Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 75.2% → 91.1%

Time: 11.9s

Alternatives: 14

Speedup: 0.8×

Specification

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

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

Initial Program: 75.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

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

Alternative 1: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-320}:\\ \;\;\;\;\frac{t_1}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t)))
        (t_2 (/ t_1 (+ (+ a 1.0) (/ (* y b) t))))
        (t_3 (/ y (/ (+ t (+ (* y b) (* t a))) z))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-320)
       (/ t_1 (+ (+ a 1.0) (* (* y b) (/ 1.0 t))))
       (if (<= t_2 0.0)
         t_3
         (if (<= t_2 5e+290) t_2 (if (<= t_2 INFINITY) t_3 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = y / ((t + ((y * b) + (t * a))) / z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-320) {
		tmp = t_1 / ((a + 1.0) + ((y * b) * (1.0 / t)));
	} else if (t_2 <= 0.0) {
		tmp = t_3;
	} else if (t_2 <= 5e+290) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	double t_3 = y / ((t + ((y * b) + (t * a))) / z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-320) {
		tmp = t_1 / ((a + 1.0) + ((y * b) * (1.0 / t)));
	} else if (t_2 <= 0.0) {
		tmp = t_3;
	} else if (t_2 <= 5e+290) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t))
	t_3 = y / ((t + ((y * b) + (t * a))) / z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-320:
		tmp = t_1 / ((a + 1.0) + ((y * b) * (1.0 / t)))
	elif t_2 <= 0.0:
		tmp = t_3
	elif t_2 <= 5e+290:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_3 = Float64(y / Float64(Float64(t + Float64(Float64(y * b) + Float64(t * a))) / z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-320)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) * Float64(1.0 / t))));
	elseif (t_2 <= 0.0)
		tmp = t_3;
	elseif (t_2 <= 5e+290)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((y * z) / t);
	t_2 = t_1 / ((a + 1.0) + ((y * b) / t));
	t_3 = y / ((t + ((y * b) + (t * a))) / z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-320)
		tmp = t_1 / ((a + 1.0) + ((y * b) * (1.0 / t)));
	elseif (t_2 <= 0.0)
		tmp = t_3;
	elseif (t_2 <= 5e+290)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(N[(t + N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-320], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], t$95$3, If[LessEqual[t$95$2, 5e+290], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or -1.99998e-320 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0 or 4.9999999999999998e290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 48.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 48.8%

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

      2. associate-/l* 47.7%

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

      3. associate-*l/ 44.7%

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

   3. Simplified 44.7%

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

   4. Taylor expanded in x around 0 59.5%

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

      1. associate-/l* 75.6%

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

      2. distribute-lft-in 75.6%

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

      3. *-rgt-identity 75.6%

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

      4. associate-*r/ 74.1%

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

      5. fma-def 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in t around 0 83.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.99998e-320

   1. Initial program 99.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

      1. associate-/l* 99.7%

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

      2. div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999998e290

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. associate-/l* 0.0%

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

      3. associate-*l/ 0.2%

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

   3. Simplified 0.2%

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

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-320}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \left(y \cdot b\right) \cdot \frac{1}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 91.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_2 := \frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-320}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))
        (t_2 (/ y (/ (+ t (+ (* y b) (* t a))) z))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e-320)
       t_1
       (if (<= t_1 0.0)
         t_2
         (if (<= t_1 5e+290) t_1 (if (<= t_1 INFINITY) t_2 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = y / ((t + ((y * b) + (t * a))) / z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e-320) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 5e+290) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double t_2 = y / ((t + ((y * b) + (t * a))) / z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -2e-320) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2;
	} else if (t_1 <= 5e+290) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	t_2 = y / ((t + ((y * b) + (t * a))) / z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -2e-320:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t_2
	elif t_1 <= 5e+290:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	t_2 = Float64(y / Float64(Float64(t + Float64(Float64(y * b) + Float64(t * a))) / z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e-320)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 5e+290)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	t_2 = y / ((t + ((y * b) + (t * a))) / z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -2e-320)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_2;
	elseif (t_1 <= 5e+290)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(N[(t + N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e-320], t$95$1, If[LessEqual[t$95$1, 0.0], t$95$2, If[LessEqual[t$95$1, 5e+290], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or -1.99998e-320 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0 or 4.9999999999999998e290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 48.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 48.8%

