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

Percentage Accurate: 99.8% → 99.9%

Time: 13.9s

Alternatives: 16

Speedup: 1.0×

• could not determine a ground truth

  1. x = -2.6296421755058018e+269
  2. y = -5.296026527605389e-239
  3. z = -1.975261474135206e-259
  4. t = 4.4235477961502967e+235
  5. a = -1.693001463804173e-37
  6. b = 1.7803175946276235e+270

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+142} \lor \neg \left(z \leq 6.2 \cdot 10^{+91} \lor \neg \left(z \leq 8.8 \cdot 10^{+120}\right) \land z \leq 8.5 \cdot 10^{+179}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e+142)
         (not (or (<= z 6.2e+91) (and (not (<= z 8.8e+120)) (<= z 8.5e+179)))))
   (+ (* z (- 1.0 (log t))) x)
   (+ (* b (- a 0.5)) (+ x (+ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e+142) || !((z <= 6.2e+91) || (!(z <= 8.8e+120) && (z <= 8.5e+179)))) {
		tmp = (z * (1.0 - log(t))) + x;
	} else {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.05d+142)) .or. (.not. (z <= 6.2d+91) .or. (.not. (z <= 8.8d+120)) .and. (z <= 8.5d+179))) then
        tmp = (z * (1.0d0 - log(t))) + x
    else
        tmp = (b * (a - 0.5d0)) + (x + (z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e+142) || !((z <= 6.2e+91) || (!(z <= 8.8e+120) && (z <= 8.5e+179)))) {
		tmp = (z * (1.0 - Math.log(t))) + x;
	} else {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e+142) or not ((z <= 6.2e+91) or (not (z <= 8.8e+120) and (z <= 8.5e+179))):
		tmp = (z * (1.0 - math.log(t))) + x
	else:
		tmp = (b * (a - 0.5)) + (x + (z + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e+142) || !((z <= 6.2e+91) || (!(z <= 8.8e+120) && (z <= 8.5e+179))))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	else
		tmp = Float64(Float64(b * Float64(a - 0.5)) + Float64(x + Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e+142) || ~(((z <= 6.2e+91) || (~((z <= 8.8e+120)) && (z <= 8.5e+179)))))
		tmp = (z * (1.0 - log(t))) + x;
	else
		tmp = (b * (a - 0.5)) + (x + (z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e+142], N[Not[Or[LessEqual[z, 6.2e+91], And[N[Not[LessEqual[z, 8.8e+120]], $MachinePrecision], LessEqual[z, 8.5e+179]]]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e142 or 6.19999999999999995e91 < z < 8.8000000000000005e120 or 8.49999999999999962e179 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in b around 0 81.3%

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

      1. associate-+r+ 81.3%

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

      2. +-commutative 81.3%

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

      3. fma-define 81.4%

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

   7. Simplified 81.4%

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

   8. Taylor expanded in y around 0 76.5%

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

   if -1.05e142 < z < 6.19999999999999995e91 or 8.8000000000000005e120 < z < 8.49999999999999962e179

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 93.1%

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

      1. +-commutative 93.1%

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

      2. +-commutative 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+142} \lor \neg \left(z \leq 6.2 \cdot 10^{+91} \lor \neg \left(z \leq 8.8 \cdot 10^{+120}\right) \land z \leq 8.5 \cdot 10^{+179}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+145}:\\ \;\;\;\;t\_1 + x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+94} \lor \neg \left(z \leq 7 \cdot 10^{+123}\right) \land z \leq 8.6 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -1.22e+145)
     (+ t_1 x)
     (if (or (<= z 1.15e+94) (and (not (<= z 7e+123)) (<= z 8.6e+169)))
       (+ (* b (- a 0.5)) (+ x (+ z y)))
       (+ t_1 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -1.22e+145) {
		tmp = t_1 + x;
	} else if ((z <= 1.15e+94) || (!(z <= 7e+123) && (z <= 8.6e+169))) {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	} else {
		tmp = t_1 + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-1.22d+145)) then
        tmp = t_1 + x
    else if ((z <= 1.15d+94) .or. (.not. (z <= 7d+123)) .and. (z <= 8.6d+169)) then
        tmp = (b * (a - 0.5d0)) + (x + (z + y))
    else
        tmp = t_1 + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -1.22e+145) {
		tmp = t_1 + x;
	} else if ((z <= 1.15e+94) || (!(z <= 7e+123) && (z <= 8.6e+169))) {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	} else {
		tmp = t_1 + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -1.22e+145:
		tmp = t_1 + x
	elif (z <= 1.15e+94) or (not (z <= 7e+123) and (z <= 8.6e+169)):
		tmp = (b * (a - 0.5)) + (x + (z + y))
	else:
		tmp = t_1 + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -1.22e+145)
		tmp = Float64(t_1 + x);
	elseif ((z <= 1.15e+94) || (!(z <= 7e+123) && (z <= 8.6e+169)))
		tmp = Float64(Float64(b * Float64(a - 0.5)) + Float64(x + Float64(z + y)));
	else
		tmp = Float64(t_1 + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -1.22e+145)
		tmp = t_1 + x;
	elseif ((z <= 1.15e+94) || (~((z <= 7e+123)) && (z <= 8.6e+169)))
		tmp = (b * (a - 0.5)) + (x + (z + y));
	else
		tmp = t_1 + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e+145], N[(t$95$1 + x), $MachinePrecision], If[Or[LessEqual[z, 1.15e+94], And[N[Not[LessEqual[z, 7e+123]], $MachinePrecision], LessEqual[z, 8.6e+169]]], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999994e145

