Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.6% → 87.1%

Time: 15.3s

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: 66.6% 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: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \mathsf{fma}\left(z, b - y, y\right)\\ t_3 := \frac{t\_1}{y + z \cdot \left(b - y\right)}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \mathsf{fma}\left(z, \frac{t - a}{x \cdot t\_2}, \frac{y}{t\_2}\right)\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-283}:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, 0 - y, y\right)\right)}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a))))
        (t_2 (fma z (- b y) y))
        (t_3 (/ t_1 (+ y (* z (- b y)))))
        (t_4 (/ (- t a) (- b y))))
   (if (<= t_3 (- INFINITY))
     (* x (fma z (/ (- t a) (* x t_2)) (/ y t_2)))
     (if (<= t_3 -5e-283)
       (/ t_1 (fma z b (fma z (- 0.0 y) y)))
       (if (<= t_3 0.0) t_4 (if (<= t_3 2e+269) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = fma(z, (b - y), y);
	double t_3 = t_1 / (y + (z * (b - y)));
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * fma(z, ((t - a) / (x * t_2)), (y / t_2));
	} else if (t_3 <= -5e-283) {
		tmp = t_1 / fma(z, b, fma(z, (0.0 - y), y));
	} else if (t_3 <= 0.0) {
		tmp = t_4;
	} else if (t_3 <= 2e+269) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = fma(z, Float64(b - y), y)
	t_3 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * fma(z, Float64(Float64(t - a) / Float64(x * t_2)), Float64(y / t_2)));
	elseif (t_3 <= -5e-283)
		tmp = Float64(t_1 / fma(z, b, fma(z, Float64(0.0 - y), y)));
	elseif (t_3 <= 0.0)
		tmp = t_4;
	elseif (t_3 <= 2e+269)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(z * N[(N[(t - a), $MachinePrecision] / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-283], N[(t$95$1 / N[(z * b + N[(z * N[(0.0 - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], t$95$4, If[LessEqual[t$95$3, 2e+269], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 37.5%

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

   3. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

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

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

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

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

      8. +-commutative N/A

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

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

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

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

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

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

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

      12. +-commutative N/A

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

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

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

      14. --lowering--.f64 84.6

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

   5. Simplified 84.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000001e-283

   1. Initial program 99.5%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

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

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

      8. --lowering--.f64 99.6

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, 0 - y, y\right)\right)}} \]

   if -5.0000000000000001e-283 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 2.0000000000000001e269 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   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 77.3

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

   5. Simplified 77.3%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e269

   1. Initial program 99.6%

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

Alternative 2: 83.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, 0 - y, y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4000000.0)
     t_1
     (if (<= z 8.5e+17)
       (/ (+ (* x y) (* z (- t a))) (fma z b (fma z (- 0.0 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 <= -4000000.0) {
		tmp = t_1;
	} else if (z <= 8.5e+17) {
		tmp = ((x * y) + (z * (t - a))) / fma(z, b, fma(z, (0.0 - 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 <= -4000000.0)
		tmp = t_1;
	elseif (z <= 8.5e+17)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / fma(z, b, fma(z, Float64(0.0 - 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, -4000000.0], t$95$1, If[LessEqual[z, 8.5e+17], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * b + N[(z * N[(0.0 - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4e6 or 8.5e17 < z

   1. Initial program 41.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   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 83.6

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

   5. Simplified 83.6%

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

   if -4e6 < z < 8.5e17

   1. Initial program 88.4%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

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

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

      8. --lowering--.f64 88.4

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

   4. Applied egg-rr 88.4%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, 0 - y, y\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4000000.0)
     t_1
     (if (<= z 2.5e+18)
       (/ (+ (* 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 <= -4000000.0) {
		tmp = t_1;
	} else if (z <= 2.5e+18) {
		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 <= (-4000000.0d0)) then
        tmp = t_1
    else if (z <= 2.5d+18) 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 <= -4000000.0) {
		tmp = t_1;
	} else if (z <= 2.5e+18) {
		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 <= -4000000.0:
		tmp = t_1
	elif z <= 2.5e+18:
		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 <= -4000000.0)
		tmp = t_1;
	elseif (z <= 2.5e+18)
		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 <= -4000000.0)
		tmp = t_1;
	elseif (z <= 2.5e+18)
		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, -4000000.0], t$95$1, If[LessEqual[z, 2.5e+18], 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 < -4e6 or 2.5e18 < z

