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

Percentage Accurate: 99.8% → 99.8%

Time: 18.2s

Alternatives: 21

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: 99.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. 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. fma-def 99.8%

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

   3. sub-neg 99.8%

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

   4. metadata-eval 99.8%

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

   5. associate--l+ 99.8%

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

   6. associate-+l+ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := t_1 + \left(x + y\right)\\ t_3 := z \cdot \log t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+88}:\\ \;\;\;\;\left(z + t_1\right) - t_3\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) - t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (+ t_1 (+ x y))) (t_3 (* z (log t))))
   (if (<= t_1 -5e+155)
     t_2
     (if (<= t_1 -2e+88)
       (- (+ z t_1) t_3)
       (if (<= t_1 5e+50) (- (+ y (+ x z)) t_3) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = t_1 + (x + y);
	double t_3 = z * log(t);
	double tmp;
	if (t_1 <= -5e+155) {
		tmp = t_2;
	} else if (t_1 <= -2e+88) {
		tmp = (z + t_1) - t_3;
	} else if (t_1 <= 5e+50) {
		tmp = (y + (x + z)) - t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    t_2 = t_1 + (x + y)
    t_3 = z * log(t)
    if (t_1 <= (-5d+155)) then
        tmp = t_2
    else if (t_1 <= (-2d+88)) then
        tmp = (z + t_1) - t_3
    else if (t_1 <= 5d+50) then
        tmp = (y + (x + z)) - t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = t_1 + (x + y);
	double t_3 = z * Math.log(t);
	double tmp;
	if (t_1 <= -5e+155) {
		tmp = t_2;
	} else if (t_1 <= -2e+88) {
		tmp = (z + t_1) - t_3;
	} else if (t_1 <= 5e+50) {
		tmp = (y + (x + z)) - t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	t_2 = t_1 + (x + y)
	t_3 = z * math.log(t)
	tmp = 0
	if t_1 <= -5e+155:
		tmp = t_2
	elif t_1 <= -2e+88:
		tmp = (z + t_1) - t_3
	elif t_1 <= 5e+50:
		tmp = (y + (x + z)) - t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(t_1 + Float64(x + y))
	t_3 = Float64(z * log(t))
	tmp = 0.0
	if (t_1 <= -5e+155)
		tmp = t_2;
	elseif (t_1 <= -2e+88)
		tmp = Float64(Float64(z + t_1) - t_3);
	elseif (t_1 <= 5e+50)
		tmp = Float64(Float64(y + Float64(x + z)) - t_3);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	t_2 = t_1 + (x + y);
	t_3 = z * log(t);
	tmp = 0.0;
	if (t_1 <= -5e+155)
		tmp = t_2;
	elseif (t_1 <= -2e+88)
		tmp = (z + t_1) - t_3;
	elseif (t_1 <= 5e+50)
		tmp = (y + (x + z)) - t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+155], t$95$2, If[LessEqual[t$95$1, -2e+88], N[(N[(z + t$95$1), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$1, 5e+50], N[(N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -4.9999999999999999e155 or 5e50 < (*.f64 (-.f64 a 1/2) 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. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate--l+ 100.0%

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

      5. fma-neg 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. *-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 96.9%

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

   if -4.9999999999999999e155 < (*.f64 (-.f64 a 1/2) b) < -1.99999999999999992e88

   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. fma-def 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

      5. associate--l+ 99.6%

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

      6. associate-+l+ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 99.6%

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

   5. Taylor expanded in x around 0 93.2%

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

   if -1.99999999999999992e88 < (*.f64 (-.f64 a 1/2) b) < 5e50

   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. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate--l+ 99.8%

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

      5. fma-neg 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. *-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. +-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 96.3%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+155}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + y\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+88}:\\ \;\;\;\;\left(z + b \cdot \left(a - 0.5\right)\right) - z \cdot \log t\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + y\right)\\ \end{array} \]