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. +-commutative 99.6%

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

      5. *-lft-identity 99.6%

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

      6. metadata-eval 99.6%

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

      7. *-commutative 99.6%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 78.4%

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

      1. associate-+r+ 78.4%

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

      2. +-commutative 78.4%

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

      3. fma-define 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in y around 0 71.3%

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

   if -1.21999999999999994e145 < z < 1.15e94 or 6.99999999999999999e123 < z < 8.6000000000000003e169

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 93.5%

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

      1. +-commutative 93.5%

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

      2. +-commutative 93.5%

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

   7. Simplified 93.5%

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

   if 1.15e94 < z < 6.99999999999999999e123 or 8.6000000000000003e169 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.6%

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

      9. metadata-eval 99.6%

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

      10. fma-define 99.6%

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

      11. sub-neg 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around 0 84.8%

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

      1. associate-+r+ 84.8%

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

      2. +-commutative 84.8%

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

      3. fma-define 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in x around 0 84.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+94} \lor \neg \left(z \leq 7 \cdot 10^{+123}\right) \land z \leq 8.6 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ t_2 := z \cdot \left(1 - \log t\right) + x\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - z \cdot \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* b (- a 0.5)) (+ x (+ z y))))
        (t_2 (+ (* z (- 1.0 (log t))) x)))
   (if (<= z -8.5e+144)
     t_2
     (if (<= z 1.65e+93)
       t_1
       (if (<= z 1e+121)
         t_2
         (if (<= z 8.4e+179) t_1 (+ x (- z (* z (log t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * (a - 0.5)) + (x + (z + y));
	double t_2 = (z * (1.0 - log(t))) + x;
	double tmp;
	if (z <= -8.5e+144) {
		tmp = t_2;
	} else if (z <= 1.65e+93) {
		tmp = t_1;
	} else if (z <= 1e+121) {
		tmp = t_2;
	} else if (z <= 8.4e+179) {
		tmp = t_1;
	} else {
		tmp = x + (z - (z * log(t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * (a - 0.5d0)) + (x + (z + y))
    t_2 = (z * (1.0d0 - log(t))) + x
    if (z <= (-8.5d+144)) then
        tmp = t_2
    else if (z <= 1.65d+93) then
        tmp = t_1
    else if (z <= 1d+121) then
        tmp = t_2
    else if (z <= 8.4d+179) then
        tmp = t_1
    else
        tmp = x + (z - (z * log(t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * (a - 0.5)) + (x + (z + y));
	double t_2 = (z * (1.0 - Math.log(t))) + x;
	double tmp;
	if (z <= -8.5e+144) {
		tmp = t_2;
	} else if (z <= 1.65e+93) {
		tmp = t_1;
	} else if (z <= 1e+121) {
		tmp = t_2;
	} else if (z <= 8.4e+179) {
		tmp = t_1;
	} else {
		tmp = x + (z - (z * Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * (a - 0.5)) + (x + (z + y))
	t_2 = (z * (1.0 - math.log(t))) + x
	tmp = 0
	if z <= -8.5e+144:
		tmp = t_2
	elif z <= 1.65e+93:
		tmp = t_1
	elif z <= 1e+121:
		tmp = t_2
	elif z <= 8.4e+179:
		tmp = t_1
	else:
		tmp = x + (z - (z * math.log(t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(a - 0.5)) + Float64(x + Float64(z + y)))
	t_2 = Float64(Float64(z * Float64(1.0 - log(t))) + x)
	tmp = 0.0
	if (z <= -8.5e+144)
		tmp = t_2;
	elseif (z <= 1.65e+93)
		tmp = t_1;
	elseif (z <= 1e+121)
		tmp = t_2;
	elseif (z <= 8.4e+179)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z - Float64(z * log(t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * (a - 0.5)) + (x + (z + y));
	t_2 = (z * (1.0 - log(t))) + x;
	tmp = 0.0;
	if (z <= -8.5e+144)
		tmp = t_2;
	elseif (z <= 1.65e+93)
		tmp = t_1;
	elseif (z <= 1e+121)
		tmp = t_2;
	elseif (z <= 8.4e+179)
		tmp = t_1;
	else
		tmp = x + (z - (z * log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -8.5e+144], t$95$2, If[LessEqual[z, 1.65e+93], t$95$1, If[LessEqual[z, 1e+121], t$95$2, If[LessEqual[z, 8.4e+179], t$95$1, N[(x + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999998e144 or 1.65000000000000004e93 < z < 1.00000000000000004e121