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

      2. associate-/l* 47.7%

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

      3. associate-*l/ 44.7%

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

   3. Simplified 44.7%

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

   4. Taylor expanded in x around 0 59.5%

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

      1. associate-/l* 75.6%

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

      2. distribute-lft-in 75.6%

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

      3. *-rgt-identity 75.6%

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

      4. associate-*r/ 74.1%

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

      5. fma-def 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in t around 0 83.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.99998e-320 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999998e290

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. associate-/l* 0.0%

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

      3. associate-*l/ 0.2%

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

   3. Simplified 0.2%

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

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-320}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1}\\ t_3 := \frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-320}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{t_1}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t)))
        (t_2 (/ (+ x (/ (* y z) t)) t_1))
        (t_3 (/ y (/ (+ t (+ (* y b) (* t a))) z))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-320)
       (/ (+ x (* (* y z) (/ 1.0 t))) t_1)
       (if (<= t_2 0.0)
         t_3
         (if (<= t_2 5e+290) t_2 (if (<= t_2 INFINITY) t_3 (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = y / ((t + ((y * b) + (t * a))) / z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-320) {
		tmp = (x + ((y * z) * (1.0 / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_3;
	} else if (t_2 <= 5e+290) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double t_3 = y / ((t + ((y * b) + (t * a))) / z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-320) {
		tmp = (x + ((y * z) * (1.0 / t))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = t_3;
	} else if (t_2 <= 5e+290) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + ((y * b) / t)
	t_2 = (x + ((y * z) / t)) / t_1
	t_3 = y / ((t + ((y * b) + (t * a))) / z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-320:
		tmp = (x + ((y * z) * (1.0 / t))) / t_1
	elif t_2 <= 0.0:
		tmp = t_3
	elif t_2 <= 5e+290:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	t_3 = Float64(y / Float64(Float64(t + Float64(Float64(y * b) + Float64(t * a))) / z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-320)
		tmp = Float64(Float64(x + Float64(Float64(y * z) * Float64(1.0 / t))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = t_3;
	elseif (t_2 <= 5e+290)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + ((y * b) / t);
	t_2 = (x + ((y * z) / t)) / t_1;
	t_3 = y / ((t + ((y * b) + (t * a))) / z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-320)
		tmp = (x + ((y * z) * (1.0 / t))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = t_3;
	elseif (t_2 <= 5e+290)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(N[(t + N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-320], N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], t$95$3, If[LessEqual[t$95$2, 5e+290], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(z / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or -1.99998e-320 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0 or 4.9999999999999998e290 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 48.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 48.8%

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

      2. associate-/l* 47.7%

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

      3. associate-*l/ 44.7%

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

   3. Simplified 44.7%

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

   4. Taylor expanded in x around 0 59.5%

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

      1. associate-/l* 75.6%

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

      2. distribute-lft-in 75.6%

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

      3. *-rgt-identity 75.6%

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

      4. associate-*r/ 74.1%

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

      5. fma-def 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in t around 0 83.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.99998e-320

