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

Percentage Accurate: 75.4% → 90.3%

Time: 13.2s

Alternatives: 13

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: 75.4% 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: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t_2 \leq 10^{+282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{b} \cdot \frac{t}{y}\\ \end{array} \end{array} \]

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)))))
   (if (<= t_2 (- INFINITY))
     (* (/ z t) (/ y (+ 1.0 (+ a (* y (/ b t))))))
     (if (<= t_2 0.0)
       (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))
       (if (<= t_2 1e+282)
         t_2
         (if (<= t_2 INFINITY)
           (* (/ y t) (/ z (+ a (fma y (/ b t) 1.0))))
           (+ (/ z b) (* (/ x b) (/ t y)))))))))

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 tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z / t) * (y / (1.0 + (a + (y * (b / t)))));
	} else if (t_2 <= 0.0) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t_2 <= 1e+282) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y / t) * (z / (a + fma(y, (b / t), 1.0)));
	} else {
		tmp = (z / b) + ((x / b) * (t / y));
	}
	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)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z / t) * Float64(y / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))));
	elseif (t_2 <= 0.0)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t_2 <= 1e+282)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + fma(y, Float64(b / t), 1.0))));
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x / b) * Float64(t / y)));
	end
	return 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]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z / t), $MachinePrecision] * N[(y / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+282], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + N[(y * N[(b / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / b), $MachinePrecision] + N[(N[(x / b), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 28.9%

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

      1. associate-/l* 28.9%

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

   3. Simplified 28.9%

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

      1. div-inv 28.9%

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

      2. associate-/l* 64.6%

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

      3. associate-/r/ 38.3%

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

      4. +-commutative 38.3%

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

      5. associate-/r/ 64.6%

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

      6. div-inv 64.6%

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

      7. clear-num 64.6%

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

      8. fma-def 64.6%

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

   5. Applied egg-rr 64.6%

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

   6. Taylor expanded in x around 0 40.3%

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

      1. *-commutative 40.3%

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

      2. associate-+r+ 40.3%

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

      3. +-commutative 40.3%

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

      4. associate-*r/ 40.3%

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

      5. associate-+r+ 40.3%

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

      6. fma-def 40.3%

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

      7. times-frac 90.8%

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

      8. fma-def 90.8%

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

      9. associate-+r+ 90.8%

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

      10. associate-*r/ 90.8%

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

      11. +-commutative 90.8%

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

      12. associate-+r+ 90.8%

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

      13. associate-*r/ 90.8%

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

      14. fma-def 90.8%

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

   8. Simplified 90.8%

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

      1. fma-udef 90.8%

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

   10. Applied egg-rr 90.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 83.4%

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

      1. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.00000000000000003e282

   1. Initial program 99.8%

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

   if 1.00000000000000003e282 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 34.7%

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

      1. +-commutative 34.7%

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

      2. associate-*l/ 58.4%

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

      3. fma-def 58.4%

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

      4. associate-+l+ 58.4%

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

      5. +-commutative 58.4%

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

      6. associate-*l/ 38.6%

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

      7. fma-def 38.6%

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

   3. Simplified 38.6%

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

   4. Taylor expanded in z around inf 58.1%

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

      1. times-frac 88.0%

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

      2. associate-+r+ 88.0%

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

      3. associate-*r/ 88.0%

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

      4. +-commutative 88.0%

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

      5. fma-def 88.0%

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

      6. +-commutative 88.0%

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

   6. Simplified 88.0%

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

   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%

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

      2. associate-*l/ 0.1%

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

      3. fma-def 0.1%

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

      4. associate-+l+ 0.1%

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

      5. +-commutative 0.1%

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

      6. associate-*l/ 5.0%

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

      7. fma-def 5.0%

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

   3. Simplified 5.0%

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

   4. Taylor expanded in y around -inf 57.8%

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

      1. +-commutative 57.8%

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

      2. associate-*r/ 57.8%

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

      3. distribute-lft-out-- 57.8%

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

      4. associate-*r* 57.8%

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

      5. metadata-eval 57.8%

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

      6. *-lft-identity 57.8%

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

      7. associate-/l* 57.8%

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

      8. associate-/l* 62.3%

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

      9. associate-/r* 85.9%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in b around inf 95.2%

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

      1. *-commutative 95.2%

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

      2. *-commutative 95.2%

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

      3. times-frac 100.0%

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

   9. Simplified 100.0%

      \[\leadsto \frac{z}{b} + \color{blue}{\frac{x}{b} \cdot \frac{t}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+282}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + \mathsf{fma}\left(y, \frac{b}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{b} \cdot \frac{t}{y}\\ \end{array} \]