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. +-commutative 99.6%

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

      5. *-lft-identity 99.6%

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

      6. metadata-eval 99.6%

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

      7. *-commutative 99.6%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 81.1%

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

      1. associate-+r+ 81.1%

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

      2. +-commutative 81.1%

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

      3. fma-define 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in y around 0 74.0%

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

   if -8.4999999999999998e144 < z < 1.65000000000000004e93 or 1.00000000000000004e121 < z < 8.3999999999999994e179

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 93.1%

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

      1. +-commutative 93.1%

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

      2. +-commutative 93.1%

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

   7. Simplified 93.1%

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

   if 8.3999999999999994e179 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.6%

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

      9. metadata-eval 99.6%

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

      10. fma-define 99.6%

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

      11. sub-neg 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around 0 81.7%

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

      1. associate-+r+ 81.7%

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

      2. +-commutative 81.7%

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

      3. fma-define 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in y around 0 79.5%

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

      1. distribute-rgt-out-- 79.5%

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

      2. *-un-lft-identity 79.5%

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

      3. *-commutative 79.5%

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

   10. Applied egg-rr 79.5%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \mathbf{elif}\;z \leq 10^{+121}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+179}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+130}:\\ \;\;\;\;t\_1 + \left(x + \left(z + y\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+130)
     (+ t_1 (+ x (+ z y)))
     (if (<= t_1 5e+36) (+ x (+ (* z (- 1.0 (log t))) y)) (+ (+ x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+130) {
		tmp = t_1 + (x + (z + y));
	} else if (t_1 <= 5e+36) {
		tmp = x + ((z * (1.0 - log(t))) + y);
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-2d+130)) then
        tmp = t_1 + (x + (z + y))
    else if (t_1 <= 5d+36) then
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    else
        tmp = (x + y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+130) {
		tmp = t_1 + (x + (z + y));
	} else if (t_1 <= 5e+36) {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -2e+130:
		tmp = t_1 + (x + (z + y))
	elif t_1 <= 5e+36:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	else:
		tmp = (x + y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -2e+130)
		tmp = Float64(t_1 + Float64(x + Float64(z + y)));
	elseif (t_1 <= 5e+36)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	else
		tmp = Float64(Float64(x + 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 (t_1 <= -2e+130)
		tmp = t_1 + (x + (z + y));
	elseif (t_1 <= 5e+36)
		tmp = x + ((z * (1.0 - log(t))) + y);
	else
		tmp = (x + y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+130], N[(t$95$1 + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+36], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -2.0000000000000001e130

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 92.2%

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

      1. +-commutative 92.2%

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

      2. +-commutative 92.2%

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

   7. Simplified 92.2%

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

   if -2.0000000000000001e130 < (*.f64 (-.f64 a 1/2) b) < 4.99999999999999977e36

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 95.4%

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

   if 4.99999999999999977e36 < (*.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. Add Preprocessing

