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

Percentage Accurate: 99.8% → 99.9%

Time: 9.9s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(b, a + -0.5, x + y\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+150}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+59)
     (fma b (+ a -0.5) (+ x y))
     (if (<= t_1 1e+150) (+ (* z (- 1.0 (log t))) (+ x 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+59) {
		tmp = fma(b, (a + -0.5), (x + y));
	} else if (t_1 <= 1e+150) {
		tmp = (z * (1.0 - log(t))) + (x + 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+59)
		tmp = fma(b, Float64(a + -0.5), Float64(x + y));
	elseif (t_1 <= 1e+150)
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	else
		tmp = Float64(Float64(x + y) + t_1);
	end
	return 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+59], N[(b * N[(a + -0.5), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+150], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.99999999999999994e59

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.9%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 92.3%

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

      1. associate-+r+ 92.3%

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

      2. +-commutative 92.3%

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

      3. fma-define 92.4%

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

      4. sub-neg 92.4%

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

      5. metadata-eval 92.4%

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

   9. Simplified 92.4%

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

   if -1.99999999999999994e59 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 9.99999999999999981e149

   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 b around -inf 73.3%

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

      1. associate-*r* 73.3%

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

      2. mul-1-neg 73.3%

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

      3. mul-1-neg 73.3%

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

      4. unsub-neg 73.3%

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

      5. sub-neg 73.3%

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

      6. metadata-eval 73.3%

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

      7. mul-1-neg 73.3%

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

      8. +-commutative 73.3%

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

      9. distribute-neg-in 73.3%

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

      10. metadata-eval 73.3%

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

      11. unsub-neg 73.3%

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

      12. +-commutative 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in b around 0 94.8%

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

   if 9.99999999999999981e149 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.5%

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

      1. +-commutative 89.5%

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

   5. Simplified 89.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(b, a + -0.5, x + y\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 10^{+150}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -2 \cdot 10^{-118}:\\ \;\;\;\;t\_1 + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(y + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= (+ x y) -2e-118)
     (+ t_1 (- (+ z x) (* z (log t))))
     (+ (* z (- 1.0 (log t))) (+ 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) <= -2e-118) {
		tmp = t_1 + ((z + x) - (z * log(t)));
	} else {
		tmp = (z * (1.0 - log(t))) + (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) <= (-2d-118)) then
        tmp = t_1 + ((z + x) - (z * log(t)))
    else
        tmp = (z * (1.0d0 - log(t))) + (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) <= -2e-118) {
		tmp = t_1 + ((z + x) - (z * Math.log(t)));
	} else {
		tmp = (z * (1.0 - Math.log(t))) + (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) <= -2e-118:
		tmp = t_1 + ((z + x) - (z * math.log(t)))
	else:
		tmp = (z * (1.0 - math.log(t))) + (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) <= -2e-118)
		tmp = Float64(t_1 + Float64(Float64(z + x) - Float64(z * log(t))));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + 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) <= -2e-118)
		tmp = t_1 + ((z + x) - (z * log(t)));
	else
		tmp = (z * (1.0 - log(t))) + (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], -2e-118], N[(t$95$1 + N[(N[(z + x), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.99999999999999997e-118

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.3%

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

      1. +-commutative 78.3%

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

   5. Simplified 78.3%

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

   if -1.99999999999999997e-118 < (+.f64 x y)

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 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 0 79.4%

      \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(y + b \cdot \left(a - 0.5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-118}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + x\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+197} \lor \neg \left(z \leq 3.6 \cdot 10^{+189}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a + -0.5, x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e+197) (not (<= z 3.6e+189)))
   (+ (* z (- 1.0 (log t))) (* a b))
   (fma b (+ a -0.5) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e+197) || !(z <= 3.6e+189)) {
		tmp = (z * (1.0 - log(t))) + (a * b);
	} else {
		tmp = fma(b, (a + -0.5), (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e+197) || !(z <= 3.6e+189))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(a * b));
	else
		tmp = fma(b, Float64(a + -0.5), Float64(x + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e+197], N[Not[LessEqual[z, 3.6e+189]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(b * N[(a + -0.5), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e197 or 3.60000000000000008e189 < 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+ 99.6%

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

      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-- 99.6%

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

      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 -inf 91.1%

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

      1. associate-*r* 91.1%

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

      2. mul-1-neg 91.1%

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

      3. mul-1-neg 91.1%

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

      4. unsub-neg 91.1%

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

      5. sub-neg 91.1%

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

      6. metadata-eval 91.1%

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

      7. mul-1-neg 91.1%

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

      8. +-commutative 91.1%

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

      9. distribute-neg-in 91.1%

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

      10. metadata-eval 91.1%

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

      11. unsub-neg 91.1%

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

      12. +-commutative 91.1%

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

   7. Simplified 91.1%

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

   8. Taylor expanded in a around inf 83.1%

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

      1. *-commutative 83.1%

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

   10. Simplified 83.1%

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

   if -1.15e197 < z < 3.60000000000000008e189

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.8%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 87.9%

