Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 93.5%

Time: 15.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
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))) / (y + (z * (b - y)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
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))) / (y + (z * (b - y)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, b - y, y\right)\\ t_2 := \mathsf{fma}\left(z, \frac{t - a}{t\_1}, x \cdot \frac{y}{t\_1}\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t\_3}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_4 \leq -1 \cdot 10^{+257}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+258}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(b - y, \frac{1}{\frac{\mathsf{fma}\left(y, x, t\_3\right)}{z}}, \frac{y}{\mathsf{fma}\left(z, t - a, x \cdot y\right)}\right)}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- b y) y))
        (t_2 (fma z (/ (- t a) t_1) (* x (/ y t_1))))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) (+ y (* z (- b y))))))
   (if (<= t_4 -1e+257)
     t_2
     (if (<= t_4 2e+258)
       (/
        1.0
        (fma
         (- b y)
         (/ 1.0 (/ (fma y x t_3) z))
         (/ y (fma z (- t a) (* x y)))))
       (if (<= t_4 INFINITY) t_2 (/ (- t a) (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (b - y), y);
	double t_2 = fma(z, ((t - a) / t_1), (x * (y / t_1)));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / (y + (z * (b - y)));
	double tmp;
	if (t_4 <= -1e+257) {
		tmp = t_2;
	} else if (t_4 <= 2e+258) {
		tmp = 1.0 / fma((b - y), (1.0 / (fma(y, x, t_3) / z)), (y / fma(z, (t - a), (x * y))));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(b - y), y)
	t_2 = fma(z, Float64(Float64(t - a) / t_1), Float64(x * Float64(y / t_1)))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_4 <= -1e+257)
		tmp = t_2;
	elseif (t_4 <= 2e+258)
		tmp = Float64(1.0 / fma(Float64(b - y), Float64(1.0 / Float64(fma(y, x, t_3) / z)), Float64(y / fma(z, Float64(t - a), Float64(x * y)))));
	elseif (t_4 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(t - a), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(x * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1e+257], t$95$2, If[LessEqual[t$95$4, 2e+258], N[(1.0 / N[(N[(b - y), $MachinePrecision] * N[(1.0 / N[(N[(y * x + t$95$3), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(z * N[(t - a), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$2, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000003e257 or 2.00000000000000011e258 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 38.4%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. associate-/l* N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-commutative N/A

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

      13. accelerator-lowering-fma.f64 N/A

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

      14. --lowering--.f64 99.9

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

   5. Simplified 99.9%

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

   if -1.00000000000000003e257 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000011e258

   1. Initial program 89.4%

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

      1. div-inv N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 89.0%

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. div-inv N/A

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

      5. *-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. un-div-inv N/A

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

      16. /-lowering-/.f64 N/A

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

   6. Applied egg-rr 98.2%

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

      1. clear-num N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. --lowering--.f64 98.4

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

   8. Applied egg-rr 98.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

      2. --lowering--.f64 N/A

         \[\leadsto \frac{\color{blue}{t - a}}{b - y} \]

      3. --lowering--.f64 77.2

         \[\leadsto \frac{t - a}{\color{blue}{b - y}} \]

   5. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+257}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)}, x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+258}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(b - y, \frac{1}{\frac{\mathsf{fma}\left(y, x, z \cdot \left(t - a\right)\right)}{z}}, \frac{y}{\mathsf{fma}\left(z, t - a, x \cdot y\right)}\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)}, x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \mathsf{fma}\left(z, b - y, y\right)\\ t_4 := \mathsf{fma}\left(z, \frac{t - a}{t\_3}, x \cdot \frac{y}{t\_3}\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+257}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-305}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_3 (fma z (- b y) y))
        (t_4 (fma z (/ (- t a) t_3) (* x (/ y t_3)))))
   (if (<= t_2 -1e+257)
     t_4
     (if (<= t_2 -5e-305)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 2e+258) t_2 (if (<= t_2 INFINITY) t_4 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = fma(z, (b - y), y);
	double t_4 = fma(z, ((t - a) / t_3), (x * (y / t_3)));
	double tmp;
	if (t_2 <= -1e+257) {
		tmp = t_4;
	} else if (t_2 <= -5e-305) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+258) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = fma(z, Float64(b - y), y)
	t_4 = fma(z, Float64(Float64(t - a) / t_3), Float64(x * Float64(y / t_3)))
	tmp = 0.0
	if (t_2 <= -1e+257)
		tmp = t_4;
	elseif (t_2 <= -5e-305)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+258)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(t - a), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(x * N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+257], t$95$4, If[LessEqual[t$95$2, -5e-305], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 2e+258], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$4, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000003e257 or 2.00000000000000011e258 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 38.4%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. associate-/l* N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-commutative N/A