Alternative 3: 92.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x + \left(\left(a + -0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\left(-0.5 \cdot b + \left(y + \left(x + z\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+102)
     (+ x (+ (* (+ a -0.5) b) (* z (- 1.0 (log t)))))
     (if (<= t_1 5e+50)
       (- (+ (* -0.5 b) (+ y (+ x z))) (* z (log t)))
       (+ t_1 (+ 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 <= -5e+102) {
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - log(t))));
	} else if (t_1 <= 5e+50) {
		tmp = ((-0.5 * b) + (y + (x + z))) - (z * log(t));
	} else {
		tmp = t_1 + (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 <= (-5d+102)) then
        tmp = x + (((a + (-0.5d0)) * b) + (z * (1.0d0 - log(t))))
    else if (t_1 <= 5d+50) then
        tmp = (((-0.5d0) * b) + (y + (x + z))) - (z * log(t))
    else
        tmp = t_1 + (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 <= -5e+102) {
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - Math.log(t))));
	} else if (t_1 <= 5e+50) {
		tmp = ((-0.5 * b) + (y + (x + z))) - (z * Math.log(t));
	} else {
		tmp = t_1 + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -5e+102:
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - math.log(t))))
	elif t_1 <= 5e+50:
		tmp = ((-0.5 * b) + (y + (x + z))) - (z * math.log(t))
	else:
		tmp = t_1 + (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 <= -5e+102)
		tmp = Float64(x + Float64(Float64(Float64(a + -0.5) * b) + Float64(z * Float64(1.0 - log(t)))));
	elseif (t_1 <= 5e+50)
		tmp = Float64(Float64(Float64(-0.5 * b) + Float64(y + Float64(x + z))) - Float64(z * log(t)));
	else
		tmp = Float64(t_1 + 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 <= -5e+102)
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - log(t))));
	elseif (t_1 <= 5e+50)
		tmp = ((-0.5 * b) + (y + (x + z))) - (z * log(t));
	else
		tmp = t_1 + (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[LessEqual[t$95$1, -5e+102], N[(x + N[(N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision] + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+50], N[(N[(N[(-0.5 * b), $MachinePrecision] + N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -5e102

   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. fma-def 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 93.0%

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

      1. fma-udef 93.0%

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

      2. +-commutative 93.0%

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

      3. associate-+r+ 93.0%

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

      4. +-commutative 93.0%

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

      5. *-commutative 93.0%

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

      6. *-un-lft-identity 93.0%

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

      7. distribute-rgt-out-- 93.0%

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

   6. Applied egg-rr 93.0%

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

   if -5e102 < (*.f64 (-.f64 a 1/2) b) < 5e50

   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. remove-double-neg 99.8%

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

      2. distribute-rgt-neg-out 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. remove-double-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 97.5%

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

   if 5e50 < (*.f64 (-.f64 a 1/2) 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. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate--l+ 100.0%

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

      5. fma-neg 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. *-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 96.7%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+102}:\\ \;\;\;\;x + \left(\left(a + -0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\left(-0.5 \cdot b + \left(y + \left(x + z\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + y\right)\\ \end{array} \]

Alternative 4: 90.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+117}:\\ \;\;\;\;y + \left(t_1 + \left(x + z\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+117)
     (+ y (+ t_1 (+ x z)))
     (if (<= t_1 5e+50) (- (+ y (+ x z)) (* z (log t))) (+ t_1 (+ 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 <= -5e+117) {
		tmp = y + (t_1 + (x + z));
	} else if (t_1 <= 5e+50) {
		tmp = (y + (x + z)) - (z * log(t));
	} else {
		tmp = t_1 + (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 <= (-5d+117)) then
        tmp = y + (t_1 + (x + z))
    else if (t_1 <= 5d+50) then
        tmp = (y + (x + z)) - (z * log(t))
    else
        tmp = t_1 + (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 <= -5e+117) {
		tmp = y + (t_1 + (x + z));
	} else if (t_1 <= 5e+50) {
		tmp = (y + (x + z)) - (z * Math.log(t));
	} else {
		tmp = t_1 + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -5e+117:
		tmp = y + (t_1 + (x + z))
	elif t_1 <= 5e+50:
		tmp = (y + (x + z)) - (z * math.log(t))
	else:
		tmp = t_1 + (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 <= -5e+117)
		tmp = Float64(y + Float64(t_1 + Float64(x + z)));
	elseif (t_1 <= 5e+50)
		tmp = Float64(Float64(y + Float64(x + z)) - Float64(z * log(t)));
	else
		tmp = Float64(t_1 + 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 <= -5e+117)
		tmp = y + (t_1 + (x + z));
	elseif (t_1 <= 5e+50)
		tmp = (y + (x + z)) - (z * log(t));
	else
		tmp = t_1 + (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[LessEqual[t$95$1, -5e+117], N[(y + N[(t$95$1 + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+50], N[(N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -4.99999999999999983e117

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate--l+ 99.9%

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

      5. fma-neg 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. *-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 90.6%

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

   if -4.99999999999999983e117 < (*.f64 (-.f64 a 1/2) b) < 5e50

   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. associate-+l- 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate--l+ 99.7%

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

      5. fma-neg 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. *-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. +-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 95.0%

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

   if 5e50 < (*.f64 (-.f64 a 1/2) 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. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate--l+ 100.0%

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

      5. fma-neg 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. *-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 96.7%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+117}:\\ \;\;\;\;y + \left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + y\right)\\ \end{array} \]