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

      1. associate-+r+ 87.9%

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

      2. +-commutative 87.9%

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

      3. fma-define 87.9%

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

      4. sub-neg 87.9%

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

      5. metadata-eval 87.9%

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

   9. Simplified 87.9%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+197} \lor \neg \left(z \leq 3.6 \cdot 10^{+189}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a + -0.5, x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(b, a + -0.5, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.5e+121)
   (fma b (+ a -0.5) (+ x y))
   (+ (* z (- 1.0 (log t))) (+ y (* b (- a 0.5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.5e+121) {
		tmp = fma(b, (a + -0.5), (x + y));
	} else {
		tmp = (z * (1.0 - log(t))) + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.5e+121)
		tmp = fma(b, Float64(a + -0.5), Float64(x + y));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(y + Float64(b * Float64(a - 0.5))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.5e+121], N[(b * N[(a + -0.5), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.50000000000000019e121

   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. Step-by-step derivation

      1. add-cube-cbrt 100.0%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.9%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.9%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 94.8%

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

      1. associate-+r+ 94.8%

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

      2. +-commutative 94.8%

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

      3. fma-define 94.8%

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

      4. sub-neg 94.8%

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

      5. metadata-eval 94.8%

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

   9. Simplified 94.8%

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

   if -6.50000000000000019e121 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 83.7%

      \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{\left(y + b \cdot \left(a - 0.5\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+200} \lor \neg \left(z \leq 1.25 \cdot 10^{+200}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a + -0.5, x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e+200) (not (<= z 1.25e+200)))
   (* z (- 1.0 (log t)))
   (fma b (+ a -0.5) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e+200) || !(z <= 1.25e+200)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = fma(b, (a + -0.5), (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e+200) || !(z <= 1.25e+200))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = fma(b, Float64(a + -0.5), Float64(x + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e+200], N[Not[LessEqual[z, 1.25e+200]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(a + -0.5), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999969e200 or 1.25000000000000005e200 < 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+ 99.6%

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

      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-- 99.6%

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

      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. Step-by-step derivation

      1. add-cube-cbrt 98.7%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 98.7%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 98.7%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in b around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. associate-+r+ 77.8%

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

      3. associate-/l* 77.9%

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

   9. Simplified 77.9%

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

   10. Taylor expanded in z around -inf 65.5%

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

   if -4.49999999999999969e200 < z < 1.25000000000000005e200

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.8%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in z around 0 87.9%

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

      1. associate-+r+ 87.9%

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

      2. +-commutative 87.9%

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

      3. fma-define 87.9%

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

      4. sub-neg 87.9%

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

      5. metadata-eval 87.9%

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

   9. Simplified 87.9%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+200} \lor \neg \left(z \leq 1.25 \cdot 10^{+200}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a + -0.5, x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+200} \lor \neg \left(z \leq 1.12 \cdot 10^{+194}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e+200) (not (<= z 1.12e+194)))
   (* z (- 1.0 (log t)))
   (+ (+ x y) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+200) || !(z <= 1.12e+194)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.2d+200)) .or. (.not. (z <= 1.12d+194))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (x + y) + (b * (a - 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+200) || !(z <= 1.12e+194)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (x + y) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.2e+200) or not (z <= 1.12e+194):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (x + y) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e+200) || !(z <= 1.12e+194))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e+200) || ~((z <= 1.12e+194)))
		tmp = z * (1.0 - log(t));
	else
		tmp = (x + y) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e+200], N[Not[LessEqual[z, 1.12e+194]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999994e200 or 1.11999999999999994e194 < 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+ 99.6%

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

      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-- 99.6%

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

      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. Step-by-step derivation

      1. add-cube-cbrt 98.7%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 98.7%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 98.7%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in b around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. associate-+r+ 77.8%

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

      3. associate-/l* 77.9%

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

   9. Simplified 77.9%

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

   10. Taylor expanded in z around -inf 65.5%

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

   if -4.19999999999999994e200 < z < 1.11999999999999994e194

   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 87.9%

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

      1. +-commutative 87.9%

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

   5. Simplified 87.9%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+200} \lor \neg \left(z \leq 1.12 \cdot 10^{+194}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 9: 35.3% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e-213) x (if (<= y 3.5e+140) (* b (- a 0.5)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e-213) {
		tmp = x;
	} else if (y <= 3.5e+140) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8d-213)) then
        tmp = x
    else if (y <= 3.5d+140) then
        tmp = b * (a - 0.5d0)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e-213) {
		tmp = x;
	} else if (y <= 3.5e+140) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e-213:
		tmp = x
	elif y <= 3.5e+140:
		tmp = b * (a - 0.5)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e-213)
		tmp = x;
	elseif (y <= 3.5e+140)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e-213)
		tmp = x;
	elseif (y <= 3.5e+140)
		tmp = b * (a - 0.5);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e-213], x, If[LessEqual[y, 3.5e+140], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9999999999999996e-213

