112) || !(z <= 2.85e+113)) {
		tmp = (z * (1.0 - log(t))) + (a * b);
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	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 <= (-8.5d+112)) .or. (.not. (z <= 2.85d+113))) then
        tmp = (z * (1.0d0 - log(t))) + (a * b)
    else
        tmp = x + (y + (b * (a - 0.5d0)))
    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 <= -8.5e+112) || !(z <= 2.85e+113)) {
		tmp = (z * (1.0 - Math.log(t))) + (a * b);
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e+112) or not (z <= 2.85e+113):
		tmp = (z * (1.0 - math.log(t))) + (a * b)
	else:
		tmp = x + (y + (b * (a - 0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e+112) || !(z <= 2.85e+113))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(a * b));
	else
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.5e+112) || ~((z <= 2.85e+113)))
		tmp = (z * (1.0 - log(t))) + (a * b);
	else
		tmp = x + (y + (b * (a - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e+112], N[Not[LessEqual[z, 2.85e+113]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000047e112 or 2.8499999999999999e113 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 81.5%

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

      1. *-commutative 81.5%

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

   7. Simplified 81.5%

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

   if -8.50000000000000047e112 < z < 2.8499999999999999e113

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. pow2 100.0%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 93.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+112} \lor \neg \left(z \leq 2.85 \cdot 10^{+113}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+102} \lor \neg \left(z \leq 2.3 \cdot 10^{+99}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e+102) (not (<= z 2.3e+99)))
   (+ (* z (- 1.0 (log t))) x)
   (+ x (+ y (* b (- a 0.5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e+102) || !(z <= 2.3e+99)) {
		tmp = (z * (1.0 - log(t))) + x;
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	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 <= (-3.8d+102)) .or. (.not. (z <= 2.3d+99))) then
        tmp = (z * (1.0d0 - log(t))) + x
    else
        tmp = x + (y + (b * (a - 0.5d0)))
    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 <= -3.8e+102) || !(z <= 2.3e+99)) {
		tmp = (z * (1.0 - Math.log(t))) + x;
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.8e+102) or not (z <= 2.3e+99):
		tmp = (z * (1.0 - math.log(t))) + x
	else:
		tmp = x + (y + (b * (a - 0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.8e+102) || !(z <= 2.3e+99))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	else
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.8e+102) || ~((z <= 2.3e+99)))
		tmp = (z * (1.0 - log(t))) + x;
	else
		tmp = x + (y + (b * (a - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.8e+102], N[Not[LessEqual[z, 2.3e+99]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999979e102 or 2.30000000000000019e99 < z

   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-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 71.0%

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

   if -3.79999999999999979e102 < z < 2.30000000000000019e99

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. pow2 100.0%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 94.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+102} \lor \neg \left(z \leq 2.3 \cdot 10^{+99}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+102}:\\ \;\;\;\;t\_1 + x\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+134}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -3.8e+102)
     (+ t_1 x)
     (if (<= z 1.42e+134) (+ x (+ y (* b (- a 0.5)))) (+ t_1 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -3.8e+102) {
		tmp = t_1 + x;
	} else if (z <= 1.42e+134) {
		tmp = x + (y + (b * (a - 0.5)));
	} else {
		tmp = t_1 + 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 = z * (1.0d0 - log(t))
    if (z <= (-3.8d+102)) then
        tmp = t_1 + x
    else if (z <= 1.42d+134) then
        tmp = x + (y + (b * (a - 0.5d0)))
    else
        tmp = t_1 + 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 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -3.8e+102) {
		tmp = t_1 + x;
	} else if (z <= 1.42e+134) {
		tmp = x + (y + (b * (a - 0.5)));
	} else {
		tmp = t_1 + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -3.8e+102:
		tmp = t_1 + x
	elif z <= 1.42e+134:
		tmp = x + (y + (b * (a - 0.5)))
	else:
		tmp = t_1 + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -3.8e+102)
		tmp = Float64(t_1 + x);
	elseif (z <= 1.42e+134)
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	else
		tmp = Float64(t_1 + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -3.8e+102)
		tmp = t_1 + x;
	elseif (z <= 1.42e+134)
		tmp = x + (y + (b * (a - 0.5)));
	else
		tmp = t_1 + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+102], N[(t$95$1 + x), $MachinePrecision], If[LessEqual[z, 1.42e+134], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.79999999999999979e102