   3. Taylor expanded in z around 0 95.2%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+36}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+247} \lor \neg \left(z \leq 1.15 \cdot 10^{+94} \lor \neg \left(z \leq 1.85 \cdot 10^{+121}\right) \land z \leq 1.05 \cdot 10^{+180}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+247)
         (not
          (or (<= z 1.15e+94) (and (not (<= z 1.85e+121)) (<= z 1.05e+180)))))
   (* z (- 1.0 (log t)))
   (+ (* b (- a 0.5)) (+ x (+ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+247) || !((z <= 1.15e+94) || (!(z <= 1.85e+121) && (z <= 1.05e+180)))) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.4d+247)) .or. (.not. (z <= 1.15d+94) .or. (.not. (z <= 1.85d+121)) .and. (z <= 1.05d+180))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (b * (a - 0.5d0)) + (x + (z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+247) || !((z <= 1.15e+94) || (!(z <= 1.85e+121) && (z <= 1.05e+180)))) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (b * (a - 0.5)) + (x + (z + y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e+247) or not ((z <= 1.15e+94) or (not (z <= 1.85e+121) and (z <= 1.05e+180))):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (b * (a - 0.5)) + (x + (z + y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+247) || !((z <= 1.15e+94) || (!(z <= 1.85e+121) && (z <= 1.05e+180))))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(b * Float64(a - 0.5)) + Float64(x + Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.4e+247) || ~(((z <= 1.15e+94) || (~((z <= 1.85e+121)) && (z <= 1.05e+180)))))
		tmp = z * (1.0 - log(t));
	else
		tmp = (b * (a - 0.5)) + (x + (z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+247], N[Not[Or[LessEqual[z, 1.15e+94], And[N[Not[LessEqual[z, 1.85e+121]], $MachinePrecision], LessEqual[z, 1.05e+180]]]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3999999999999999e247 or 1.15e94 < z < 1.85000000000000006e121 or 1.05e180 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in b around 0 84.5%

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

      1. associate-+r+ 84.5%

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

      2. +-commutative 84.5%

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

      3. fma-define 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in z around inf 82.1%

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

   if -1.3999999999999999e247 < z < 1.15e94 or 1.85000000000000006e121 < z < 1.05e180

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.7%

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

      2. pow3 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 88.5%

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

      1. +-commutative 88.5%

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

      2. +-commutative 88.5%

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

   7. Simplified 88.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+247} \lor \neg \left(z \leq 1.15 \cdot 10^{+94} \lor \neg \left(z \leq 1.85 \cdot 10^{+121}\right) \land z \leq 1.05 \cdot 10^{+180}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(z + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 8: 67.9% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+170} \lor \neg \left(t\_1 \leq 10^{+168}\right):\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -5e+170) (not (<= t_1 1e+168))) (+ x 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+170) || !(t_1 <= 1e+168)) {
		tmp = x + 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 <= (-5d+170)) .or. (.not. (t_1 <= 1d+168))) then
        tmp = x + 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 <= -5e+170) || !(t_1 <= 1e+168)) {
		tmp = x + 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 <= -5e+170) or not (t_1 <= 1e+168):
		tmp = x + 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 <= -5e+170) || !(t_1 <= 1e+168))
		tmp = Float64(x + 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 <= -5e+170) || ~((t_1 <= 1e+168)))
		tmp = x + 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, -5e+170], N[Not[LessEqual[t$95$1, 1e+168]], $MachinePrecision]], N[(x + t$95$1), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -4.99999999999999977e170 or 9.9999999999999993e167 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 82.9%

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

   if -4.99999999999999977e170 < (*.f64 (-.f64 a 1/2) b) < 9.9999999999999993e167

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 92.2%

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

      1. associate-+r+ 92.2%

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

      2. +-commutative 92.2%

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

      3. fma-define 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in z around 0 57.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+170} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 10^{+168}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 28.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-185}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 540000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.8e-297)
   x
   (if (<= y 1.26e-185)
     (* a b)
     (if (<= y 1.7e-86) x (if (<= y 540000000000.0) (* a b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.8e-297) {
		tmp = x;
	} else if (y <= 1.26e-185) {
		tmp = a * b;
	} else if (y <= 1.7e-86) {
		tmp = x;
	} else if (y <= 540000000000.0) {
		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 <= (-2.8d-297)) then
        tmp = x
    else if (y <= 1.26d-185) then
        tmp = a * b
    else if (y <= 1.7d-86) then
        tmp = x
    else if (y <= 540000000000.0d0) 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 <= -2.8e-297) {
		tmp = x;
	} else if (y <= 1.26e-185) {
		tmp = a * b;
	} else if (y <= 1.7e-86) {
		tmp = x;
	} else if (y <= 540000000000.0) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.8e-297:
		tmp = x
	elif y <= 1.26e-185:
		tmp = a * b
	elif y <= 1.7e-86:
		tmp = x
	elif y <= 540000000000.0:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.8e-297)
		tmp = x;
	elseif (y <= 1.26e-185)
		tmp = Float64(a * b);
	elseif (y <= 1.7e-86)
		tmp = x;
	elseif (y <= 540000000000.0)
		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 <= -2.8e-297)
		tmp = x;
	elseif (y <= 1.26e-185)
		tmp = a * b;
	elseif (y <= 1.7e-86)
		tmp = x;
	elseif (y <= 540000000000.0)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.8e-297], x, If[LessEqual[y, 1.26e-185], N[(a * b), $MachinePrecision], If[LessEqual[y, 1.7e-86], x, If[LessEqual[y, 540000000000.0], N[(a * b), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999984e-297 or 1.2599999999999999e-185 < y < 1.7e-86