   1. Initial program 99.7%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. div-inv 99.8%

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

      2. *-commutative 99.8%

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

   3. Applied egg-rr 99.8%

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

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999998e290

   1. Initial program 99.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. associate-/l* 0.0%

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

      3. associate-*l/ 0.2%

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

   3. Simplified 0.2%

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

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -2 \cdot 10^{-320}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -7 \cdot 10^{-61}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+119}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (/ y t))))
   (if (<= t -7e-61)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= t 2.05e+17)
       (/ y (/ (+ t (+ (* y b) (* t a))) z))
       (if (<= t 1.75e+87)
         (/ x (+ 1.0 (+ a (/ (* y b) t))))
         (if (<= t 3.4e+119)
           (* (/ y t) (/ z (+ 1.0 (+ a t_1))))
           (/ x (+ (+ a 1.0) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y / t);
	double tmp;
	if (t <= -7e-61) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 2.05e+17) {
		tmp = y / ((t + ((y * b) + (t * a))) / z);
	} else if (t <= 1.75e+87) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 3.4e+119) {
		tmp = (y / t) * (z / (1.0 + (a + t_1)));
	} else {
		tmp = x / ((a + 1.0) + 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 * (y / t)
    if (t <= (-7d-61)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (t <= 2.05d+17) then
        tmp = y / ((t + ((y * b) + (t * a))) / z)
    else if (t <= 1.75d+87) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (t <= 3.4d+119) then
        tmp = (y / t) * (z / (1.0d0 + (a + t_1)))
    else
        tmp = x / ((a + 1.0d0) + 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 * (y / t);
	double tmp;
	if (t <= -7e-61) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 2.05e+17) {
		tmp = y / ((t + ((y * b) + (t * a))) / z);
	} else if (t <= 1.75e+87) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (t <= 3.4e+119) {
		tmp = (y / t) * (z / (1.0 + (a + t_1)));
	} else {
		tmp = x / ((a + 1.0) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y / t)
	tmp = 0
	if t <= -7e-61:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif t <= 2.05e+17:
		tmp = y / ((t + ((y * b) + (t * a))) / z)
	elif t <= 1.75e+87:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif t <= 3.4e+119:
		tmp = (y / t) * (z / (1.0 + (a + t_1)))
	else:
		tmp = x / ((a + 1.0) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y / t))
	tmp = 0.0
	if (t <= -7e-61)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (t <= 2.05e+17)
		tmp = Float64(y / Float64(Float64(t + Float64(Float64(y * b) + Float64(t * a))) / z));
	elseif (t <= 1.75e+87)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (t <= 3.4e+119)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + t_1))));
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y / t);
	tmp = 0.0;
	if (t <= -7e-61)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (t <= 2.05e+17)
		tmp = y / ((t + ((y * b) + (t * a))) / z);
	elseif (t <= 1.75e+87)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (t <= 3.4e+119)
		tmp = (y / t) * (z / (1.0 + (a + t_1)));
	else
		tmp = x / ((a + 1.0) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-61], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+17], N[(y / N[(N[(t + N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+87], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+119], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.0000000000000006e-61

   1. Initial program 89.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 89.5%

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

      2. associate-/l* 86.9%

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

      3. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in b around 0 85.2%

      \[\leadsto \color{blue}{\frac{\frac{y \cdot z}{t} + x}{1 + a}} \]

   if -7.0000000000000006e-61 < t < 2.05e17

   1. Initial program 61.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 61.6%

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

      2. associate-/l* 53.9%

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

      3. associate-*l/ 50.2%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in x around 0 45.4%

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

      1. associate-/l* 47.9%

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

      2. distribute-lft-in 47.9%

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

      3. *-rgt-identity 47.9%

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

      4. associate-*r/ 44.6%

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

      5. fma-def 44.6%

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

   6. Simplified 44.6%

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

   7. Taylor expanded in t around 0 65.5%

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

   if 2.05e17 < t < 1.74999999999999993e87

   1. Initial program 90.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 90.4%

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

      2. associate-/l* 90.4%

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

      3. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around inf 85.5%

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

   if 1.74999999999999993e87 < t < 3.40000000000000013e119

   1. Initial program 81.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. add-cube-cbrt 79.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x + \frac{y \cdot z}{t}} \cdot \sqrt[3]{x + \frac{y \cdot z}{t}}\right) \cdot \sqrt[3]{x + \frac{y \cdot z}{t}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      2. pow2 79.0%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x + \frac{y \cdot z}{t}}\right)}^{2}} \cdot \sqrt[3]{x + \frac{y \cdot z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      3. associate-/l* 60.2%

         \[\leadsto \frac{{\left(\sqrt[3]{x + \color{blue}{\frac{y}{\frac{t}{z}}}}\right)}^{2} \cdot \sqrt[3]{x + \frac{y \cdot z}{t}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