Alternative 5: 90.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+88}:\\ \;\;\;\;x + \left(\left(a + -0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+88)
     (+ x (+ (* (+ a -0.5) b) (* z (- 1.0 (log t)))))
     (if (<= t_1 5e+50) (- (+ y (+ x z)) (* z (log t))) (+ t_1 (+ x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+88) {
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - log(t))));
	} else if (t_1 <= 5e+50) {
		tmp = (y + (x + z)) - (z * log(t));
	} else {
		tmp = t_1 + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-2d+88)) then
        tmp = x + (((a + (-0.5d0)) * b) + (z * (1.0d0 - log(t))))
    else if (t_1 <= 5d+50) then
        tmp = (y + (x + z)) - (z * log(t))
    else
        tmp = t_1 + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+88) {
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - Math.log(t))));
	} else if (t_1 <= 5e+50) {
		tmp = (y + (x + z)) - (z * Math.log(t));
	} else {
		tmp = t_1 + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -2e+88:
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - math.log(t))))
	elif t_1 <= 5e+50:
		tmp = (y + (x + z)) - (z * math.log(t))
	else:
		tmp = t_1 + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -2e+88)
		tmp = Float64(x + Float64(Float64(Float64(a + -0.5) * b) + Float64(z * Float64(1.0 - log(t)))));
	elseif (t_1 <= 5e+50)
		tmp = Float64(Float64(y + Float64(x + z)) - Float64(z * log(t)));
	else
		tmp = Float64(t_1 + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -2e+88)
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - log(t))));
	elseif (t_1 <= 5e+50)
		tmp = (y + (x + z)) - (z * log(t));
	else
		tmp = t_1 + (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[LessEqual[t$95$1, -2e+88], N[(x + N[(N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision] + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+50], N[(N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1.99999999999999992e88

   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. fma-def 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 93.3%

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

      1. fma-udef 93.3%

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

      2. +-commutative 93.3%

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

      3. associate-+r+ 93.3%

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

      4. +-commutative 93.3%

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

      5. *-commutative 93.3%

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

      6. *-un-lft-identity 93.3%

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

      7. distribute-rgt-out-- 93.2%

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

   6. Applied egg-rr 93.2%

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

   if -1.99999999999999992e88 < (*.f64 (-.f64 a 1/2) b) < 5e50

   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. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate--l+ 99.8%

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

      5. fma-neg 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. *-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. +-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 96.3%

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

   if 5e50 < (*.f64 (-.f64 a 1/2) 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. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate--l+ 100.0%

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

      5. fma-neg 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. *-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 96.7%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+88}:\\ \;\;\;\;x + \left(\left(a + -0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + y\right)\\ \end{array} \]

Alternative 6: 78.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{-158}:\\ \;\;\;\;x + \left(\left(a + -0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(a - 0.5\right) + \left(y + z\right)\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 5e-158)
   (+ x (+ (* (+ a -0.5) b) (* z (- 1.0 (log t)))))
   (- (+ (* b (- a 0.5)) (+ y z)) (* z (log t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 5e-158) {
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - log(t))));
	} else {
		tmp = ((b * (a - 0.5)) + (y + 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) :: tmp
    if ((x + y) <= 5d-158) then
        tmp = x + (((a + (-0.5d0)) * b) + (z * (1.0d0 - log(t))))
    else
        tmp = ((b * (a - 0.5d0)) + (y + 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 tmp;
	if ((x + y) <= 5e-158) {
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - Math.log(t))));
	} else {
		tmp = ((b * (a - 0.5)) + (y + z)) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 5e-158:
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - math.log(t))))
	else:
		tmp = ((b * (a - 0.5)) + (y + z)) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 5e-158)
		tmp = Float64(x + Float64(Float64(Float64(a + -0.5) * b) + Float64(z * Float64(1.0 - log(t)))));
	else
		tmp = Float64(Float64(Float64(b * Float64(a - 0.5)) + Float64(y + z)) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= 5e-158)
		tmp = x + (((a + -0.5) * b) + (z * (1.0 - log(t))));
	else
		tmp = ((b * (a - 0.5)) + (y + z)) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 5e-158], N[(x + N[(N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision] + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(y + z), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 4.99999999999999972e-158

   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. fma-def 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 82.3%

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

      1. fma-udef 82.3%

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

      2. +-commutative 82.3%

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

      3. associate-+r+ 82.3%

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

      4. +-commutative 82.3%

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

      5. *-commutative 82.3%

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

      6. *-un-lft-identity 82.3%

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

      7. distribute-rgt-out-- 82.3%

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

   6. Applied egg-rr 82.3%

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

   if 4.99999999999999972e-158 < (+.f64 x y)

   1. Initial program 99.8%

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

      1. remove-double-neg 99.8%

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

      2. distribute-rgt-neg-out 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. remove-double-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 76.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{-158}:\\ \;\;\;\;x + \left(\left(a + -0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(a - 0.5\right) + \left(y + z\right)\right) - z \cdot \log t\\ \end{array} \]