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

      13. accelerator-lowering-fma.f64 N/A

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

      14. --lowering--.f64 99.9

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

   5. Simplified 99.9%

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

   if -1.00000000000000003e257 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999985e-305 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000011e258

   1. Initial program 99.1%

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

   if -4.99999999999999985e-305 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 9.8%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

      2. --lowering--.f64 N/A

         \[\leadsto \frac{\color{blue}{t - a}}{b - y} \]

      3. --lowering--.f64 79.2

         \[\leadsto \frac{t - a}{\color{blue}{b - y}} \]

   5. Simplified 79.2%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 93.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, t - a, x \cdot y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \mathsf{fma}\left(z, b - y, y\right)\\ t_4 := \mathsf{fma}\left(z, \frac{t - a}{t\_3}, x \cdot \frac{y}{t\_3}\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+257}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+258}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(b - y, \frac{z}{t\_1}, \frac{y}{t\_1}\right)}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- t a) (* x y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_3 (fma z (- b y) y))
        (t_4 (fma z (/ (- t a) t_3) (* x (/ y t_3)))))
   (if (<= t_2 -1e+257)
     t_4
     (if (<= t_2 2e+258)
       (/ 1.0 (fma (- b y) (/ z t_1) (/ y t_1)))
       (if (<= t_2 INFINITY) t_4 (/ (- t a) (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (t - a), (x * y));
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = fma(z, (b - y), y);
	double t_4 = fma(z, ((t - a) / t_3), (x * (y / t_3)));
	double tmp;
	if (t_2 <= -1e+257) {
		tmp = t_4;
	} else if (t_2 <= 2e+258) {
		tmp = 1.0 / fma((b - y), (z / t_1), (y / t_1));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(t - a), Float64(x * y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = fma(z, Float64(b - y), y)
	t_4 = fma(z, Float64(Float64(t - a) / t_3), Float64(x * Float64(y / t_3)))
	tmp = 0.0
	if (t_2 <= -1e+257)
		tmp = t_4;
	elseif (t_2 <= 2e+258)
		tmp = Float64(1.0 / fma(Float64(b - y), Float64(z / t_1), Float64(y / t_1)));
	elseif (t_2 <= Inf)
		tmp = t_4;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(t - a), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(x * N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+257], t$95$4, If[LessEqual[t$95$2, 2e+258], N[(1.0 / N[(N[(b - y), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$4, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000003e257 or 2.00000000000000011e258 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 38.4%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. associate-/l* N/A

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

      10. *-lowering-*.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-commutative N/A

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

      13. accelerator-lowering-fma.f64 N/A

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

      14. --lowering--.f64 99.9

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

   5. Simplified 99.9%

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

   if -1.00000000000000003e257 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000011e258

   1. Initial program 89.4%

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

      1. div-inv N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. frac-times N/A

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

      5. metadata-eval N/A

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

      6. /-lowering-/.f64 N/A

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

      7. *-lowering-*.f64 N/A

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

   4. Applied egg-rr 89.0%

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. div-inv N/A

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

      5. *-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 N/A

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

      14. *-commutative N/A

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

      15. un-div-inv N/A

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

      16. /-lowering-/.f64 N/A

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

   6. Applied egg-rr 98.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

      2. --lowering--.f64 N/A

         \[\leadsto \frac{\color{blue}{t - a}}{b - y} \]

      3. --lowering--.f64 77.2

         \[\leadsto \frac{t - a}{\color{blue}{b - y}} \]