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-cube-cbrt 99.5%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.5%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.5%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in b around inf 79.2%

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

      1. associate--l+ 79.2%

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

      2. associate-+r+ 79.2%

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

      3. associate-/l* 79.2%

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

   9. Simplified 79.2%

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

   10. Taylor expanded in x around inf 24.8%

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

   if -7.9999999999999996e-213 < y < 3.49999999999999989e140

   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 b around inf 47.4%

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

   if 3.49999999999999989e140 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 99.7%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.7%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in y around inf 59.5%

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

Alternative 10: 28.7% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.7e-216) x (if (<= y 3.5e+140) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.7e-216) {
		tmp = x;
	} else if (y <= 3.5e+140) {
		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 <= (-4.7d-216)) then
        tmp = x
    else if (y <= 3.5d+140) 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 <= -4.7e-216) {
		tmp = x;
	} else if (y <= 3.5e+140) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.7e-216:
		tmp = x
	elif y <= 3.5e+140:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.7e-216)
		tmp = x;
	elseif (y <= 3.5e+140)
		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 <= -4.7e-216)
		tmp = x;
	elseif (y <= 3.5e+140)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.7e-216], x, If[LessEqual[y, 3.5e+140], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7e-216

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-cube-cbrt 99.5%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.5%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.5%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in b around inf 79.2%

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

      1. associate--l+ 79.2%

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

      2. associate-+r+ 79.2%

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

      3. associate-/l* 79.2%

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

   9. Simplified 79.2%

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

   10. Taylor expanded in x around inf 24.8%

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

   if -4.7e-216 < y < 3.49999999999999989e140

   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 a around inf 36.3%

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

      1. *-commutative 36.3%

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

   5. Simplified 36.3%

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

   if 3.49999999999999989e140 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 99.7%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.7%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in y around inf 59.5%

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

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;y \leq 3.3:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= y 3.3) (+ 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 (y <= 3.3) {
		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 (y <= 3.3d0) 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 (y <= 3.3) {
		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 y <= 3.3:
		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 (y <= 3.3)
		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 (y <= 3.3)
		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[y, 3.3], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 3.2999999999999998

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 62.8%

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

   if 3.2999999999999998 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 69.6%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.3:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.9% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+140}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 3.8e+140) (+ x (* b (- a 0.5))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.8e+140) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 3.8d+140) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.8e+140) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 3.8e+140:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 3.8e+140)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 3.8e+140)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 3.8e+140], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if y < 3.8000000000000001e140

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 61.9%

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

   if 3.8000000000000001e140 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. *-lft-identity 100.0%

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

      6. metadata-eval 100.0%

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

      7. *-commutative 100.0%

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

      8. distribute-rgt-out-- 100.0%

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

      9. metadata-eval 100.0%

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

      10. fma-define 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. add-cube-cbrt 99.7%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.7%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in y around inf 59.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+140}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.8% 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 78.8%

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

   1. +-commutative 78.8%

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

5. Simplified 78.8%

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

6. Final simplification 78.8%

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

Alternative 14: 27.6% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 280000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 280000000.0) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 280000000.0) {
		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 <= 280000000.0d0) 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 <= 280000000.0) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 280000000.0:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 280000000.0)
		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 <= 280000000.0)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 280000000.0], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.8e8

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-cube-cbrt 99.6%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.6%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.6%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in b around inf 83.3%

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

      1. associate--l+ 83.3%

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

      2. associate-+r+ 83.3%

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

      3. associate-/l* 83.3%

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

   9. Simplified 83.3%

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

   10. Taylor expanded in x around inf 23.5%

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

   if 2.8e8 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      8. distribute-rgt-out-- 99.9%

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

      9. metadata-eval 99.9%

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

      10. fma-define 99.9%

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

      11. sub-neg 99.9%

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

      12. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. add-cube-cbrt 99.7%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

      2. pow3 99.7%

         \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   7. Taylor expanded in y around inf 43.0%

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

Alternative 15: 21.8% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

   1. add-cube-cbrt 99.6%

      \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \log t} \cdot \sqrt[3]{1 - \log t}\right) \cdot \sqrt[3]{1 - \log t}\right)} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

   2. pow3 99.6%

      \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

6. Applied egg-rr 99.6%

   \[\leadsto z \cdot \color{blue}{{\left(\sqrt[3]{1 - \log t}\right)}^{3}} + \mathsf{fma}\left(a + -0.5, b, x + y\right) \]

7. Taylor expanded in b around inf 80.0%

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

   1. associate--l+ 80.0%

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

   2. associate-+r+ 80.0%

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

   3. associate-/l* 80.0%

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

9. Simplified 80.0%

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

10. Taylor expanded in x around inf 22.2%

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

Developer target: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (+ (+ (+ 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)))