Alternative 2: 89.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ t_3 := \frac{z}{t} \cdot \frac{y}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t_2 \leq 10^{+282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{b} \cdot \frac{t}{y}\\ \end{array} \end{array} \]

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 (* (/ z t) (/ y (+ 1.0 (+ a (* y (/ b t))))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 0.0)
       (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))
       (if (<= t_2 1e+282)
         t_2
         (if (<= t_2 INFINITY) t_3 (+ (/ z b) (* (/ x b) (/ t y)))))))))

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 = (z / t) * (y / (1.0 + (a + (y * (b / t)))));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t_2 <= 1e+282) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (z / b) + ((x / b) * (t / y));
	}
	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 = (z / t) * (y / (1.0 + (a + (y * (b / t)))));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t_2 <= 1e+282) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (z / b) + ((x / b) * (t / y));
	}
	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 = (z / t) * (y / (1.0 + (a + (y * (b / t)))))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= 0.0:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	elif t_2 <= 1e+282:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = (z / b) + ((x / b) * (t / y))
	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(Float64(z / t) * Float64(y / Float64(1.0 + Float64(a + Float64(y * Float64(b / t))))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t_2 <= 1e+282)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(x / b) * Float64(t / y)));
	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 = (z / t) * (y / (1.0 + (a + (y * (b / t)))));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	elseif (t_2 <= 1e+282)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = (z / b) + ((x / b) * (t / y));
	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[(N[(z / t), $MachinePrecision] * N[(y / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 0.0], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+282], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(z / b), $MachinePrecision] + N[(N[(x / b), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $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 1.00000000000000003e282 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 31.8%

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

      1. associate-/l* 31.8%

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

   3. Simplified 31.8%

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

      1. div-inv 31.8%

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

      2. associate-/l* 61.5%

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

      3. associate-/r/ 38.4%

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

      4. +-commutative 38.4%

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

      5. associate-/r/ 61.5%

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

      6. div-inv 61.5%

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

      7. clear-num 61.5%

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

      8. fma-def 61.5%

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

   5. Applied egg-rr 61.5%

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

   6. Taylor expanded in x around 0 49.2%

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

      1. *-commutative 49.2%

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

      2. associate-+r+ 49.2%

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

      3. +-commutative 49.2%

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

      4. associate-*r/ 49.1%

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

      5. associate-+r+ 49.1%

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

      6. fma-def 49.1%

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

      7. times-frac 89.1%

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

      8. fma-def 89.1%

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

      9. associate-+r+ 89.1%

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

      10. associate-*r/ 89.1%

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

      11. +-commutative 89.1%

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

      12. associate-+r+ 89.1%

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

      13. associate-*r/ 89.1%

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

      14. fma-def 89.1%

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

   8. Simplified 89.1%

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

      1. fma-udef 89.1%

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

   10. Applied egg-rr 89.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 83.4%

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

      1. associate-/l* 89.0%

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

   3. Simplified 89.0%

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

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.00000000000000003e282

   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%

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

      2. associate-*l/ 0.1%

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

      3. fma-def 0.1%

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

      4. associate-+l+ 0.1%

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

      5. +-commutative 0.1%

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

      6. associate-*l/ 5.0%

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

      7. fma-def 5.0%

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

   3. Simplified 5.0%

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

   4. Taylor expanded in y around -inf 57.8%

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

      1. +-commutative 57.8%

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

      2. associate-*r/ 57.8%

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

      3. distribute-lft-out-- 57.8%

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

      4. associate-*r* 57.8%

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

      5. metadata-eval 57.8%

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

      6. *-lft-identity 57.8%

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

      7. associate-/l* 57.8%

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

      8. associate-/l* 62.3%

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

      9. associate-/r* 85.9%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in b around inf 95.2%

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

      1. *-commutative 95.2%

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

      2. *-commutative 95.2%

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

      3. times-frac 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 0:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+282}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x}{b} \cdot \frac{t}{y}\\ \end{array} \]