   5. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{+257}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)}, x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+258}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(b - y, \frac{z}{\mathsf{fma}\left(z, t - a, x \cdot y\right)}, \frac{y}{\mathsf{fma}\left(z, t - a, x \cdot y\right)}\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t - a}{\mathsf{fma}\left(z, b - y, y\right)}, x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 465000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5.2e+18)
     t_1
     (if (<= z 465000.0)
       (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.2e+18) {
		tmp = t_1;
	} else if (z <= 465000.0) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	} 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 = (t - a) / (b - y)
    if (z <= (-5.2d+18)) then
        tmp = t_1
    else if (z <= 465000.0d0) then
        tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    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 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.2e+18) {
		tmp = t_1;
	} else if (z <= 465000.0) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -5.2e+18:
		tmp = t_1
	elif z <= 465000.0:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.2e+18)
		tmp = t_1;
	elseif (z <= 465000.0)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5.2e+18)
		tmp = t_1;
	elseif (z <= 465000.0)
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+18], t$95$1, If[LessEqual[z, 465000.0], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e18 or 465000 < z

   1. Initial program 38.4%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

      2. --lowering--.f64 N/A

         \[\leadsto \frac{\color{blue}{t - a}}{b - y} \]

      3. --lowering--.f64 84.6

         \[\leadsto \frac{t - a}{\color{blue}{b - y}} \]

   5. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -5.2e18 < z < 465000

   1. Initial program 86.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.65e-39)
     t_1
     (if (<= z 2.6e-42) (* x (/ y (fma z (- b y) y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.65e-39) {
		tmp = t_1;
	} else if (z <= 2.6e-42) {
		tmp = x * (y / fma(z, (b - y), y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.65e-39)
		tmp = t_1;
	elseif (z <= 2.6e-42)
		tmp = Float64(x * Float64(y / fma(z, Float64(b - y), y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-39], t$95$1, If[LessEqual[z, 2.6e-42], N[(x * N[(y / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999992e-39 or 2.6e-42 < z

   1. Initial program 48.6%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

      2. --lowering--.f64 N/A

         \[\leadsto \frac{\color{blue}{t - a}}{b - y} \]

      3. --lowering--.f64 81.0

         \[\leadsto \frac{t - a}{\color{blue}{b - y}} \]

   5. Simplified 81.0%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.64999999999999992e-39 < z < 2.6e-42

   1. Initial program 84.5%

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

   3. Taylor expanded in x around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. --lowering--.f64 64.3

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

   5. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 47.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+137}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)))
   (if (<= z -3.6e+137)
     (/ t (- b y))
     (if (<= z -4.1e-36) t_1 (if (<= z 2.05e-55) (/ x (- 1.0 z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double tmp;
	if (z <= -3.6e+137) {
		tmp = t / (b - y);
	} else if (z <= -4.1e-36) {
		tmp = t_1;
	} else if (z <= 2.05e-55) {
		tmp = x / (1.0 - z);
	} 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 = (t - a) / b
    if (z <= (-3.6d+137)) then
        tmp = t / (b - y)
    else if (z <= (-4.1d-36)) then
        tmp = t_1
    else if (z <= 2.05d-55) then
        tmp = x / (1.0d0 - z)
    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 = (t - a) / b;
	double tmp;
	if (z <= -3.6e+137) {
		tmp = t / (b - y);
	} else if (z <= -4.1e-36) {
		tmp = t_1;
	} else if (z <= 2.05e-55) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	tmp = 0
	if z <= -3.6e+137:
		tmp = t / (b - y)
	elif z <= -4.1e-36:
		tmp = t_1
	elif z <= 2.05e-55:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	tmp = 0.0
	if (z <= -3.6e+137)
		tmp = Float64(t / Float64(b - y));
	elseif (z <= -4.1e-36)
		tmp = t_1;
	elseif (z <= 2.05e-55)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	tmp = 0.0;
	if (z <= -3.6e+137)
		tmp = t / (b - y);
	elseif (z <= -4.1e-36)
		tmp = t_1;
	elseif (z <= 2.05e-55)
		tmp = x / (1.0 - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[z, -3.6e+137], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e-36], t$95$1, If[LessEqual[z, 2.05e-55], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e137

   1. Initial program 26.2%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. --lowering--.f64 21.4

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

   5. Simplified 21.4%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t}{b - y}} \]

      2. --lowering--.f64 66.1

         \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   8. Simplified 66.1%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -3.6e137 < z < -4.10000000000000013e-36 or 2.0499999999999999e-55 < z