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. remove-double-neg 99.8%

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

   2. distribute-rgt-neg-out 99.8%

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

   3. associate--l+ 99.8%

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

   4. distribute-rgt-neg-in 99.8%

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

   5. sub-neg 99.8%

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

   6. metadata-eval 99.8%

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

   7. remove-double-neg 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 8: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+182} \lor \neg \left(z \leq 6.2 \cdot 10^{+153}\right):\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9e+182) (not (<= z 6.2e+153)))
   (+ y (* z (- 1.0 (log t))))
   (+ y (+ (* b (- a 0.5)) (+ x z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9e+182) || !(z <= 6.2e+153)) {
		tmp = y + (z * (1.0 - log(t)));
	} else {
		tmp = y + ((b * (a - 0.5)) + (x + z));
	}
	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 <= (-9d+182)) .or. (.not. (z <= 6.2d+153))) then
        tmp = y + (z * (1.0d0 - log(t)))
    else
        tmp = y + ((b * (a - 0.5d0)) + (x + z))
    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 <= -9e+182) || !(z <= 6.2e+153)) {
		tmp = y + (z * (1.0 - Math.log(t)));
	} else {
		tmp = y + ((b * (a - 0.5)) + (x + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9e+182) or not (z <= 6.2e+153):
		tmp = y + (z * (1.0 - math.log(t)))
	else:
		tmp = y + ((b * (a - 0.5)) + (x + z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9e+182) || !(z <= 6.2e+153))
		tmp = Float64(y + Float64(z * Float64(1.0 - log(t))));
	else
		tmp = Float64(y + Float64(Float64(b * Float64(a - 0.5)) + Float64(x + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9e+182) || ~((z <= 6.2e+153)))
		tmp = y + (z * (1.0 - log(t)));
	else
		tmp = y + ((b * (a - 0.5)) + (x + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9e+182], N[Not[LessEqual[z, 6.2e+153]], $MachinePrecision]], N[(y + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000058e182 or 6.2e153 < 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. associate-+l- 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. associate--l+ 99.6%

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

      5. fma-neg 99.6%

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

      6. distribute-lft-neg-in 99.6%

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

      7. *-commutative 99.6%

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

      8. sub-neg 99.6%

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

      9. +-commutative 99.6%

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

      10. distribute-neg-in 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

      13. unsub-neg 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 64.4%

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

   if -9.00000000000000058e182 < z < 6.2e153

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate--l+ 99.9%

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

      5. fma-neg 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. *-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 89.7%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+182} \lor \neg \left(z \leq 6.2 \cdot 10^{+153}\right):\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right)\\ \end{array} \]

Alternative 9: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+184}:\\ \;\;\;\;y + t_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+151}:\\ \;\;\;\;y + \left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -2.6e+184)
     (+ y t_1)
     (if (<= z 4.1e+151) (+ y (+ (* b (- a 0.5)) (+ x z))) (+ x t_1)))))

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 <= -2.6e+184) {
		tmp = y + t_1;
	} else if (z <= 4.1e+151) {
		tmp = y + ((b * (a - 0.5)) + (x + z));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-2.6d+184)) then
        tmp = y + t_1
    else if (z <= 4.1d+151) then
        tmp = y + ((b * (a - 0.5d0)) + (x + z))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -2.6e+184) {
		tmp = y + t_1;
	} else if (z <= 4.1e+151) {
		tmp = y + ((b * (a - 0.5)) + (x + z));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -2.6e+184:
		tmp = y + t_1
	elif z <= 4.1e+151:
		tmp = y + ((b * (a - 0.5)) + (x + z))
	else:
		tmp = x + t_1
	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 <= -2.6e+184)
		tmp = Float64(y + t_1);
	elseif (z <= 4.1e+151)
		tmp = Float64(y + Float64(Float64(b * Float64(a - 0.5)) + Float64(x + z)));
	else
		tmp = Float64(x + t_1);
	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 <= -2.6e+184)
		tmp = y + t_1;
	elseif (z <= 4.1e+151)
		tmp = y + ((b * (a - 0.5)) + (x + z));
	else
		tmp = x + t_1;
	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, -2.6e+184], N[(y + t$95$1), $MachinePrecision], If[LessEqual[z, 4.1e+151], N[(y + N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999993e184

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

      2. +-commutative 99.5%

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

      3. associate-+l+ 99.5%

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

      4. associate--l+ 99.5%

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

      5. fma-neg 99.5%

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

      6. distribute-lft-neg-in 99.5%

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

      7. *-commutative 99.5%

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

      8. sub-neg 99.5%

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

      9. +-commutative 99.5%

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

      10. distribute-neg-in 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

      13. unsub-neg 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around inf 61.4%