Alternative 3: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-99} \lor \neg \left(t \leq 1.9 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.5e-99) (not (<= t 1.9e-68)))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* b (/ y t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.5e-99) || !(t <= 1.9e-68)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + ((x * t) / y)) / 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 <= (-2.5d-99)) .or. (.not. (t <= 1.9d-68))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (z + ((x * t) / y)) / 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 <= -2.5e-99) || !(t <= 1.9e-68)) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.5e-99) or not (t <= 1.9e-68):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.5e-99) || !(t <= 1.9e-68))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.5e-99) || ~((t <= 1.9e-68)))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.5e-99], N[Not[LessEqual[t, 1.9e-68]], $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[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.49999999999999985e-99 or 1.90000000000000019e-68 < t

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-/l* 85.9%

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

      3. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

      1. associate-/r/ 90.1%

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

   5. Applied egg-rr 90.1%

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

   if -2.49999999999999985e-99 < t < 1.90000000000000019e-68

   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%

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

      2. associate-*l/ 57.8%

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

      3. fma-def 57.8%

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

      4. associate-+l+ 57.8%

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

      5. +-commutative 57.8%

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

      6. associate-*l/ 51.1%

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

      7. fma-def 51.1%

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

   3. Simplified 51.1%

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

   4. Taylor expanded in y around -inf 52.4%

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

      1. +-commutative 52.4%

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

      2. associate-*r/ 52.4%

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

      3. distribute-lft-out-- 52.4%

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

      4. associate-*r* 52.4%

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

      5. metadata-eval 52.4%

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

      6. *-lft-identity 52.4%

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

      7. associate-/l* 51.3%

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

      8. associate-/l* 48.4%

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

      9. associate-/r* 52.5%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 52.5%

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

   6. Simplified 52.5%

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

   7. Taylor expanded in b around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. *-commutative 69.8%

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

      3. times-frac 62.4%

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

   9. Simplified 62.4%

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

   10. Taylor expanded in b around 0 69.9%

       \[\leadsto \color{blue}{\frac{\frac{t \cdot x}{y} + z}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-99} \lor \neg \left(t \leq 1.9 \cdot 10^{-68}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 4: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.26e+82)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 3.5e+103)
     (/ (+ x (/ z (/ t y))) (+ (+ a 1.0) (* b (/ y t))))
     (/ (+ z (* x (/ t y))) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.26e+82) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 3.5e+103) {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + (x * (t / y))) / 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 <= (-1.26d+82)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 3.5d+103) then
        tmp = (x + (z / (t / y))) / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (z + (x * (t / y))) / 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 <= -1.26e+82) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 3.5e+103) {
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (z + (x * (t / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.26e+82:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 3.5e+103:
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (z + (x * (t / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.26e+82)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 3.5e+103)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.26e+82)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 3.5e+103)
		tmp = (x + (z / (t / y))) / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (z + (x * (t / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.26e+82], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 3.5e+103], 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], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2600000000000001e82

   1. Initial program 39.6%

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

      1. +-commutative 39.6%

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

      2. associate-*l/ 41.3%

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

      3. fma-def 41.3%

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

      4. associate-+l+ 41.3%

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

      5. +-commutative 41.3%

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

      6. associate-*l/ 38.0%

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

      7. fma-def 38.0%

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

   3. Simplified 38.0%

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

   4. Taylor expanded in y around -inf 47.1%

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

      1. +-commutative 47.1%

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

      2. associate-*r/ 47.1%

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

      3. distribute-lft-out-- 47.1%

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

      4. associate-*r* 47.1%

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

      5. metadata-eval 47.1%

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

      6. *-lft-identity 47.1%

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

      7. associate-/l* 47.1%

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

      8. associate-/l* 42.9%

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

      9. associate-/r* 51.6%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 51.6%

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

   6. Simplified 51.6%

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

   7. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. *-commutative 65.6%

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

      3. times-frac 56.8%

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

   9. Simplified 56.8%

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

   10. Taylor expanded in b around 0 67.7%

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

   if -1.2600000000000001e82 < y < 3.5e103

   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* 92.1%

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

      3. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   if 3.5e103 < y

   1. Initial program 54.1%

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

      1. +-commutative 54.1%

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

      2. associate-*l/ 53.7%

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

      3. fma-def 53.7%

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

      4. associate-+l+ 53.7%

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

      5. +-commutative 53.7%

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

      6. associate-*l/ 55.0%

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

      7. fma-def 55.0%

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

   3. Simplified 55.0%

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

   4. Taylor expanded in y around -inf 50.7%

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

      1. +-commutative 50.7%

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

      2. associate-*r/ 50.7%

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

      3. distribute-lft-out-- 50.7%

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

      4. associate-*r* 50.7%

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

      5. metadata-eval 50.7%

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

      6. *-lft-identity 50.7%

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

      7. associate-/l* 54.3%

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

      8. associate-/l* 58.2%

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

      9. associate-/r* 62.0%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in b around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. times-frac 69.7%