   1. Initial program 57.5%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t - a}{b}} \]

      2. --lowering--.f64 55.6

         \[\leadsto \frac{\color{blue}{t - a}}{b} \]

   5. Simplified 55.6%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]

   if -4.10000000000000013e-36 < z < 2.0499999999999999e-55

   1. Initial program 84.4%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot z}} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{x}{1 + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}} \]

      3. unsub-neg N/A

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

      4. --lowering--.f64 53.4

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   5. Simplified 53.4%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+77}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.4e-38)
   (/ t b)
   (if (<= z 1.02e-39) x (if (<= z 7.6e+77) (- (/ a b)) (/ t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.4e-38) {
		tmp = t / b;
	} else if (z <= 1.02e-39) {
		tmp = x;
	} else if (z <= 7.6e+77) {
		tmp = -(a / b);
	} else {
		tmp = t / 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 (z <= (-1.4d-38)) then
        tmp = t / b
    else if (z <= 1.02d-39) then
        tmp = x
    else if (z <= 7.6d+77) then
        tmp = -(a / b)
    else
        tmp = t / 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 (z <= -1.4e-38) {
		tmp = t / b;
	} else if (z <= 1.02e-39) {
		tmp = x;
	} else if (z <= 7.6e+77) {
		tmp = -(a / b);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.4e-38:
		tmp = t / b
	elif z <= 1.02e-39:
		tmp = x
	elif z <= 7.6e+77:
		tmp = -(a / b)
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.4e-38)
		tmp = Float64(t / b);
	elseif (z <= 1.02e-39)
		tmp = x;
	elseif (z <= 7.6e+77)
		tmp = Float64(-Float64(a / b));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.4e-38)
		tmp = t / b;
	elseif (z <= 1.02e-39)
		tmp = x;
	elseif (z <= 7.6e+77)
		tmp = -(a / b);
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.4e-38], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.02e-39], x, If[LessEqual[z, 7.6e+77], (-N[(a / b), $MachinePrecision]), N[(t / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e-38 or 7.6000000000000002e77 < z

   1. Initial program 41.1%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. --lowering--.f64 25.4

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

   5. Simplified 25.4%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{t}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 37.5

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

   8. Simplified 37.5%

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

   if -1.4e-38 < z < 1.02000000000000007e-39

   1. Initial program 84.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 52.6%

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

   if 1.02000000000000007e-39 < z < 7.6000000000000002e77

   1. Initial program 82.7%

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

   3. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 49.4

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

   5. Simplified 49.4%

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

   6. Taylor expanded in a around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{b}} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{a}{b}\right)} \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{a}{b}\right)} \]

      3. /-lowering-/.f64 41.9

         \[\leadsto -\color{blue}{\frac{a}{b}} \]

   8. Simplified 41.9%

      \[\leadsto \color{blue}{-\frac{a}{b}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 63.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.35e-39) t_1 (if (<= z 9.8e-46) (/ x (- 1.0 z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.35e-39) {
		tmp = t_1;
	} else if (z <= 9.8e-46) {
		tmp = x / (1.0 - z);
	} 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 = (t - a) / (b - y)
    if (z <= (-1.35d-39)) then
        tmp = t_1
    else if (z <= 9.8d-46) then
        tmp = x / (1.0d0 - z)
    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 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.35e-39) {
		tmp = t_1;
	} else if (z <= 9.8e-46) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.35e-39:
		tmp = t_1
	elif z <= 9.8e-46:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.35e-39)
		tmp = t_1;
	elseif (z <= 9.8e-46)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.35e-39)
		tmp = t_1;
	elseif (z <= 9.8e-46)
		tmp = x / (1.0 - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e-39], t$95$1, If[LessEqual[z, 9.8e-46], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e-39 or 9.8000000000000002e-46 < z

   1. Initial program 48.6%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

      2. --lowering--.f64 N/A

         \[\leadsto \frac{\color{blue}{t - a}}{b - y} \]

      3. --lowering--.f64 81.0

         \[\leadsto \frac{t - a}{\color{blue}{b - y}} \]

   5. Simplified 81.0%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.35e-39 < z < 9.8000000000000002e-46

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot z}} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{x}{1 + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}} \]