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

   if -2.59999999999999993e184 < z < 4.0999999999999998e151

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate--l+ 99.9%

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

      5. fma-neg 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. *-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 89.7%

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

   if 4.0999999999999998e151 < 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. fma-def 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. associate--l+ 99.7%

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

      6. associate-+l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 99.0%

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

      1. fma-udef 99.0%

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

      2. +-commutative 99.0%

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

      3. associate-+r+ 99.0%

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

      4. +-commutative 99.0%

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

      5. *-commutative 99.0%

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

      6. *-un-lft-identity 99.0%

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

      7. distribute-rgt-out-- 99.0%

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

   6. Applied egg-rr 99.0%

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

   7. Taylor expanded in a around 0 77.9%

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

   8. Taylor expanded in b around 0 77.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+184}:\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+151}:\\ \;\;\;\;y + \left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \end{array} \]

Alternative 10: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+176}:\\ \;\;\;\;-0.5 \cdot b - z \cdot \left(\log t + -1\right)\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{+151}:\\ \;\;\;\;y + \left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.2e+176)
   (- (* -0.5 b) (* z (+ (log t) -1.0)))
   (if (<= z 1.92e+151)
     (+ y (+ (* b (- a 0.5)) (+ x z)))
     (+ x (* z (- 1.0 (log t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.2e+176) {
		tmp = (-0.5 * b) - (z * (log(t) + -1.0));
	} else if (z <= 1.92e+151) {
		tmp = y + ((b * (a - 0.5)) + (x + z));
	} else {
		tmp = x + (z * (1.0 - 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) :: tmp
    if (z <= (-2.2d+176)) then
        tmp = ((-0.5d0) * b) - (z * (log(t) + (-1.0d0)))
    else if (z <= 1.92d+151) then
        tmp = y + ((b * (a - 0.5d0)) + (x + z))
    else
        tmp = x + (z * (1.0d0 - 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 tmp;
	if (z <= -2.2e+176) {
		tmp = (-0.5 * b) - (z * (Math.log(t) + -1.0));
	} else if (z <= 1.92e+151) {
		tmp = y + ((b * (a - 0.5)) + (x + z));
	} else {
		tmp = x + (z * (1.0 - Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.2e+176:
		tmp = (-0.5 * b) - (z * (math.log(t) + -1.0))
	elif z <= 1.92e+151:
		tmp = y + ((b * (a - 0.5)) + (x + z))
	else:
		tmp = x + (z * (1.0 - math.log(t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.2e+176)
		tmp = Float64(Float64(-0.5 * b) - Float64(z * Float64(log(t) + -1.0)));
	elseif (z <= 1.92e+151)
		tmp = Float64(y + Float64(Float64(b * Float64(a - 0.5)) + Float64(x + z)));
	else
		tmp = Float64(x + Float64(z * Float64(1.0 - log(t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.2e+176)
		tmp = (-0.5 * b) - (z * (log(t) + -1.0));
	elseif (z <= 1.92e+151)
		tmp = y + ((b * (a - 0.5)) + (x + z));
	else
		tmp = x + (z * (1.0 - log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.2e+176], N[(N[(-0.5 * b), $MachinePrecision] - N[(z * N[(N[Log[t], $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.92e+151], N[(y + N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000007e176

   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. fma-def 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

      5. associate--l+ 99.6%

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

      6. associate-+l+ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 96.5%

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

      1. fma-udef 96.5%

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

      2. +-commutative 96.5%

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

      3. associate-+r+ 96.5%

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

      4. +-commutative 96.5%

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

      5. *-commutative 96.5%

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

      6. *-un-lft-identity 96.5%

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

      7. distribute-rgt-out-- 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in a around 0 79.2%

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

   8. Taylor expanded in x around 0 74.2%

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

   if -2.20000000000000007e176 < z < 1.92000000000000002e151

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate--l+ 99.9%

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

      5. fma-neg 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. *-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 90.0%

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

   if 1.92000000000000002e151 < 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. fma-def 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. associate--l+ 99.7%

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

      6. associate-+l+ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 99.0%

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

      1. fma-udef 99.0%

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

      2. +-commutative 99.0%

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

      3. associate-+r+ 99.0%

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

      4. +-commutative 99.0%

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

      5. *-commutative 99.0%

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

      6. *-un-lft-identity 99.0%

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

      7. distribute-rgt-out-- 99.0%

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

   6. Applied egg-rr 99.0%

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

   7. Taylor expanded in a around 0 77.9%

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

   8. Taylor expanded in b around 0 77.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+176}:\\ \;\;\;\;-0.5 \cdot b - z \cdot \left(\log t + -1\right)\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{+151}:\\ \;\;\;\;y + \left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \end{array} \]