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

   9. Simplified 69.7%

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

   10. Taylor expanded in b around 0 70.4%

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

       1. +-commutative 70.4%

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

       2. *-commutative 70.4%

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

       3. associate-*r/ 74.0%

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

   12. Simplified 74.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+82}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \]

Alternative 5: 69.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 14000000:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y}{t} \cdot \frac{z}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e-25)
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (if (<= t 14000000.0)
     (/ (+ z (/ (* x t) y)) b)
     (+ (/ x (+ a 1.0)) (* (/ y t) (/ z (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e-25) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= 14000000.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	}
	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 <= (-3.2d-25)) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if (t <= 14000000.0d0) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x / (a + 1.0d0)) + ((y / t) * (z / (a + 1.0d0)))
    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 <= -3.2e-25) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= 14000000.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.2e-25:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif t <= 14000000.0:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.2e-25)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif (t <= 14000000.0)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x / Float64(a + 1.0)) + Float64(Float64(y / t) * Float64(z / Float64(a + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.2e-25)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif (t <= 14000000.0)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x / (a + 1.0)) + ((y / t) * (z / (a + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e-25], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 14000000.0], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2000000000000001e-25

   1. Initial program 84.4%

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

      1. +-commutative 84.4%

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

      2. associate-*l/ 91.0%

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

      3. fma-def 91.0%

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

      4. associate-+l+ 91.0%

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

      5. +-commutative 91.0%

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

      6. associate-*l/ 95.0%

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

      7. fma-def 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in b around 0 75.6%

      \[\leadsto \color{blue}{\frac{\frac{y \cdot z}{t} + x}{1 + a}} \]
   5. Step-by-step derivation

      1. div-inv 75.6%

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

   6. Applied egg-rr 75.6%

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

   7. Taylor expanded in y around 0 75.6%

      \[\leadsto \frac{\color{blue}{\frac{y \cdot z}{t}} + x}{1 + a} \]
   8. Step-by-step derivation

      1. associate-*r/ 82.3%

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

   9. Simplified 82.3%

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

   if -3.2000000000000001e-25 < t < 1.4e7

   1. Initial program 68.0%

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

      1. +-commutative 68.0%

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

      2. associate-*l/ 63.0%

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

      3. fma-def 63.0%

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

      4. associate-+l+ 63.0%

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

      5. +-commutative 63.0%

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

      6. associate-*l/ 57.0%

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

      7. fma-def 57.0%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in y around -inf 51.6%

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

      1. +-commutative 51.6%

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

      2. associate-*r/ 51.6%

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

      3. distribute-lft-out-- 51.6%

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

      4. associate-*r* 51.6%

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

      5. metadata-eval 51.6%

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

      6. *-lft-identity 51.6%

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

      7. associate-/l* 50.8%

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

      8. associate-/l* 48.5%

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

      9. associate-/r* 54.0%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 54.0%

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

   6. Simplified 54.0%

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

   7. Taylor expanded in b around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. times-frac 62.5%

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

   9. Simplified 62.5%

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

   10. Taylor expanded in b around 0 68.2%

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

   if 1.4e7 < t

   1. Initial program 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-*l/ 83.4%

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

      3. fma-def 83.4%

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

      4. associate-+l+ 83.4%

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

      5. +-commutative 83.4%

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

      6. associate-*l/ 93.3%

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

      7. fma-def 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in b around 0 65.8%

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

   5. Taylor expanded in y around 0 65.6%

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

      1. times-frac 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 14000000:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1} + \frac{y}{t} \cdot \frac{z}{a + 1}\\ \end{array} \]

Alternative 6: 70.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-33} \lor \neg \left(t \leq 2700\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.95e-33) (not (<= t 2700.0)))
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.95e-33) || !(t <= 2700.0)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / 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 <= (-2.95d-33)) .or. (.not. (t <= 2700.0d0))) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / 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 <= -2.95e-33) || !(t <= 2700.0)) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.95e-33) or not (t <= 2700.0):
		tmp = (x + (y * (z / t))) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.95e-33) || !(t <= 2700.0))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.95e-33) || ~((t <= 2700.0)))
		tmp = (x + (y * (z / t))) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.95e-33], N[Not[LessEqual[t, 2700.0]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.94999999999999993e-33 or 2700 < t