   1. Initial program 41.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   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 83.6

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

   5. Simplified 83.6%

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

   if -4e6 < z < 2.5e18

   1. Initial program 88.4%

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

Alternative 4: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-33}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.18e-85)
     t_1
     (if (<= z -1.75e-302)
       (* x (/ y (fma z (- b y) y)))
       (if (<= z 4.3e-33) (/ (+ (* x y) (* z (- t a))) 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 <= -1.18e-85) {
		tmp = t_1;
	} else if (z <= -1.75e-302) {
		tmp = x * (y / fma(z, (b - y), y));
	} else if (z <= 4.3e-33) {
		tmp = ((x * y) + (z * (t - a))) / 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 <= -1.18e-85)
		tmp = t_1;
	elseif (z <= -1.75e-302)
		tmp = Float64(x * Float64(y / fma(z, Float64(b - y), y)));
	elseif (z <= 4.3e-33)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / 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, -1.18e-85], t$95$1, If[LessEqual[z, -1.75e-302], N[(x * N[(y / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e-33], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.18e-85 or 4.30000000000000031e-33 < z

   1. Initial program 49.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   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 80.2

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

   5. Simplified 80.2%

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

   if -1.18e-85 < z < -1.7500000000000001e-302

   1. Initial program 82.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   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. flip3-+ N/A

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

      3. clear-num N/A

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

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

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

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

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

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

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

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

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

      8. clear-num N/A

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

      9. flip3-+ N/A

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

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

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

      11. +-commutative N/A

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

   4. Applied egg-rr 82.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 48.5

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

   7. Simplified 48.5%

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

      1. un-div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 65.5

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

   9. Applied egg-rr 65.5%

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

   if -1.7500000000000001e-302 < z < 4.30000000000000031e-33

   1. Initial program 91.7%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 72.8%

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

Alternative 5: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2e-85) t_1 (if (<= z 9e-89) (* 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 <= -2e-85) {
		tmp = t_1;
	} else if (z <= 9e-89) {
		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 <= -2e-85)
		tmp = t_1;
	elseif (z <= 9e-89)
		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, -2e-85], t$95$1, If[LessEqual[z, 9e-89], 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 < -2e-85 or 8.9999999999999998e-89 < z

   1. Initial program 51.5%

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

   3. Taylor expanded in z around 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 78.1

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

   5. Simplified 78.1%

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

   if -2e-85 < z < 8.9999999999999998e-89

   1. Initial program 86.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   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. flip3-+ N/A

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

      3. clear-num N/A

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

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

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

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

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

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

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

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

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

      8. clear-num N/A

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

      9. flip3-+ N/A

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

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

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

      11. +-commutative N/A

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

   4. Applied egg-rr 86.7%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 52.2

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

   7. Simplified 52.2%

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

      1. un-div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 65.2

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

   9. Applied egg-rr 65.2%

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

Alternative 6: 45.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -82000000:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -5.5e+131)
     t_1
     (if (<= z -82000000.0)
       (/ a (- y b))
       (if (<= z 5.8e-9) (/ 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 <= -5.5e+131) {
		tmp = t_1;
	} else if (z <= -82000000.0) {
		tmp = a / (y - b);
	} else if (z <= 5.8e-9) {
		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 <= (-5.5d+131)) then
        tmp = t_1
    else if (z <= (-82000000.0d0)) then
        tmp = a / (y - b)
    else if (z <= 5.8d-9) 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 <= -5.5e+131) {
		tmp = t_1;
	} else if (z <= -82000000.0) {
		tmp = a / (y - b);
	} else if (z <= 5.8e-9) {
		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 <= -5.5e+131:
		tmp = t_1
	elif z <= -82000000.0:
		tmp = a / (y - b)
	elif z <= 5.8e-9:
		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 <= -5.5e+131)
		tmp = t_1;
	elseif (z <= -82000000.0)
		tmp = Float64(a / Float64(y - b));
	elseif (z <= 5.8e-9)
		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 <= -5.5e+131)
		tmp = t_1;
	elseif (z <= -82000000.0)
		tmp = a / (y - b);
	elseif (z <= 5.8e-9)
		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, -5.5e+131], t$95$1, If[LessEqual[z, -82000000.0], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-9], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999971e131 or 5.79999999999999982e-9 < z

   1. Initial program 35.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   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 23.5