      4. associate-/l* 78.1%

         \[\leadsto \frac{{\left(\sqrt[3]{x + \frac{y}{\frac{t}{z}}}\right)}^{2} \cdot \sqrt[3]{x + \color{blue}{\frac{y}{\frac{t}{z}}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   3. Applied egg-rr 78.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x + \frac{y}{\frac{t}{z}}}\right)}^{2} \cdot \sqrt[3]{x + \frac{y}{\frac{t}{z}}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   4. Taylor expanded in x around 0 81.1%

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

      1. times-frac 93.4%

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

      2. associate-/l* 93.1%

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

      3. +-commutative 93.1%

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

      4. associate-/r/ 93.1%

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

   6. Simplified 93.1%

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

   if 3.40000000000000013e119 < t

   1. Initial program 91.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 91.3%

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

      2. associate-/l* 92.9%

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

      3. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 83.2%

      \[\leadsto \frac{\color{blue}{x}}{\left(a + 1\right) + \frac{y}{t} \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-61}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+119}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 5: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-165} \lor \neg \left(t \leq 4.6 \cdot 10^{-128}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.8e-165) (not (<= t 4.6e-128)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* b (/ y t))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.8e-165) || !(t <= 4.6e-128)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.8d-165)) .or. (.not. (t <= 4.6d-128))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.8e-165) || !(t <= 4.6e-128)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.8e-165) or not (t <= 4.6e-128):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.8e-165) || !(t <= 4.6e-128))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.8e-165) || ~((t <= 4.6e-128)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.8e-165], N[Not[LessEqual[t, 4.6e-128]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8000000000000004e-165 or 4.6000000000000002e-128 < t

   1. Initial program 86.0%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 86.0%

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

      2. associate-/l* 84.3%

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

      3. associate-*l/ 85.5%

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

   3. Simplified 85.5%

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

      1. associate-/r/ 85.2%

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

   5. Applied egg-rr 85.2%

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

   if -4.8000000000000004e-165 < t < 4.6000000000000002e-128

   1. Initial program 51.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 51.8%

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

      2. associate-/l* 42.1%

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

      3. associate-*l/ 35.9%

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

   3. Simplified 35.9%

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

   4. Taylor expanded in t around 0 70.6%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-165} \lor \neg \left(t \leq 4.6 \cdot 10^{-128}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 6: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + b \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-167}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{t_1}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-128}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* b (/ y t)))))
   (if (<= t -4.6e-167)
     (/ (+ x (* y (/ z t))) t_1)
     (if (<= t 2.6e-128) (/ z b) (/ (+ x (/ z (/ t y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (b * (y / t));
	double tmp;
	if (t <= -4.6e-167) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 2.6e-128) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (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 = (a + 1.0d0) + (b * (y / t))
    if (t <= (-4.6d-167)) then
        tmp = (x + (y * (z / t))) / t_1
    else if (t <= 2.6d-128) then
        tmp = z / b
    else
        tmp = (x + (z / (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 = (a + 1.0) + (b * (y / t));
	double tmp;
	if (t <= -4.6e-167) {
		tmp = (x + (y * (z / t))) / t_1;
	} else if (t <= 2.6e-128) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (b * (y / t))
	tmp = 0
	if t <= -4.6e-167:
		tmp = (x + (y * (z / t))) / t_1
	elif t <= 2.6e-128:
		tmp = z / b
	else:
		tmp = (x + (z / (t / y))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(b * Float64(y / t)))
	tmp = 0.0
	if (t <= -4.6e-167)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / t_1);
	elseif (t <= 2.6e-128)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (b * (y / t));
	tmp = 0.0;
	if (t <= -4.6e-167)
		tmp = (x + (y * (z / t))) / t_1;
	elseif (t <= 2.6e-128)
		tmp = z / b;
	else
		tmp = (x + (z / (t / y))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e-167], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 2.6e-128], N[(z / b), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.6000000000000003e-167