   1. Initial program 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-*l/ 87.6%

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

      3. fma-def 87.6%

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

      4. associate-+l+ 87.6%

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

      5. +-commutative 87.6%

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

      6. associate-*l/ 94.2%

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

      7. fma-def 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in b around 0 71.3%

      \[\leadsto \color{blue}{\frac{\frac{y \cdot z}{t} + x}{1 + a}} \]
   5. Step-by-step derivation

      1. div-inv 71.3%

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

   6. Applied egg-rr 71.3%

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

   7. Taylor expanded in y around 0 71.3%

      \[\leadsto \frac{\color{blue}{\frac{y \cdot z}{t}} + x}{1 + a} \]
   8. Step-by-step derivation

      1. associate-*r/ 77.2%

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

   9. Simplified 77.2%

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

   if -2.94999999999999993e-33 < t < 2700

   1. Initial program 68.0%

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

      1. +-commutative 68.0%

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

      2. associate-*l/ 63.0%

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

      3. fma-def 63.0%

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

      4. associate-+l+ 63.0%

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

      5. +-commutative 63.0%

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

      6. associate-*l/ 57.0%

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

      7. fma-def 57.0%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in y around -inf 51.6%

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

      1. +-commutative 51.6%

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

      2. associate-*r/ 51.6%

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

      3. distribute-lft-out-- 51.6%

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

      4. associate-*r* 51.6%

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

      5. metadata-eval 51.6%

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

      6. *-lft-identity 51.6%

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

      7. associate-/l* 50.8%

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

      8. associate-/l* 48.5%

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

      9. associate-/r* 54.0%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 54.0%

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

   6. Simplified 54.0%

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

   7. Taylor expanded in b around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. times-frac 62.5%

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

   9. Simplified 62.5%

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

   10. Taylor expanded in b around 0 68.2%

       \[\leadsto \color{blue}{\frac{\frac{t \cdot x}{y} + z}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-33} \lor \neg \left(t \leq 2700\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 7: 65.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.6e+80)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 1.46e+40)
     (/ x (+ 1.0 (+ a (/ (* y b) t))))
     (/ (+ z (* x (/ t y))) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.6e+80) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 1.46e+40) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (z + (x * (t / y))) / 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 <= (-4.6d+80)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 1.46d+40) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = (z + (x * (t / y))) / 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 <= -4.6e+80) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 1.46e+40) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (z + (x * (t / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.6e+80:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 1.46e+40:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = (z + (x * (t / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.6e+80)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 1.46e+40)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.6e+80)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 1.46e+40)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = (z + (x * (t / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.6e+80], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 1.46e+40], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000008e80

   1. Initial program 39.6%

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

      1. +-commutative 39.6%

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

      2. associate-*l/ 41.3%

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

      3. fma-def 41.3%

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

      4. associate-+l+ 41.3%

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

      5. +-commutative 41.3%

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

      6. associate-*l/ 38.0%

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

      7. fma-def 38.0%

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

   3. Simplified 38.0%

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

   4. Taylor expanded in y around -inf 47.1%

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

      1. +-commutative 47.1%

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

      2. associate-*r/ 47.1%

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

      3. distribute-lft-out-- 47.1%

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

      4. associate-*r* 47.1%

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

      5. metadata-eval 47.1%

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

      6. *-lft-identity 47.1%

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

      7. associate-/l* 47.1%

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

      8. associate-/l* 42.9%

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

      9. associate-/r* 51.6%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 51.6%

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

   6. Simplified 51.6%

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

   7. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. *-commutative 65.6%

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

      3. times-frac 56.8%

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

   9. Simplified 56.8%

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

   10. Taylor expanded in b around 0 67.7%

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

   if -4.60000000000000008e80 < y < 1.46e40

   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%

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

      2. associate-*l/ 93.9%

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

      3. fma-def 93.9%

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

      4. associate-+l+ 93.9%

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

      5. +-commutative 93.9%

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

      6. associate-*l/ 94.5%

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

      7. fma-def 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 74.0%

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

   if 1.46e40 < y

   1. Initial program 56.0%

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

      1. +-commutative 56.0%

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

      2. associate-*l/ 57.2%

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

      3. fma-def 57.2%

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

      4. associate-+l+ 57.2%

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

      5. +-commutative 57.2%

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

      6. associate-*l/ 59.8%

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

      7. fma-def 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in y around -inf 48.2%

