Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Percentage Accurate: 88.1% → 99.9%

Time: 7.7s

Alternatives: 10

Speedup: 0.8×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x * ((y - z) + 1.0)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 88.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x * ((y - z) + 1.0)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x\_m, \mathsf{fma}\left(-x\_m, z, x\_m\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\frac{z}{\left(y - z\right) - -1}}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 2.4e-14)
    (/ (fma y x_m (fma (- x_m) z x_m)) z)
    (/ x_m (/ z (- (- y z) -1.0))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 2.4e-14) {
		tmp = fma(y, x_m, fma(-x_m, z, x_m)) / z;
	} else {
		tmp = x_m / (z / ((y - z) - -1.0));
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 2.4e-14)
		tmp = Float64(fma(y, x_m, fma(Float64(-x_m), z, x_m)) / z);
	else
		tmp = Float64(x_m / Float64(z / Float64(Float64(y - z) - -1.0)));
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 2.4e-14], N[(N[(y * x$95$m + N[((-x$95$m) * z + x$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x$95$m / N[(z / N[(N[(y - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.4e-14

   1. Initial program 91.1%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. distribute-lft-in N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-rgt-in N/A

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

      7. *-rgt-identity N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. *-rgt-identity N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-neg.f64 91.1

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

   4. Applied rewrites 91.1%

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

   if 2.4e-14 < x

   1. Initial program 72.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-+l- N/A

          \[\leadsto \frac{x}{\frac{z}{\color{blue}{y - \left(z - 1\right)}}} \]

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. associate--r+ N/A

          \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(y - z\right) - -1}}} \]

      14. lift--.f64 N/A

          \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(y - z\right)} - -1}} \]

      15. lower--.f64 99.9

          \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(y - z\right) - -1}}} \]

   4. Applied rewrites 99.9%

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

Alternative 2: 93.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+134}:\\ \;\;\;\;-x\_m\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+173}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y - z, x\_m, x\_m\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z -5.5e+134)
    (- x_m)
    (if (<= z 3.2e+173) (/ (fma (- y z) x_m x_m) z) (- x_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -5.5e+134) {
		tmp = -x_m;
	} else if (z <= 3.2e+173) {
		tmp = fma((y - z), x_m, x_m) / z;
	} else {
		tmp = -x_m;
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= -5.5e+134)
		tmp = Float64(-x_m);
	elseif (z <= 3.2e+173)
		tmp = Float64(fma(Float64(y - z), x_m, x_m) / z);
	else
		tmp = Float64(-x_m);
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, -5.5e+134], (-x$95$m), If[LessEqual[z, 3.2e+173], N[(N[(N[(y - z), $MachinePrecision] * x$95$m + x$95$m), $MachinePrecision] / z), $MachinePrecision], (-x$95$m)]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999999e134 or 3.2000000000000003e173 < z

   1. Initial program 58.8%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(x\right)} \]

      2. lower-neg.f64 93.1

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

   5. Applied rewrites 93.1%

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

   if -5.4999999999999999e134 < z < 3.2000000000000003e173

   1. Initial program 95.0%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 95.0

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

   4. Applied rewrites 95.0%

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

Alternative 3: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.3 \cdot 10^{-45}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x\_m, \mathsf{fma}\left(-x\_m, z, x\_m\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \left(\left(y - z\right) - -1\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1.3e-45)
    (/ (fma y x_m (fma (- x_m) z x_m)) z)
    (* (/ x_m z) (- (- y z) -1.0)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 1.3e-45) {
		tmp = fma(y, x_m, fma(-x_m, z, x_m)) / z;
	} else {
		tmp = (x_m / z) * ((y - z) - -1.0);
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 1.3e-45)
		tmp = Float64(fma(y, x_m, fma(Float64(-x_m), z, x_m)) / z);
	else
		tmp = Float64(Float64(x_m / z) * Float64(Float64(y - z) - -1.0));
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 1.3e-45], N[(N[(y * x$95$m + N[((-x$95$m) * z + x$95$m), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.29999999999999993e-45

   1. Initial program 91.0%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. distribute-lft-in N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-rgt-in N/A

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

      7. *-rgt-identity N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. neg-mul-1 N/A

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

      12. associate-*r* N/A

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

      13. metadata-eval N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. *-rgt-identity N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-neg.f64 91.0

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

   4. Applied rewrites 91.0%

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

   if 1.29999999999999993e-45 < x

   1. Initial program 73.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.9

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-+l- N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. associate--r+ N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 4: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+26}:\\ \;\;\;\;\frac{y \cdot x\_m}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{x\_m}{z} - x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -8e+26)
    (/ (* y x_m) z)
    (if (<= y 2.5e+99) (- (/ x_m z) x_m) (* (/ y z) x_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -8e+26) {
		tmp = (y * x_m) / z;
	} else if (y <= 2.5e+99) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = (y / z) * x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8d+26)) then
        tmp = (y * x_m) / z
    else if (y <= 2.5d+99) then
        tmp = (x_m / z) - x_m
    else
        tmp = (y / z) * x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -8e+26) {
		tmp = (y * x_m) / z;
	} else if (y <= 2.5e+99) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = (y / z) * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -8e+26:
		tmp = (y * x_m) / z
	elif y <= 2.5e+99:
		tmp = (x_m / z) - x_m
	else:
		tmp = (y / z) * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -8e+26)
		tmp = Float64(Float64(y * x_m) / z);
	elseif (y <= 2.5e+99)
		tmp = Float64(Float64(x_m / z) - x_m);
	else
		tmp = Float64(Float64(y / z) * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -8e+26)
		tmp = (y * x_m) / z;
	elseif (y <= 2.5e+99)
		tmp = (x_m / z) - x_m;
	else
		tmp = (y / z) * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -8e+26], N[(N[(y * x$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.5e+99], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000038e26