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

   5. Simplified 23.5%

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

   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 50.8

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

   8. Simplified 50.8%

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

   if -5.49999999999999971e131 < z < -8.2e7

   1. Initial program 79.7%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

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

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

      8. --lowering--.f64 79.9

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

   4. Applied egg-rr 79.9%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, 0 - y, y\right)\right)}} \]

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. associate-*r/ N/A

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

      8. mul-1-neg N/A

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

      9. distribute-neg-frac2 N/A

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

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

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

      11. *-commutative N/A

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

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

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

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

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

      14. +-commutative N/A

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

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

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

      16. --lowering--.f64 46.8

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

   7. Simplified 46.8%

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

   8. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 60.1

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

   10. Simplified 60.1%

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

   if -8.2e7 < z < 5.79999999999999982e-9

   1. Initial program 87.1%

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

   3. Taylor expanded in 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 45.2

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

   5. Simplified 45.2%

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

Alternative 7: 61.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.8e-214) t_1 (if (<= z 2.05e-89) x 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 <= -2.8e-214) {
		tmp = t_1;
	} else if (z <= 2.05e-89) {
		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 - a) / (b - y)
    if (z <= (-2.8d-214)) then
        tmp = t_1
    else if (z <= 2.05d-89) 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 - a) / (b - y);
	double tmp;
	if (z <= -2.8e-214) {
		tmp = t_1;
	} else if (z <= 2.05e-89) {
		tmp = x;
	} 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 <= -2.8e-214:
		tmp = t_1
	elif z <= 2.05e-89:
		tmp = x
	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 <= -2.8e-214)
		tmp = t_1;
	elseif (z <= 2.05e-89)
		tmp = x;
	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 <= -2.8e-214)
		tmp = t_1;
	elseif (z <= 2.05e-89)
		tmp = x;
	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, -2.8e-214], t$95$1, If[LessEqual[z, 2.05e-89], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000002e-214 or 2.0499999999999999e-89 < z

   1. Initial program 56.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   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 72.6

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

   5. Simplified 72.6%

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

   if -2.8000000000000002e-214 < z < 2.0499999999999999e-89

   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 55.9%

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

Alternative 8: 54.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+63}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -8.6e-40) t_1 (if (<= y 4e+63) (/ (- t a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -8.6e-40) {
		tmp = t_1;
	} else if (y <= 4e+63) {
		tmp = (t - a) / 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 = x / (1.0d0 - z)
    if (y <= (-8.6d-40)) then
        tmp = t_1
    else if (y <= 4d+63) then
        tmp = (t - a) / 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 = x / (1.0 - z);
	double tmp;
	if (y <= -8.6e-40) {
		tmp = t_1;
	} else if (y <= 4e+63) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -8.6e-40:
		tmp = t_1
	elif y <= 4e+63:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -8.6e-40)
		tmp = t_1;
	elseif (y <= 4e+63)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -8.6e-40)
		tmp = t_1;
	elseif (y <= 4e+63)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e-40], t$95$1, If[LessEqual[y, 4e+63], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.6000000000000005e-40 or 4.00000000000000023e63 < y

   1. Initial program 47.1%

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

   3. Taylor expanded in 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 45.2

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

   5. Simplified 45.2%

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

   if -8.6000000000000005e-40 < y < 4.00000000000000023e63

   1. Initial program 80.6%

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

   3. Taylor expanded in 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 56.4

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

   5. Simplified 56.4%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 40.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+112}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= t -4.6e-5) t_1 (if (<= t 4.8e+112) (/ a (- y b)) 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 (t <= -4.6e-5) {
		tmp = t_1;
	} else if (t <= 4.8e+112) {
		tmp = a / (y - 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 = t / (b - y)
    if (t <= (-4.6d-5)) then
        tmp = t_1
    else if (t <= 4.8d+112) then
        tmp = a / (y - 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 = t / (b - y);
	double tmp;
	if (t <= -4.6e-5) {
		tmp = t_1;
	} else if (t <= 4.8e+112) {
		tmp = a / (y - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if t <= -4.6e-5:
		tmp = t_1
	elif t <= 4.8e+112:
		tmp = a / (y - b)
	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 (t <= -4.6e-5)
		tmp = t_1;
	elseif (t <= 4.8e+112)
		tmp = Float64(a / Float64(y - b));
	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 (t <= -4.6e-5)
		tmp = t_1;
	elseif (t <= 4.8e+112)
		tmp = a / (y - b);
	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[t, -4.6e-5], t$95$1, If[LessEqual[t, 4.8e+112], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6e-5 or 4.8e112 < t