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

      1. +-commutative 48.2%

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

      2. associate-*r/ 48.2%

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

      3. distribute-lft-out-- 48.2%

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

      4. associate-*r* 48.2%

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

      5. metadata-eval 48.2%

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

      6. *-lft-identity 48.2%

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

      7. associate-/l* 51.2%

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

      8. associate-/l* 57.5%

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

      9. associate-/r* 60.7%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in b around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. *-commutative 66.2%

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

      3. times-frac 68.8%

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

   9. Simplified 68.8%

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

   10. Taylor expanded in b around 0 67.9%

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

       1. +-commutative 67.9%

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

       2. *-commutative 67.9%

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

       3. associate-*r/ 70.9%

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

   12. Simplified 70.9%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \]

Alternative 8: 60.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+19} \lor \neg \left(y \leq 5.6 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e+19) (not (<= y 5.6e-34)))
   (/ (+ z (* x (/ t y))) b)
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e+19) || !(y <= 5.6e-34)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	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 <= (-1.25d+19)) .or. (.not. (y <= 5.6d-34))) then
        tmp = (z + (x * (t / y))) / b
    else
        tmp = x / (a + 1.0d0)
    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 <= -1.25e+19) || !(y <= 5.6e-34)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e+19) or not (y <= 5.6e-34):
		tmp = (z + (x * (t / y))) / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e+19) || !(y <= 5.6e-34))
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e+19) || ~((y <= 5.6e-34)))
		tmp = (z + (x * (t / y))) / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e+19], N[Not[LessEqual[y, 5.6e-34]], $MachinePrecision]], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e19 or 5.59999999999999994e-34 < y

   1. Initial program 57.1%

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

      1. +-commutative 57.1%

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

      2. associate-*l/ 58.2%

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

      3. fma-def 58.2%

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

      4. associate-+l+ 58.2%

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

      5. +-commutative 58.2%

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

      6. associate-*l/ 59.0%

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

      7. fma-def 59.0%

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

   3. Simplified 59.0%

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

   4. Taylor expanded in y around -inf 48.4%

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

      1. +-commutative 48.4%

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

      2. associate-*r/ 48.4%

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

      3. distribute-lft-out-- 48.4%

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

      4. associate-*r* 48.4%

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

      5. metadata-eval 48.4%

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

      6. *-lft-identity 48.4%

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

      7. associate-/l* 49.8%

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

      8. associate-/l* 51.4%

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

      9. associate-/r* 55.7%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 55.7%

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

   6. Simplified 55.7%

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

   7. Taylor expanded in b around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. *-commutative 63.6%

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

      3. times-frac 62.0%

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

   9. Simplified 62.0%

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

   10. Taylor expanded in b around 0 65.1%

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

       1. +-commutative 65.1%

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

       2. *-commutative 65.1%

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

       3. associate-*r/ 66.5%

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

   12. Simplified 66.5%

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

   if -1.25e19 < y < 5.59999999999999994e-34

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-*l/ 95.3%

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

      3. fma-def 95.3%

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

      4. associate-+l+ 95.3%

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

      5. +-commutative 95.3%

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

      6. associate-*l/ 95.3%

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

      7. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in y around 0 68.6%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+19} \lor \neg \left(y \leq 5.6 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 9: 59.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.7e+23)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 1.25e-33) (/ x (+ a 1.0)) (/ (+ z (* x (/ t y))) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.7e+23) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 1.25e-33) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + (x * (t / y))) / 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 <= (-2.7d+23)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 1.25d-33) then
        tmp = x / (a + 1.0d0)
    else
        tmp = (z + (x * (t / y))) / 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 <= -2.7e+23) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 1.25e-33) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + (x * (t / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.7e+23:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 1.25e-33:
		tmp = x / (a + 1.0)
	else:
		tmp = (z + (x * (t / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.7e+23)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 1.25e-33)
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.7e+23)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 1.25e-33)
		tmp = x / (a + 1.0);
	else
		tmp = (z + (x * (t / y))) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.7e+23], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 1.25e-33], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6999999999999999e23

   1. Initial program 48.2%

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

      1. +-commutative 48.2%

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

      2. associate-*l/ 49.5%

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

      3. fma-def 49.5%

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

      4. associate-+l+ 49.5%

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

      5. +-commutative 49.5%

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

      6. associate-*l/ 48.5%

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

      7. fma-def 48.5%

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

   3. Simplified 48.5%

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

   4. Taylor expanded in y around -inf 47.9%

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

      1. +-commutative 47.9%

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

      2. associate-*r/ 47.9%

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

      3. distribute-lft-out-- 47.9%

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

      4. associate-*r* 47.9%

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

      5. metadata-eval 47.9%

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

      6. *-lft-identity 47.9%

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

      7. associate-/l* 48.1%

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

      8. associate-/l* 44.8%

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

      9. associate-/r* 51.6%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 51.6%