Alternative 11: 83.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+180} \lor \neg \left(z \leq 8.2 \cdot 10^{+154}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.05e+180) (not (<= z 8.2e+154)))
   (* z (- 1.0 (log t)))
   (+ y (+ (* b (- a 0.5)) (+ x z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.05e+180) || !(z <= 8.2e+154)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = y + ((b * (a - 0.5)) + (x + z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.05d+180)) .or. (.not. (z <= 8.2d+154))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = y + ((b * (a - 0.5d0)) + (x + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.05e+180) || !(z <= 8.2e+154)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = y + ((b * (a - 0.5)) + (x + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.05e+180) or not (z <= 8.2e+154):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = y + ((b * (a - 0.5)) + (x + z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.05e+180) || !(z <= 8.2e+154))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(y + Float64(Float64(b * Float64(a - 0.5)) + Float64(x + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.05e+180) || ~((z <= 8.2e+154)))
		tmp = z * (1.0 - log(t));
	else
		tmp = y + ((b * (a - 0.5)) + (x + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.05e+180], N[Not[LessEqual[z, 8.2e+154]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e180 or 8.2e154 < 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. remove-double-neg 99.6%

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

      2. distribute-rgt-neg-out 99.6%

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

      3. associate--l+ 99.6%

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

      4. distribute-rgt-neg-in 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

      7. remove-double-neg 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 79.4%

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

   5. Taylor expanded in z around inf 62.2%

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

   if -2.05e180 < z < 8.2e154

   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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate--l+ 99.9%

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

      5. fma-neg 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. *-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 89.7%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+180} \lor \neg \left(z \leq 8.2 \cdot 10^{+154}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right)\\ \end{array} \]

Alternative 12: 70.0% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+87} \lor \neg \left(t_1 \leq 5 \cdot 10^{+50}\right):\\ \;\;\;\;y + t_1\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -4e+87) (not (<= t_1 5e+50))) (+ y t_1) (+ z (+ 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 <= -4e+87) || !(t_1 <= 5e+50)) {
		tmp = y + t_1;
	} else {
		tmp = z + (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 <= (-4d+87)) .or. (.not. (t_1 <= 5d+50))) then
        tmp = y + t_1
    else
        tmp = z + (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 <= -4e+87) || !(t_1 <= 5e+50)) {
		tmp = y + t_1;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -4e+87) or not (t_1 <= 5e+50):
		tmp = y + t_1
	else:
		tmp = z + (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 <= -4e+87) || !(t_1 <= 5e+50))
		tmp = Float64(y + t_1);
	else
		tmp = Float64(z + 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 <= -4e+87) || ~((t_1 <= 5e+50)))
		tmp = y + t_1;
	else
		tmp = z + (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, -4e+87], N[Not[LessEqual[t$95$1, 5e+50]], $MachinePrecision]], N[(y + t$95$1), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -3.9999999999999998e87 or 5e50 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate--l+ 99.9%

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

      5. fma-neg 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. *-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 80.8%

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

   if -3.9999999999999998e87 < (*.f64 (-.f64 a 1/2) b) < 5e50

   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. remove-double-neg 99.8%

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

      2. distribute-rgt-neg-out 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. remove-double-neg 99.8%

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

   3. Simplified 99.8%

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

      1. add-cube-cbrt 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right)\right) + \left(a + -0.5\right) \cdot b \]

      2. pow3 99.3%

         \[\leadsto \left(\left(x + y\right) + \left(z - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right)\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 99.3%

      \[\leadsto \left(\left(x + y\right) + \left(z - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right)\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 68.2%

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

   7. Taylor expanded in a around 0 66.3%

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

   8. Taylor expanded in b around 0 65.3%

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

      1. +-commutative 65.3%

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

      2. associate-+r+ 65.3%

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

      3. +-commutative 65.3%

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

   10. Simplified 65.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -4 \cdot 10^{+87} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+50}\right):\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]

Alternative 13: 65.3% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+88} \lor \neg \left(t_1 \leq 5 \cdot 10^{+132}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -2e+88) (not (<= t_1 5e+132))) t_1 (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -2e+88) || !(t_1 <= 5e+132)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-2d+88)) .or. (.not. (t_1 <= 5d+132))) then
        tmp = t_1
    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 t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -2e+88) || !(t_1 <= 5e+132)) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -2e+88) or not (t_1 <= 5e+132):
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -2e+88) || !(t_1 <= 5e+132))
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -2e+88) || ~((t_1 <= 5e+132)))
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+88], N[Not[LessEqual[t$95$1, 5e+132]], $MachinePrecision]], t$95$1, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1.99999999999999992e88 or 5.0000000000000001e132 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. 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. fma-def 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 93.9%