   1. Initial program 87.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 87.9%

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

      2. associate-/l* 83.3%

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

      3. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

      1. associate-/r/ 86.2%

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

   5. Applied egg-rr 86.2%

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

   if -4.6000000000000003e-167 < t < 2.59999999999999981e-128

   1. Initial program 51.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 51.8%

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

      2. associate-/l* 42.1%

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

      3. associate-*l/ 35.9%

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

   3. Simplified 35.9%

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

   4. Taylor expanded in t around 0 70.6%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 2.59999999999999981e-128 < t

   1. Initial program 83.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 83.9%

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

      2. associate-/l* 85.4%

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

      3. associate-*l/ 86.4%

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

   3. Simplified 86.4%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-167}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-128}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 7: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-152}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-128}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.8e-152)
   (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ y (/ t b))))
   (if (<= t 1.85e-128)
     (/ z b)
     (/ (+ x (/ z (/ t y))) (+ (+ a 1.0) (* b (/ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.8e-152) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 1.85e-128) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.8d-152)) then
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= 1.85d-128) then
        tmp = z / b
    else
        tmp = (x + (z / (t / y))) / ((a + 1.0d0) + (b * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.8e-152) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 1.85e-128) {
		tmp = z / b;
	} else {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.8e-152:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)))
	elif t <= 1.85e-128:
		tmp = z / b
	else:
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.8e-152)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= 1.85e-128)
		tmp = Float64(z / b);
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.8e-152)
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (y / (t / b)));
	elseif (t <= 1.85e-128)
		tmp = z / b;
	else
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.8e-152], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-128], N[(z / b), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999984e-152

   1. Initial program 88.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   if -2.79999999999999984e-152 < t < 1.85e-128

   1. Initial program 52.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 52.4%

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

      2. associate-/l* 43.1%

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

      3. associate-*l/ 37.1%

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

   3. Simplified 37.1%

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

   4. Taylor expanded in t around 0 69.1%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 1.85e-128 < t

   1. Initial program 83.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 83.9%

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

      2. associate-/l* 85.4%

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

      3. associate-*l/ 86.4%

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

   3. Simplified 86.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-152}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-128}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 8: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+114}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 10^{-17}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+137}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a} + \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.18e+114)
   (/ z b)
   (if (<= y 1e-17)
     (/ x (+ 1.0 (+ a (/ (* y b) t))))
     (if (<= y 4e+79)
       (/ (* y z) (+ t (* y b)))
       (if (<= y 3.1e+137) (+ (* (/ z t) (/ y a)) (/ x a)) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.18e+114) {
		tmp = z / b;
	} else if (y <= 1e-17) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 4e+79) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= 3.1e+137) {
		tmp = ((z / t) * (y / a)) + (x / a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.18d+114)) then
        tmp = z / b
    else if (y <= 1d-17) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if (y <= 4d+79) then
        tmp = (y * z) / (t + (y * b))
    else if (y <= 3.1d+137) then
        tmp = ((z / t) * (y / a)) + (x / a)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.18e+114) {
		tmp = z / b;
	} else if (y <= 1e-17) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if (y <= 4e+79) {
		tmp = (y * z) / (t + (y * b));
	} else if (y <= 3.1e+137) {
		tmp = ((z / t) * (y / a)) + (x / a);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.18e+114:
		tmp = z / b
	elif y <= 1e-17:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif y <= 4e+79:
		tmp = (y * z) / (t + (y * b))
	elif y <= 3.1e+137:
		tmp = ((z / t) * (y / a)) + (x / a)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.18e+114)
		tmp = Float64(z / b);
	elseif (y <= 1e-17)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif (y <= 4e+79)
		tmp = Float64(Float64(y * z) / Float64(t + Float64(y * b)));
	elseif (y <= 3.1e+137)
		tmp = Float64(Float64(Float64(z / t) * Float64(y / a)) + Float64(x / a));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.18e+114)
		tmp = z / b;
	elseif (y <= 1e-17)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif (y <= 4e+79)
		tmp = (y * z) / (t + (y * b));
	elseif (y <= 3.1e+137)
		tmp = ((z / t) * (y / a)) + (x / a);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.18e+114], N[(z / b), $MachinePrecision], If[LessEqual[y, 1e-17], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+79], N[(N[(y * z), $MachinePrecision] / N[(t + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+137], N[(N[(N[(z / t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision] + N[(x / a), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.18000000000000005e114 or 3.0999999999999999e137 < y