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

   6. Simplified 51.6%

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

   7. Taylor expanded in b around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. *-commutative 62.6%

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

      3. times-frac 56.0%

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

   9. Simplified 56.0%

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

   10. Taylor expanded in b around 0 64.3%

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

   if -2.6999999999999999e23 < y < 1.25000000000000007e-33

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-*l/ 95.3%

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

      3. fma-def 95.3%

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

      4. associate-+l+ 95.3%

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

      5. +-commutative 95.3%

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

      6. associate-*l/ 95.3%

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

      7. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in y around 0 68.6%

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

   if 1.25000000000000007e-33 < y

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. associate-*l/ 64.6%

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

      3. fma-def 64.6%

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

      4. associate-+l+ 64.6%

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

      5. +-commutative 64.6%

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

      6. associate-*l/ 66.6%

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

      7. fma-def 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in y around -inf 48.7%

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

      1. +-commutative 48.7%

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

      2. associate-*r/ 48.7%

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

      3. distribute-lft-out-- 48.7%

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

      4. associate-*r* 48.7%

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

      5. metadata-eval 48.7%

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

      6. *-lft-identity 48.7%

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

      7. associate-/l* 51.1%

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

      8. associate-/l* 56.2%

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

      9. associate-/r* 58.7%

         \[\leadsto \frac{z}{b} + \frac{\frac{t}{\frac{b}{x}} - \frac{t}{\color{blue}{\frac{\frac{{b}^{2}}{1 + a}}{z}}}}{y} \]

      10. unpow2 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

      2. *-commutative 64.3%

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

      3. times-frac 66.4%

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

   9. Simplified 66.4%

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

   10. Taylor expanded in b around 0 65.7%

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

       1. +-commutative 65.7%

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

       2. *-commutative 65.7%

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

       3. associate-*r/ 68.1%

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

   12. Simplified 68.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \]

Alternative 10: 42.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 10^{-242}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.5e+109)
   (/ x a)
   (if (<= a 1e-242)
     (/ z b)
     (if (<= a 3e-35) x (if (<= a 9e+30) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.5e+109) {
		tmp = x / a;
	} else if (a <= 1e-242) {
		tmp = z / b;
	} else if (a <= 3e-35) {
		tmp = x;
	} else if (a <= 9e+30) {
		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 <= (-6.5d+109)) then
        tmp = x / a
    else if (a <= 1d-242) then
        tmp = z / b
    else if (a <= 3d-35) then
        tmp = x
    else if (a <= 9d+30) 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 <= -6.5e+109) {
		tmp = x / a;
	} else if (a <= 1e-242) {
		tmp = z / b;
	} else if (a <= 3e-35) {
		tmp = x;
	} else if (a <= 9e+30) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.5e+109:
		tmp = x / a
	elif a <= 1e-242:
		tmp = z / b
	elif a <= 3e-35:
		tmp = x
	elif a <= 9e+30:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.5e+109)
		tmp = Float64(x / a);
	elseif (a <= 1e-242)
		tmp = Float64(z / b);
	elseif (a <= 3e-35)
		tmp = x;
	elseif (a <= 9e+30)
		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 <= -6.5e+109)
		tmp = x / a;
	elseif (a <= 1e-242)
		tmp = z / b;
	elseif (a <= 3e-35)
		tmp = x;
	elseif (a <= 9e+30)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.5e+109], N[(x / a), $MachinePrecision], If[LessEqual[a, 1e-242], N[(z / b), $MachinePrecision], If[LessEqual[a, 3e-35], x, If[LessEqual[a, 9e+30], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5e109 or 8.9999999999999999e30 < a

   1. Initial program 74.5%

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

      1. +-commutative 74.5%

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

      2. associate-*l/ 75.3%

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

      3. fma-def 75.3%

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

      4. associate-+l+ 75.3%

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

      5. +-commutative 75.3%

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

      6. associate-*l/ 76.6%

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

      7. fma-def 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in y around 0 56.6%

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

   5. Taylor expanded in a around inf 56.6%

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

   if -6.5e109 < a < 1e-242 or 2.99999999999999989e-35 < a < 8.9999999999999999e30

   1. Initial program 67.6%

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

      1. +-commutative 67.6%

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

      2. associate-*l/ 68.3%

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

      3. fma-def 68.3%

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

      4. associate-+l+ 68.3%

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

      5. +-commutative 68.3%

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

      6. associate-*l/ 69.0%

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

      7. fma-def 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in y around inf 50.6%