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

   5. Taylor expanded in b around inf 77.5%

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

   if -1.99999999999999992e88 < (*.f64 (-.f64 a 1/2) b) < 5.0000000000000001e132

   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. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate--l+ 99.8%

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

      5. fma-neg 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. *-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. +-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 64.4%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+88} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+132}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 14: 66.0% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+87} \lor \neg \left(t_1 \leq 5 \cdot 10^{+132}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -4e+87) (not (<= t_1 5e+132))) t_1 (+ z (+ 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 <= -4e+87) || !(t_1 <= 5e+132)) {
		tmp = t_1;
	} else {
		tmp = z + (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 <= (-4d+87)) .or. (.not. (t_1 <= 5d+132))) then
        tmp = t_1
    else
        tmp = z + (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 <= -4e+87) || !(t_1 <= 5e+132)) {
		tmp = t_1;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -4e+87) or not (t_1 <= 5e+132):
		tmp = t_1
	else:
		tmp = z + (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 <= -4e+87) || !(t_1 <= 5e+132))
		tmp = t_1;
	else
		tmp = Float64(z + 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 <= -4e+87) || ~((t_1 <= 5e+132)))
		tmp = t_1;
	else
		tmp = z + (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, -4e+87], N[Not[LessEqual[t$95$1, 5e+132]], $MachinePrecision]], t$95$1, N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -3.9999999999999998e87 or 5.0000000000000001e132 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. 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. fma-def 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 94.0%

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

   5. Taylor expanded in b around inf 76.8%

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

   if -3.9999999999999998e87 < (*.f64 (-.f64 a 1/2) b) < 5.0000000000000001e132

   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. remove-double-neg 99.8%

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

      2. distribute-rgt-neg-out 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. remove-double-neg 99.8%

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

   3. Simplified 99.8%

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

      1. add-cube-cbrt 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - \color{blue}{\left(\sqrt[3]{z \cdot \log t} \cdot \sqrt[3]{z \cdot \log t}\right) \cdot \sqrt[3]{z \cdot \log t}}\right)\right) + \left(a + -0.5\right) \cdot b \]

      2. pow3 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right)\right) + \left(a + -0.5\right) \cdot b \]

   5. Applied egg-rr 99.4%

      \[\leadsto \left(\left(x + y\right) + \left(z - \color{blue}{{\left(\sqrt[3]{z \cdot \log t}\right)}^{3}}\right)\right) + \left(a + -0.5\right) \cdot b \]

   6. Taylor expanded in z around 0 70.2%

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

   7. Taylor expanded in a around 0 67.0%

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

   8. Taylor expanded in b around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. associate-+r+ 65.8%

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

      3. +-commutative 65.8%

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

   10. Simplified 65.8%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -4 \cdot 10^{+87} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+132}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]

Alternative 15: 30.4% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-135}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq -7.9 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+93}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.75e-102)
   x
   (if (<= y -4.2e-135)
     (* a b)
     (if (<= y -7.9e-215) x (if (<= y 8e+93) (* a b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.75e-102) {
		tmp = x;
	} else if (y <= -4.2e-135) {
		tmp = a * b;
	} else if (y <= -7.9e-215) {
		tmp = x;
	} else if (y <= 8e+93) {
		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 <= (-1.75d-102)) then
        tmp = x
    else if (y <= (-4.2d-135)) then
        tmp = a * b
    else if (y <= (-7.9d-215)) then
        tmp = x
    else if (y <= 8d+93) 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 <= -1.75e-102) {
		tmp = x;
	} else if (y <= -4.2e-135) {
		tmp = a * b;
	} else if (y <= -7.9e-215) {
		tmp = x;
	} else if (y <= 8e+93) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.75e-102:
		tmp = x
	elif y <= -4.2e-135:
		tmp = a * b
	elif y <= -7.9e-215:
		tmp = x
	elif y <= 8e+93:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.75e-102)
		tmp = x;
	elseif (y <= -4.2e-135)
		tmp = Float64(a * b);
	elseif (y <= -7.9e-215)
		tmp = x;
	elseif (y <= 8e+93)
		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 <= -1.75e-102)
		tmp = x;
	elseif (y <= -4.2e-135)
		tmp = a * b;
	elseif (y <= -7.9e-215)
		tmp = x;
	elseif (y <= 8e+93)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.75e-102], x, If[LessEqual[y, -4.2e-135], N[(a * b), $MachinePrecision], If[LessEqual[y, -7.9e-215], x, If[LessEqual[y, 8e+93], N[(a * b), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999993e-102 or -4.2e-135 < y < -7.8999999999999996e-215