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 70.3%

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

   if -3.79999999999999979e102 < z < 1.42000000000000002e134

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. pow2 100.0%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 94.2%

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

   if 1.42000000000000002e134 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 70.2%

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

Alternative 10: 82.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+137} \lor \neg \left(z \leq 1.42 \cdot 10^{+134}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e+137) (not (<= z 1.42e+134)))
   (* z (- 1.0 (log t)))
   (+ x (+ y (* b (- a 0.5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e+137) || !(z <= 1.42e+134)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	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 <= (-6d+137)) .or. (.not. (z <= 1.42d+134))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = x + (y + (b * (a - 0.5d0)))
    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 <= -6e+137) || !(z <= 1.42e+134)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e+137) or not (z <= 1.42e+134):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = x + (y + (b * (a - 0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e+137) || !(z <= 1.42e+134))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6e+137) || ~((z <= 1.42e+134)))
		tmp = z * (1.0 - log(t));
	else
		tmp = x + (y + (b * (a - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e+137], N[Not[LessEqual[z, 1.42e+134]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000002e137 or 1.42000000000000002e134 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 74.4%

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

   6. Taylor expanded in z around inf 66.1%

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

   if -6.0000000000000002e137 < z < 1.42000000000000002e134

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 99.9%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. pow2 100.0%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 92.6%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+137} \lor \neg \left(z \leq 1.42 \cdot 10^{+134}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 12: 62.2% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+157}:\\ \;\;\;\;y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= b -1e+90)
     t_1
     (if (<= b 9.2e-93) (+ x y) (if (<= b 7.2e+157) (+ y (* a b)) 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 (b <= -1e+90) {
		tmp = t_1;
	} else if (b <= 9.2e-93) {
		tmp = x + y;
	} else if (b <= 7.2e+157) {
		tmp = y + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (b <= (-1d+90)) then
        tmp = t_1
    else if (b <= 9.2d-93) then
        tmp = x + y
    else if (b <= 7.2d+157) then
        tmp = y + (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (b <= -1e+90) {
		tmp = t_1;
	} else if (b <= 9.2e-93) {
		tmp = x + y;
	} else if (b <= 7.2e+157) {
		tmp = y + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if b <= -1e+90:
		tmp = t_1
	elif b <= 9.2e-93:
		tmp = x + y
	elif b <= 7.2e+157:
		tmp = y + (a * b)
	else:
		tmp = 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 (b <= -1e+90)
		tmp = t_1;
	elseif (b <= 9.2e-93)
		tmp = Float64(x + y);
	elseif (b <= 7.2e+157)
		tmp = Float64(y + Float64(a * b));
	else
		tmp = 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 (b <= -1e+90)
		tmp = t_1;
	elseif (b <= 9.2e-93)
		tmp = x + y;
	elseif (b <= 7.2e+157)
		tmp = y + (a * b);
	else
		tmp = 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[b, -1e+90], t$95$1, If[LessEqual[b, 9.2e-93], N[(x + y), $MachinePrecision], If[LessEqual[b, 7.2e+157], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.99999999999999966e89 or 7.20000000000000049e157 < b

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. pow2 99.9%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in b around inf 84.9%

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

   if -9.99999999999999966e89 < b < 9.1999999999999993e-93

   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-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 90.4%