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

   if 1e-242 < a < 2.99999999999999989e-35

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-*l/ 93.1%

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

      3. fma-def 93.1%

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

      4. associate-+l+ 93.1%

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

      5. +-commutative 93.1%

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

      6. associate-*l/ 90.6%

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

      7. fma-def 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in y around 0 50.4%

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

   5. Taylor expanded in a around 0 50.4%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 10^{-242}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 11: 56.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.6e+25) (/ z b) (if (<= y 1.02e+42) (/ x (+ a 1.0)) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.6e+25) {
		tmp = z / b;
	} else if (y <= 1.02e+42) {
		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 (y <= (-3.6d+25)) then
        tmp = z / b
    else if (y <= 1.02d+42) 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 (y <= -3.6e+25) {
		tmp = z / b;
	} else if (y <= 1.02e+42) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.6e+25:
		tmp = z / b
	elif y <= 1.02e+42:
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.6e+25)
		tmp = Float64(z / b);
	elseif (y <= 1.02e+42)
		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 (y <= -3.6e+25)
		tmp = z / b;
	elseif (y <= 1.02e+42)
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.6e+25], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.02e+42], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.60000000000000015e25 or 1.01999999999999996e42 < y

   1. Initial program 52.3%

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

      1. +-commutative 52.3%

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

      2. associate-*l/ 53.5%

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

      3. fma-def 53.5%

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

      4. associate-+l+ 53.5%

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

      5. +-commutative 53.5%

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

      6. associate-*l/ 54.4%

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

      7. fma-def 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in y around inf 59.4%

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

   if -3.60000000000000015e25 < y < 1.01999999999999996e42

   1. Initial program 94.4%

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

      1. +-commutative 94.4%

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

      2. associate-*l/ 95.1%

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

      3. fma-def 95.1%

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

      4. associate-+l+ 95.1%

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

      5. +-commutative 95.1%

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

      6. associate-*l/ 95.1%

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

      7. fma-def 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around 0 65.2%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 39.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.15e+76) (/ x a) (if (<= a 8e-26) x (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.15e+76) {
		tmp = x / a;
	} else if (a <= 8e-26) {
		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 <= (-1.15d+76)) then
        tmp = x / a
    else if (a <= 8d-26) 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 <= -1.15e+76) {
		tmp = x / a;
	} else if (a <= 8e-26) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.15e+76:
		tmp = x / a
	elif a <= 8e-26:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.15e+76)
		tmp = Float64(x / a);
	elseif (a <= 8e-26)
		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 <= -1.15e+76)
		tmp = x / a;
	elseif (a <= 8e-26)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.15e+76], N[(x / a), $MachinePrecision], If[LessEqual[a, 8e-26], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15000000000000001e76 or 8.0000000000000003e-26 < a

   1. Initial program 72.7%

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

      1. +-commutative 72.7%

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

      2. associate-*l/ 74.1%

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

      3. fma-def 74.1%

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

      4. associate-+l+ 74.1%

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

      5. +-commutative 74.1%

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

      6. associate-*l/ 75.3%

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

      7. fma-def 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in y around 0 52.3%

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

   5. Taylor expanded in a around inf 52.3%

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

   if -1.15000000000000001e76 < a < 8.0000000000000003e-26

   1. Initial program 76.6%

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

      1. +-commutative 76.6%

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

      2. associate-*l/ 77.0%

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

      3. fma-def 77.0%

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

      4. associate-+l+ 77.0%

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

      5. +-commutative 77.0%

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

      6. associate-*l/ 76.8%

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

      7. fma-def 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in y around 0 32.5%

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

   5. Taylor expanded in a around 0 32.5%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 13: 20.3% 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 74.6%

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

   1. +-commutative 74.6%

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

   2. associate-*l/ 75.6%

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

   3. fma-def 75.6%

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

   4. associate-+l+ 75.6%

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

   5. +-commutative 75.6%

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

   6. associate-*l/ 76.0%

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

   7. fma-def 76.0%

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

3. Simplified 76.0%

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

4. Taylor expanded in y around 0 42.2%

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

5. Taylor expanded in a around 0 18.4%

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

6. Final simplification 18.4%

   \[\leadsto x \]

Developer target: 79.8% 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 2023196 
(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))))