   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. remove-double-neg 99.9%

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

      2. distribute-rgt-neg-out 99.9%

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

      3. associate--l+ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

      7. remove-double-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 75.8%

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

   5. Taylor expanded in x around inf 26.7%

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

   if -1.74999999999999993e-102 < y < -4.2e-135 or -7.8999999999999996e-215 < y < 8.00000000000000035e93

   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. fma-def 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. associate--l+ 99.8%

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

      6. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 94.8%

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

   5. Taylor expanded in a around inf 32.9%

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

      1. *-commutative 32.9%

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

   7. Simplified 32.9%

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

   if 8.00000000000000035e93 < 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. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate--l+ 99.9%

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

      5. fma-neg 99.9%

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

      6. distribute-lft-neg-in 99.9%

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

      7. *-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 42.4%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-135}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq -7.9 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+93}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16: 57.2% accurate, 10.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) -5e-64) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -5e-64) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= (-5d-64)) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -5e-64) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -5e-64:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -5e-64)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -5e-64)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e-64], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.00000000000000033e-64

   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. fma-def 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate--l+ 99.9%

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

      6. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 77.6%

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

   5. Taylor expanded in z around 0 62.0%

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

   if -5.00000000000000033e-64 < (+.f64 x y)

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate--l+ 99.8%

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

      5. fma-neg 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. *-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. +-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around inf 56.2%

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

4. Final simplification 58.6%

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

Alternative 17: 79.3% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.8%

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

   2. +-commutative 99.8%

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

   3. associate-+l+ 99.8%

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

   4. associate--l+ 99.8%

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

   5. fma-neg 99.8%

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

   6. distribute-lft-neg-in 99.8%

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

   7. *-commutative 99.8%

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

   8. sub-neg 99.8%

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

   9. +-commutative 99.8%

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

   10. distribute-neg-in 99.8%

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

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. unsub-neg 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in z around 0 79.0%

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

5. Final simplification 79.0%

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

Alternative 18: 78.6% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.8%

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

   2. +-commutative 99.8%

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

   3. associate-+l+ 99.8%

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

   4. associate--l+ 99.8%

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

   5. fma-neg 99.8%

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

   6. distribute-lft-neg-in 99.8%

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

   7. *-commutative 99.8%

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

   8. sub-neg 99.8%

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

   9. +-commutative 99.8%

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

   10. distribute-neg-in 99.8%

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

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. unsub-neg 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in z around 0 78.4%

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

5. Final simplification 78.4%

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

Alternative 19: 51.3% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+63}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq 320:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.6e+63) (* a b) (if (<= a 320.0) (+ x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.6e+63) {
		tmp = a * b;
	} else if (a <= 320.0) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-6.6d+63)) then
        tmp = a * b
    else if (a <= 320.0d0) then
        tmp = x + y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.6e+63) {
		tmp = a * b;
	} else if (a <= 320.0) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.6e+63:
		tmp = a * b
	elif a <= 320.0:
		tmp = x + y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.6e+63)
		tmp = Float64(a * b);
	elseif (a <= 320.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.6e+63)
		tmp = a * b;
	elseif (a <= 320.0)
		tmp = x + y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.6e+63], N[(a * b), $MachinePrecision], If[LessEqual[a, 320.0], N[(x + y), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.6000000000000003e63 or 320 < a

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. 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. fma-def 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. associate--l+ 99.8%

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

      6. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 84.3%

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

   5. Taylor expanded in a around inf 55.5%

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

      1. *-commutative 55.5%

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

   7. Simplified 55.5%

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

   if -6.6000000000000003e63 < a < 320

   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. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate--l+ 99.8%

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

      5. fma-neg 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. *-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. +-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 59.0%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+63}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq 320:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 20: 27.3% accurate, 37.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -1.15e-69) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.15e-69) {
		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 <= (-1.15d-69)) 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 <= -1.15e-69) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.15e-69:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.15e-69)
		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 <= -1.15e-69)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.15e-69], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e-69

   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. remove-double-neg 99.9%

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

      2. distribute-rgt-neg-out 99.9%

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

      3. associate--l+ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

      7. remove-double-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 73.5%

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

   5. Taylor expanded in x around inf 35.9%

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

   if -1.15e-69 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate--l+ 99.8%

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

      5. fma-neg 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. *-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. +-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. unsub-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 23.2%

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

4. Final simplification 27.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 21: 22.3% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. remove-double-neg 99.8%

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

   2. distribute-rgt-neg-out 99.8%

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

   3. associate--l+ 99.8%

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

   4. distribute-rgt-neg-in 99.8%

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

   5. sub-neg 99.8%

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

   6. metadata-eval 99.8%

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

   7. remove-double-neg 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in a around 0 72.9%

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

5. Taylor expanded in x around inf 23.6%

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

6. Final simplification 23.6%

   \[\leadsto x \]

Developer target: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

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

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