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

   6. Taylor expanded in z around 0 60.9%

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

   if 9.1999999999999993e-93 < b < 7.20000000000000049e157

   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 82.6%

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

   4. Taylor expanded in z around 0 46.8%

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

   5. Taylor expanded in a around inf 42.3%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+90}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-93}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+157}:\\ \;\;\;\;y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.9% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+148} \lor \neg \left(b \leq 1.32 \cdot 10^{+166}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.2e+148) (not (<= b 1.32e+166)))
   (* b (- a 0.5))
   (+ x (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.2e+148) || !(b <= 1.32e+166)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + (y + (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.2d+148)) .or. (.not. (b <= 1.32d+166))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + (y + (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.2e+148) || !(b <= 1.32e+166)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.2e+148) or not (b <= 1.32e+166):
		tmp = b * (a - 0.5)
	else:
		tmp = x + (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.2e+148) || !(b <= 1.32e+166))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.2e+148) || ~((b <= 1.32e+166)))
		tmp = b * (a - 0.5);
	else
		tmp = x + (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.2e+148], N[Not[LessEqual[b, 1.32e+166]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.1999999999999999e148 or 1.3199999999999999e166 < b

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. pow2 99.9%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in b around inf 87.6%

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

   if -3.1999999999999999e148 < b < 1.3199999999999999e166

   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-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 99.8%

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

      3. associate-*l/ 99.4%

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

      4. metadata-eval 99.4%

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

      5. pow2 99.4%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 71.3%

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

   8. Taylor expanded in a around inf 70.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+148} \lor \neg \left(b \leq 1.32 \cdot 10^{+166}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.6% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+149}:\\ \;\;\;\;y + t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+166}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= b -1.3e+149)
     (+ y t_1)
     (if (<= b 1.5e+166) (+ x (+ y (* a b))) 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 (b <= -1.3e+149) {
		tmp = y + t_1;
	} else if (b <= 1.5e+166) {
		tmp = x + (y + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (b <= (-1.3d+149)) then
        tmp = y + t_1
    else if (b <= 1.5d+166) then
        tmp = x + (y + (a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (b <= -1.3e+149) {
		tmp = y + t_1;
	} else if (b <= 1.5e+166) {
		tmp = x + (y + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if b <= -1.3e+149:
		tmp = y + t_1
	elif b <= 1.5e+166:
		tmp = x + (y + (a * b))
	else:
		tmp = 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 (b <= -1.3e+149)
		tmp = Float64(y + t_1);
	elseif (b <= 1.5e+166)
		tmp = Float64(x + Float64(y + Float64(a * b)));
	else
		tmp = 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 (b <= -1.3e+149)
		tmp = y + t_1;
	elseif (b <= 1.5e+166)
		tmp = x + (y + (a * b));
	else
		tmp = 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[b, -1.3e+149], N[(y + t$95$1), $MachinePrecision], If[LessEqual[b, 1.5e+166], N[(x + N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.29999999999999989e149

   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. Taylor expanded in x around 0 97.3%

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

   4. Taylor expanded in z around 0 85.8%

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

   if -1.29999999999999989e149 < b < 1.49999999999999999e166

   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-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 99.8%

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

      3. associate-*l/ 99.4%

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

      4. metadata-eval 99.4%

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

      5. pow2 99.4%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 71.3%

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

   8. Taylor expanded in a around inf 70.2%

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

   if 1.49999999999999999e166 < b

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. pow2 100.0%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in b around inf 92.0%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+149}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+166}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.7% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+90} \lor \neg \left(b \leq 6.8 \cdot 10^{+165}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.5e+90) (not (<= b 6.8e+165))) (* 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 <= -6.5e+90) || !(b <= 6.8e+165)) {
		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 <= (-6.5d+90)) .or. (.not. (b <= 6.8d+165))) 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 <= -6.5e+90) || !(b <= 6.8e+165)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.5e+90) or not (b <= 6.8e+165):
		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 <= -6.5e+90) || !(b <= 6.8e+165))
		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 <= -6.5e+90) || ~((b <= 6.8e+165)))
		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, -6.5e+90], N[Not[LessEqual[b, 6.8e+165]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5000000000000001e90 or 6.80000000000000022e165 < b

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. pow2 99.9%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in b around inf 86.8%

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

   if -6.5000000000000001e90 < b < 6.80000000000000022e165

   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-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 85.4%