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 26.2%

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

   if -2.79999999999999984e-297 < y < 1.2599999999999999e-185 or 1.7e-86 < y < 5.4e11

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 23.3%

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

      1. *-commutative 23.3%

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

   7. Simplified 23.3%

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

   if 5.4e11 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 53.5%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-185}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 540000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.5% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+105} \lor \neg \left(b \leq 4.5 \cdot 10^{+54}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.15e+105) (not (<= b 4.5e+54))) (* b (- a 0.5)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.15e+105) || !(b <= 4.5e+54)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.15d+105)) .or. (.not. (b <= 4.5d+54))) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.15e+105) || !(b <= 4.5e+54)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.15e+105) or not (b <= 4.5e+54):
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.15e+105) || !(b <= 4.5e+54))
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.15e+105) || ~((b <= 4.5e+54)))
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.15e+105], N[Not[LessEqual[b, 4.5e+54]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1499999999999999e105 or 4.49999999999999984e54 < b

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf 71.5%

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

   if -1.1499999999999999e105 < b < 4.49999999999999984e54

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 87.9%

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

      1. associate-+r+ 87.9%

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

      2. +-commutative 87.9%

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

      3. fma-define 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in z around 0 54.4%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+105} \lor \neg \left(b \leq 4.5 \cdot 10^{+54}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.5% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq 40:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) 40.0) (+ 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) <= 40.0) {
		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) <= 40.0d0) 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) <= 40.0) {
		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) <= 40.0:
		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) <= 40.0)
		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) <= 40.0)
		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], 40.0], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 40

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.3%

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

      2. pow3 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x around inf 51.9%

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

   if 40 < (+.f64 x y)

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.7%

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

      2. pow3 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 61.0%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 40:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.8% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+174} \lor \neg \left(b \leq 9.8 \cdot 10^{+54}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.8e+174) (not (<= b 9.8e+54))) (* a b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.8e+174) || !(b <= 9.8e+54)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.8d+174)) .or. (.not. (b <= 9.8d+54))) then
        tmp = a * b
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.8e+174) || !(b <= 9.8e+54)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.8e+174) or not (b <= 9.8e+54):
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.8e+174) || !(b <= 9.8e+54))
		tmp = Float64(a * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.8e+174) || ~((b <= 9.8e+54)))
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.8e+174], N[Not[LessEqual[b, 9.8e+54]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.7999999999999999e174 or 9.80000000000000002e54 < b

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 44.5%

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

      1. *-commutative 44.5%

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

   7. Simplified 44.5%

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

   if -5.7999999999999999e174 < b < 9.80000000000000002e54

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0 85.1%

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

      1. associate-+r+ 85.1%

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

      2. +-commutative 85.1%

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

      3. fma-define 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in z around 0 53.7%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+174} \lor \neg \left(b \leq 9.8 \cdot 10^{+54}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 79.6% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.5%

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

   2. pow3 99.5%

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

4. Applied egg-rr 99.5%

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

5. Taylor expanded in z around 0 74.9%

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

   1. +-commutative 74.9%

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

   2. +-commutative 74.9%

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

7. Simplified 74.9%

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

8. Final simplification 74.9%

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

Alternative 14: 78.9% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0 73.9%

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

4. Final simplification 73.9%

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

Alternative 15: 28.2% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 2.9e-10) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.9e-10) {
		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 (y <= 2.9d-10) 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 (y <= 2.9e-10) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.9e-10:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.9e-10)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 2.9e-10)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.9e-10], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.89999999999999981e-10

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. *-lft-identity 99.8%

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

      6. metadata-eval 99.8%

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

      7. *-commutative 99.8%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 26.6%

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

   if 2.89999999999999981e-10 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 49.2%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 22.7% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in x around inf 22.0%

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

6. Final simplification 22.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024052 
(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)))