   1. Initial program 64.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   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 39.5

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

   5. Simplified 39.5%

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

   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 54.2

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

   8. Simplified 54.2%

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

   if -4.6e-5 < t < 4.8e112

   1. Initial program 64.9%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

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

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

      8. --lowering--.f64 64.9

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

   4. Applied egg-rr 64.9%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, 0 - y, y\right)\right)}} \]

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. associate-*r/ N/A

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

      8. mul-1-neg N/A

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

      9. distribute-neg-frac2 N/A

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

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

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

      11. *-commutative N/A

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

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

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

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

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

      14. +-commutative N/A

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

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

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

      16. --lowering--.f64 31.1

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

   7. Simplified 31.1%

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

   8. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 41.8

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

   10. Simplified 41.8%

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

Alternative 10: 44.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{y - b}\\ \mathbf{if}\;z \leq -7 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- y b)))) (if (<= z -7e-61) t_1 (if (<= z 8.8e-57) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (y - b);
	double tmp;
	if (z <= -7e-61) {
		tmp = t_1;
	} else if (z <= 8.8e-57) {
		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 = a / (y - b)
    if (z <= (-7d-61)) then
        tmp = t_1
    else if (z <= 8.8d-57) 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 = a / (y - b);
	double tmp;
	if (z <= -7e-61) {
		tmp = t_1;
	} else if (z <= 8.8e-57) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (y - b)
	tmp = 0
	if z <= -7e-61:
		tmp = t_1
	elif z <= 8.8e-57:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(y - b))
	tmp = 0.0
	if (z <= -7e-61)
		tmp = t_1;
	elseif (z <= 8.8e-57)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (y - b);
	tmp = 0.0;
	if (z <= -7e-61)
		tmp = t_1;
	elseif (z <= 8.8e-57)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e-61], t$95$1, If[LessEqual[z, 8.8e-57], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000006e-61 or 8.79999999999999994e-57 < z

   1. Initial program 48.3%

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

      1. +-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

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

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

      8. --lowering--.f64 48.3

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, \color{blue}{0 - y}, y\right)\right)} \]

   4. Applied egg-rr 48.3%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{\mathsf{fma}\left(z, b, \mathsf{fma}\left(z, 0 - y, y\right)\right)}} \]

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-in N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. associate-*r/ N/A

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

      8. mul-1-neg N/A

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

      9. distribute-neg-frac2 N/A

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

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

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

      11. *-commutative N/A

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

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

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

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

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

      14. +-commutative N/A

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

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

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

      16. --lowering--.f64 23.7

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

   7. Simplified 23.7%

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

   8. Taylor expanded in z around inf

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

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

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

      2. --lowering--.f64 42.8

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

   10. Simplified 42.8%

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

   if -7.0000000000000006e-61 < z < 8.79999999999999994e-57

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 47.5%

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

Alternative 11: 35.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.8e-107) (/ t b) (if (<= z 7.5e-89) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.8e-107) {
		tmp = t / b;
	} else if (z <= 7.5e-89) {
		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 <= (-3.8d-107)) then
        tmp = t / b
    else if (z <= 7.5d-89) 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 <= -3.8e-107) {
		tmp = t / b;
	} else if (z <= 7.5e-89) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.8e-107:
		tmp = t / b
	elif z <= 7.5e-89:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.8e-107)
		tmp = Float64(t / b);
	elseif (z <= 7.5e-89)
		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 <= -3.8e-107)
		tmp = t / b;
	elseif (z <= 7.5e-89)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.8e-107], N[(t / b), $MachinePrecision], If[LessEqual[z, 7.5e-89], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000002e-107 or 7.4999999999999999e-89 < z

   1. Initial program 52.4%

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

   3. Taylor expanded in 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 27.3

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

   5. Simplified 27.3%

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

   6. Taylor expanded in b around inf

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

      1. /-lowering-/.f64 28.2

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

   8. Simplified 28.2%

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

   if -3.8000000000000002e-107 < z < 7.4999999999999999e-89

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 51.6%

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

Alternative 12: 25.1% 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 64.6%

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

3. Taylor expanded in z around 0

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

5. Simplified 22.0%

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

Developer Target 1: 73.3% 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 2024196 
(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)))))