      3. unsub-neg N/A

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

      4. --lowering--.f64 52.9

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 43.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -3.65 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -3.65e-37) t_1 (if (<= z 1.02e-44) (/ x (- 1.0 z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3.65e-37) {
		tmp = t_1;
	} else if (z <= 1.02e-44) {
		tmp = x / (1.0 - z);
	} 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 = t / (b - y)
    if (z <= (-3.65d-37)) then
        tmp = t_1
    else if (z <= 1.02d-44) then
        tmp = x / (1.0d0 - z)
    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 = t / (b - y);
	double tmp;
	if (z <= -3.65e-37) {
		tmp = t_1;
	} else if (z <= 1.02e-44) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -3.65e-37:
		tmp = t_1
	elif z <= 1.02e-44:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -3.65e-37)
		tmp = t_1;
	elseif (z <= 1.02e-44)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -3.65e-37)
		tmp = t_1;
	elseif (z <= 1.02e-44)
		tmp = x / (1.0 - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.65e-37], t$95$1, If[LessEqual[z, 1.02e-44], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6499999999999998e-37 or 1.0199999999999999e-44 < z

   1. Initial program 48.6%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. --lowering--.f64 26.9

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

   5. Simplified 26.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t}{b - y}} \]

      2. --lowering--.f64 50.0

         \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   8. Simplified 50.0%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -3.6499999999999998e-37 < z < 1.0199999999999999e-44

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot z}} \]

      2. mul-1-neg N/A

         \[\leadsto \frac{x}{1 + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}} \]

      3. unsub-neg N/A

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

      4. --lowering--.f64 52.9

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 43.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -6.8e-38) t_1 (if (<= z 7.5e-44) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -6.8e-38) {
		tmp = t_1;
	} else if (z <= 7.5e-44) {
		tmp = x;
	} 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 = t / (b - y)
    if (z <= (-6.8d-38)) then
        tmp = t_1
    else if (z <= 7.5d-44) then
        tmp = x
    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 = t / (b - y);
	double tmp;
	if (z <= -6.8e-38) {
		tmp = t_1;
	} else if (z <= 7.5e-44) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -6.8e-38:
		tmp = t_1
	elif z <= 7.5e-44:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -6.8e-38)
		tmp = t_1;
	elseif (z <= 7.5e-44)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -6.8e-38)
		tmp = t_1;
	elseif (z <= 7.5e-44)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e-38], t$95$1, If[LessEqual[z, 7.5e-44], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000004e-38 or 7.50000000000000008e-44 < z

   1. Initial program 48.6%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. --lowering--.f64 26.9

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

   5. Simplified 26.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{t}{b - y}} \]

      2. --lowering--.f64 50.0

         \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   8. Simplified 50.0%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -6.8000000000000004e-38 < z < 7.50000000000000008e-44

   1. Initial program 84.5%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 52.9%

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

Alternative 11: 36.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.8e-38) (/ t b) (if (<= z 7e-41) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.8e-38) {
		tmp = t / b;
	} else if (z <= 7e-41) {
		tmp = x;
	} else {
		tmp = t / 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 (z <= (-8.8d-38)) then
        tmp = t / b
    else if (z <= 7d-41) then
        tmp = x
    else
        tmp = t / 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 (z <= -8.8e-38) {
		tmp = t / b;
	} else if (z <= 7e-41) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.8e-38:
		tmp = t / b
	elif z <= 7e-41:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.8e-38)
		tmp = Float64(t / b);
	elseif (z <= 7e-41)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.8e-38)
		tmp = t / b;
	elseif (z <= 7e-41)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.8e-38], N[(t / b), $MachinePrecision], If[LessEqual[z, 7e-41], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000029e-38 or 6.9999999999999999e-41 < z

   1. Initial program 48.6%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. +-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. --lowering--.f64 26.9

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

   5. Simplified 26.9%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{t}{b}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 34.3

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

   8. Simplified 34.3%

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

   if -8.80000000000000029e-38 < z < 6.9999999999999999e-41

   1. Initial program 84.5%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 52.9%

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

Alternative 12: 25.0% accurate, 39.0× 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 65.6%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 27.1%

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

Developer Target 1: 74.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024198 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z)))))

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