   1. Initial program 50.8%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 50.8%

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

      2. associate-/l* 44.8%

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

      3. associate-*l/ 42.1%

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

   3. Simplified 42.1%

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

   4. Taylor expanded in t around 0 66.9%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if -1.18000000000000005e114 < y < 1.00000000000000007e-17

   1. Initial program 93.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 93.2%

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

      2. associate-/l* 90.2%

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

      3. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around inf 78.0%

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

   if 1.00000000000000007e-17 < y < 3.99999999999999987e79

   1. Initial program 63.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 63.2%

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

      2. associate-/l* 58.3%

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

      3. associate-*l/ 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in x around 0 43.3%

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

      1. associate-/l* 47.5%

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

      2. distribute-lft-in 47.5%

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

      3. *-rgt-identity 47.5%

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

      4. associate-*r/ 47.5%

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

      5. fma-def 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in a around 0 58.9%

      \[\leadsto \color{blue}{\frac{y \cdot z}{y \cdot b + t}} \]

   if 3.99999999999999987e79 < y < 3.0999999999999999e137

   1. Initial program 67.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 67.9%

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

      2. associate-/l* 67.9%

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

      3. associate-*l/ 67.6%

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

   3. Simplified 67.6%

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

      1. associate-/r/ 67.6%

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

   5. Applied egg-rr 67.6%

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

   6. Taylor expanded in a around inf 48.4%

      \[\leadsto \frac{x + \frac{z}{t} \cdot y}{\color{blue}{a}} \]

   7. Taylor expanded in x around 0 54.5%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a \cdot t} + \frac{x}{a}} \]
   8. Step-by-step derivation

      1. times-frac 65.6%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{z}{t}} + \frac{x}{a} \]

   9. Simplified 65.6%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{z}{t} + \frac{x}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+114}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 10^{-17}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+79}:\\ \;\;\;\;\frac{y \cdot z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+137}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a} + \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 9: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.6e-67)
   (/ (+ x (/ (* y z) t)) (+ a 1.0))
   (if (<= t 2.5e+15)
     (/ y (/ (+ t (+ (* y b) (* t a))) z))
     (/ x (+ (+ a 1.0) (* b (/ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.6e-67) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 2.5e+15) {
		tmp = y / ((t + ((y * b) + (t * a))) / z);
	} else {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-8.6d-67)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (t <= 2.5d+15) then
        tmp = y / ((t + ((y * b) + (t * a))) / z)
    else
        tmp = x / ((a + 1.0d0) + (b * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.6e-67) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 2.5e+15) {
		tmp = y / ((t + ((y * b) + (t * a))) / z);
	} else {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -8.6e-67:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif t <= 2.5e+15:
		tmp = y / ((t + ((y * b) + (t * a))) / z)
	else:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.6e-67)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (t <= 2.5e+15)
		tmp = Float64(y / Float64(Float64(t + Float64(Float64(y * b) + Float64(t * a))) / z));
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -8.6e-67)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (t <= 2.5e+15)
		tmp = y / ((t + ((y * b) + (t * a))) / z);
	else
		tmp = x / ((a + 1.0) + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.6e-67], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+15], N[(y / N[(N[(t + N[(N[(y * b), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.60000000000000053e-67

   1. Initial program 89.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 89.5%

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

      2. associate-/l* 86.9%

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

      3. associate-*l/ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in b around 0 85.2%

      \[\leadsto \color{blue}{\frac{\frac{y \cdot z}{t} + x}{1 + a}} \]

   if -8.60000000000000053e-67 < t < 2.5e15

   1. Initial program 61.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 61.6%

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

      2. associate-/l* 53.9%

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

      3. associate-*l/ 50.2%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in x around 0 45.4%