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

   6. Taylor expanded in z around 0 55.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+90} \lor \neg \left(b \leq 6.8 \cdot 10^{+165}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.7% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+96} \lor \neg \left(b \leq 6.8 \cdot 10^{+165}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.4e+96) (not (<= b 6.8e+165))) (* a b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.4e+96) || !(b <= 6.8e+165)) {
		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 ((b <= (-3.4d+96)) .or. (.not. (b <= 6.8d+165))) 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 ((b <= -3.4e+96) || !(b <= 6.8e+165)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.4e+96) or not (b <= 6.8e+165):
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.4e+96) || !(b <= 6.8e+165))
		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 ((b <= -3.4e+96) || ~((b <= 6.8e+165)))
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.4e+96], N[Not[LessEqual[b, 6.8e+165]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.4000000000000001e96 or 6.80000000000000022e165 < b

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. pow2 99.9%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in a around inf 62.8%

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

      1. *-commutative 62.8%

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

   9. Simplified 62.8%

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

   if -3.4000000000000001e96 < b < 6.80000000000000022e165

   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-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 85.4%

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

   6. Taylor expanded in z around 0 55.1%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+96} \lor \neg \left(b \leq 6.8 \cdot 10^{+165}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.1% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+169}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e-275) x (if (<= y 3.4e+169) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e-275) {
		tmp = x;
	} else if (y <= 3.4e+169) {
		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 (y <= (-1.7d-275)) then
        tmp = x
    else if (y <= 3.4d+169) 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 (y <= -1.7e-275) {
		tmp = x;
	} else if (y <= 3.4e+169) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e-275:
		tmp = x
	elif y <= 3.4e+169:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e-275)
		tmp = x;
	elseif (y <= 3.4e+169)
		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 (y <= -1.7e-275)
		tmp = x;
	elseif (y <= 3.4e+169)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e-275], x, If[LessEqual[y, 3.4e+169], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999984e-275

   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-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 99.8%

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

      3. associate-*l/ 99.8%

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

      4. metadata-eval 99.8%

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

      5. pow2 99.8%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in x around inf 21.5%

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

   if -1.69999999999999984e-275 < y < 3.40000000000000028e169

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. flip-- 99.9%

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

      3. associate-*l/ 99.2%

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

      4. metadata-eval 99.2%

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

      5. pow2 99.2%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in a around inf 31.8%

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

      1. *-commutative 31.8%

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

   9. Simplified 31.8%

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

   if 3.40000000000000028e169 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. flip-- 99.9%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. pow2 99.9%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in y around inf 54.6%

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

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+169}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 79.1% 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 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 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. Step-by-step derivation

   1. *-commutative 99.9%

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

   2. flip-- 99.9%

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

   3. associate-*l/ 99.5%

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

   4. metadata-eval 99.5%

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

   5. pow2 99.5%

      \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

6. Applied egg-rr 99.5%

   \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

7. Taylor expanded in z around 0 76.8%

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

Alternative 19: 28.4% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -4.3e+67) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.3e+67) {
		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 <= (-4.3d+67)) 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 <= -4.3e+67) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.3e+67:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.3e+67)
		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 <= -4.3e+67)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.3e+67], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -4.3000000000000001e67

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*l/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. pow2 99.9%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in x around inf 44.1%

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

   if -4.3000000000000001e67 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. flip-- 99.9%

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

      3. associate-*l/ 99.5%

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

      4. metadata-eval 99.5%

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

      5. pow2 99.5%

         \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in y around inf 23.8%

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

Alternative 20: 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 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 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. Step-by-step derivation

   1. *-commutative 99.9%

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

   2. flip-- 99.9%

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

   3. associate-*l/ 99.5%

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

   4. metadata-eval 99.5%

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

   5. pow2 99.5%

      \[\leadsto \frac{\left(1 - \color{blue}{{\log t}^{2}}\right) \cdot z}{1 + \log t} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

6. Applied egg-rr 99.5%

   \[\leadsto \color{blue}{\frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

7. Taylor expanded in x around inf 21.1%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + y) + (((1.0d0 - (log(t) ** 2.0d0)) * z) / (1.0d0 + log(t)))) + ((a - 0.5d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024174 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

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

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