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

      1. associate-/l* 47.9%

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

      2. distribute-lft-in 47.9%

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

      3. *-rgt-identity 47.9%

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

      4. associate-*r/ 44.6%

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

      5. fma-def 44.6%

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

   6. Simplified 44.6%

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

   7. Taylor expanded in t around 0 65.5%

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

   if 2.5e15 < t

   1. Initial program 90.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 90.2%

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

      2. associate-/l* 92.6%

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

      3. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in x around inf 77.2%

      \[\leadsto \frac{\color{blue}{x}}{\left(a + 1\right) + \frac{y}{t} \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{\frac{t + \left(y \cdot b + t \cdot a\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 10: 62.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.2e-129)
   (/ (+ x (/ (* y z) t)) (+ a 1.0))
   (if (<= t 2.4e+21) (/ z b) (/ x (+ (+ a 1.0) (* b (/ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e-129) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 2.4e+21) {
		tmp = z / b;
	} else {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.2d-129)) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (t <= 2.4d+21) then
        tmp = z / b
    else
        tmp = x / ((a + 1.0d0) + (b * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e-129) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (t <= 2.4e+21) {
		tmp = z / b;
	} else {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.2e-129:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif t <= 2.4e+21:
		tmp = z / b
	else:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.2e-129)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (t <= 2.4e+21)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.2e-129)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (t <= 2.4e+21)
		tmp = z / b;
	else
		tmp = x / ((a + 1.0) + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.2e-129], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+21], N[(z / b), $MachinePrecision], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.20000000000000003e-129

   1. Initial program 88.6%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 88.6%

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

      2. associate-/l* 85.2%

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

      3. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in b around 0 81.4%

      \[\leadsto \color{blue}{\frac{\frac{y \cdot z}{t} + x}{1 + a}} \]

   if -2.20000000000000003e-129 < t < 2.4e21

   1. Initial program 59.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 59.4%

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

      2. associate-/l* 51.9%

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

      3. associate-*l/ 47.9%

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

   3. Simplified 47.9%

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

   4. Taylor expanded in t around 0 63.1%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 2.4e21 < t

   1. Initial program 91.5%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 91.5%

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

      2. associate-/l* 94.1%

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

      3. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in x around inf 79.8%

      \[\leadsto \frac{\color{blue}{x}}{\left(a + 1\right) + \frac{y}{t} \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]

Alternative 11: 42.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -9e+19)
   (/ x a)
   (if (<= a -8.8e-53)
     (/ z b)
     (if (<= a -2.6e-224) x (if (<= a 2.9e+44) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9e+19) {
		tmp = x / a;
	} else if (a <= -8.8e-53) {
		tmp = z / b;
	} else if (a <= -2.6e-224) {
		tmp = x;
	} else if (a <= 2.9e+44) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-9d+19)) then
        tmp = x / a
    else if (a <= (-8.8d-53)) then
        tmp = z / b
    else if (a <= (-2.6d-224)) then
        tmp = x
    else if (a <= 2.9d+44) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -9e+19) {
		tmp = x / a;
	} else if (a <= -8.8e-53) {
		tmp = z / b;
	} else if (a <= -2.6e-224) {
		tmp = x;
	} else if (a <= 2.9e+44) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -9e+19:
		tmp = x / a
	elif a <= -8.8e-53:
		tmp = z / b
	elif a <= -2.6e-224:
		tmp = x
	elif a <= 2.9e+44:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -9e+19)
		tmp = Float64(x / a);
	elseif (a <= -8.8e-53)
		tmp = Float64(z / b);
	elseif (a <= -2.6e-224)
		tmp = x;
	elseif (a <= 2.9e+44)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -9e+19)
		tmp = x / a;
	elseif (a <= -8.8e-53)
		tmp = z / b;
	elseif (a <= -2.6e-224)
		tmp = x;
	elseif (a <= 2.9e+44)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -9e+19], N[(x / a), $MachinePrecision], If[LessEqual[a, -8.8e-53], N[(z / b), $MachinePrecision], If[LessEqual[a, -2.6e-224], x, If[LessEqual[a, 2.9e+44], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9e19 or 2.9000000000000002e44 < a

   1. Initial program 72.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 72.4%

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

      2. associate-/l* 69.8%

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

      3. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in x around inf 57.8%

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

   5. Taylor expanded in a around inf 54.3%

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

   if -9e19 < a < -8.80000000000000073e-53 or -2.6000000000000002e-224 < a < 2.9000000000000002e44

   1. Initial program 74.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 74.2%

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

      2. associate-/l* 69.0%

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

      3. associate-*l/ 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in t around 0 51.6%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if -8.80000000000000073e-53 < a < -2.6000000000000002e-224

   1. Initial program 91.3%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 91.3%

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

      2. associate-/l* 87.1%

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

      3. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 73.2%

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

   5. Taylor expanded in a around 0 73.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{y \cdot b}{t} + 1}} \]

   6. Taylor expanded in y around 0 55.2%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 12: 56.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-71} \lor \neg \left(t \leq 4.1 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.26e-71) (not (<= t 4.1e+21))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.26e-71) || !(t <= 4.1e+21)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.26d-71)) .or. (.not. (t <= 4.1d+21))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.26e-71) || !(t <= 4.1e+21)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.26e-71) or not (t <= 4.1e+21):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.26e-71) || !(t <= 4.1e+21))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.26e-71) || ~((t <= 4.1e+21)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.26e-71], N[Not[LessEqual[t, 4.1e+21]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2600000000000001e-71 or 4.1e21 < t

   1. Initial program 90.4%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 90.4%

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

      2. associate-/l* 90.1%

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

      3. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around inf 69.2%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   if -1.2600000000000001e-71 < t < 4.1e21

   1. Initial program 61.2%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 61.2%

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

      2. associate-/l* 53.5%

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

      3. associate-*l/ 49.8%

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

   3. Simplified 49.8%

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

   4. Taylor expanded in t around 0 61.3%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-71} \lor \neg \left(t \leq 4.1 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13: 41.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.85e-7) (/ x a) (if (<= a 1.0) x (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.85e-7) {
		tmp = x / a;
	} else if (a <= 1.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-1.85d-7)) then
        tmp = x / a
    else if (a <= 1.0d0) then
        tmp = x
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.85e-7) {
		tmp = x / a;
	} else if (a <= 1.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.85e-7:
		tmp = x / a
	elif a <= 1.0:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.85e-7)
		tmp = Float64(x / a);
	elseif (a <= 1.0)
		tmp = x;
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -1.85e-7)
		tmp = x / a;
	elseif (a <= 1.0)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.85e-7], N[(x / a), $MachinePrecision], If[LessEqual[a, 1.0], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.85000000000000002e-7 or 1 < a

   1. Initial program 74.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 74.9%

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

      2. associate-/l* 71.8%

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

      3. associate-*l/ 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in x around inf 57.2%

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

   5. Taylor expanded in a around inf 49.4%

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

   if -1.85000000000000002e-7 < a < 1

   1. Initial program 78.1%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Step-by-step derivation

      1. *-commutative 78.1%

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

      2. associate-/l* 73.4%

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

      3. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in x around inf 55.0%

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

   5. Taylor expanded in a around 0 54.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{y \cdot b}{t} + 1}} \]

   6. Taylor expanded in y around 0 38.1%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 14: 20.1% accurate, 17.0× 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 76.5%

   \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
2. Step-by-step derivation

   1. *-commutative 76.5%

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

   2. associate-/l* 72.6%

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

   3. associate-*l/ 71.7%

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

3. Simplified 71.7%

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

4. Taylor expanded in x around inf 56.1%

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

5. Taylor expanded in a around 0 34.2%

   \[\leadsto \frac{x}{\color{blue}{\frac{y \cdot b}{t} + 1}} \]

6. Taylor expanded in y around 0 21.0%

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

7. Final simplification 21.0%

   \[\leadsto x \]

Developer target: 79.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023178 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))