   1. Initial program 96.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 85.2

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

   5. Applied rewrites 85.2%

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

   if -8.00000000000000038e26 < y < 2.50000000000000004e99

   1. Initial program 81.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. sub-neg N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. associate-/l* N/A

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

      8. *-rgt-identity N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 93.6

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

   5. Applied rewrites 93.6%

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

   if 2.50000000000000004e99 < y

   1. Initial program 85.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 95.8

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

      7. lift-+.f64 N/A

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

      8. lift--.f64 N/A

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

      9. associate-+l- N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. associate--r+ N/A

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

      13. lift--.f64 N/A

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

      14. lower--.f64 95.8

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

   4. Applied rewrites 95.8%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y}{z}} \cdot x \]
   6. Step-by-step derivation

      1. lower-/.f64 85.4

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

   7. Applied rewrites 85.4%

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

Alternative 5: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+26}:\\ \;\;\;\;\frac{x\_m}{z} \cdot y\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{x\_m}{z} - x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -8e+26)
    (* (/ x_m z) y)
    (if (<= y 2.5e+99) (- (/ x_m z) x_m) (* (/ y z) x_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -8e+26) {
		tmp = (x_m / z) * y;
	} else if (y <= 2.5e+99) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = (y / z) * x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8d+26)) then
        tmp = (x_m / z) * y
    else if (y <= 2.5d+99) then
        tmp = (x_m / z) - x_m
    else
        tmp = (y / z) * x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= -8e+26) {
		tmp = (x_m / z) * y;
	} else if (y <= 2.5e+99) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = (y / z) * x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -8e+26:
		tmp = (x_m / z) * y
	elif y <= 2.5e+99:
		tmp = (x_m / z) - x_m
	else:
		tmp = (y / z) * x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -8e+26)
		tmp = Float64(Float64(x_m / z) * y);
	elseif (y <= 2.5e+99)
		tmp = Float64(Float64(x_m / z) - x_m);
	else
		tmp = Float64(Float64(y / z) * x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= -8e+26)
		tmp = (x_m / z) * y;
	elseif (y <= 2.5e+99)
		tmp = (x_m / z) - x_m;
	else
		tmp = (y / z) * x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, -8e+26], N[(N[(x$95$m / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 2.5e+99], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000038e26

   1. Initial program 96.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 81.8

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

   5. Applied rewrites 81.8%

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

   if -8.00000000000000038e26 < y < 2.50000000000000004e99

   1. Initial program 81.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. sub-neg N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. associate-/l* N/A

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

      8. *-rgt-identity N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 93.6

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

   5. Applied rewrites 93.6%

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

   if 2.50000000000000004e99 < y

   1. Initial program 85.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 95.8

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

      7. lift-+.f64 N/A

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

      8. lift--.f64 N/A

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

      9. associate-+l- N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. associate--r+ N/A

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

      13. lift--.f64 N/A

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

      14. lower--.f64 95.8

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

   4. Applied rewrites 95.8%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y}{z}} \cdot x \]
   6. Step-by-step derivation

      1. lower-/.f64 85.4

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

   7. Applied rewrites 85.4%

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

Alternative 6: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{x\_m}{z} \cdot y\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+99}:\\ \;\;\;\;\frac{x\_m}{z} - x\_m\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* (/ x_m z) y)))
   (* x_s (if (<= y -8e+26) t_0 (if (<= y 1.85e+99) (- (/ x_m z) x_m) t_0)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = (x_m / z) * y;
	double tmp;
	if (y <= -8e+26) {
		tmp = t_0;
	} else if (y <= 1.85e+99) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = t_0;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x_m / z) * y
    if (y <= (-8d+26)) then
        tmp = t_0
    else if (y <= 1.85d+99) then
        tmp = (x_m / z) - x_m
    else
        tmp = t_0
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = (x_m / z) * y;
	double tmp;
	if (y <= -8e+26) {
		tmp = t_0;
	} else if (y <= 1.85e+99) {
		tmp = (x_m / z) - x_m;
	} else {
		tmp = t_0;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	t_0 = (x_m / z) * y
	tmp = 0
	if y <= -8e+26:
		tmp = t_0
	elif y <= 1.85e+99:
		tmp = (x_m / z) - x_m
	else:
		tmp = t_0
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(Float64(x_m / z) * y)
	tmp = 0.0
	if (y <= -8e+26)
		tmp = t_0;
	elseif (y <= 1.85e+99)
		tmp = Float64(Float64(x_m / z) - x_m);
	else
		tmp = t_0;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = (x_m / z) * y;
	tmp = 0.0;
	if (y <= -8e+26)
		tmp = t_0;
	elseif (y <= 1.85e+99)
		tmp = (x_m / z) - x_m;
	else
		tmp = t_0;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(N[(x$95$m / z), $MachinePrecision] * y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -8e+26], t$95$0, If[LessEqual[y, 1.85e+99], N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision], t$95$0]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000038e26 or 1.85000000000000005e99 < y

   1. Initial program 91.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if -8.00000000000000038e26 < y < 1.85000000000000005e99

   1. Initial program 81.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. sub-neg N/A

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

      4. *-inverses N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-in N/A

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

      7. associate-/l* N/A

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

      8. *-rgt-identity N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 93.6

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

   5. Applied rewrites 93.6%

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

Alternative 7: 99.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.3 \cdot 10^{-45}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y - z, x\_m, x\_m\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \left(\left(y - z\right) - -1\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1.3e-45)
    (/ (fma (- y z) x_m x_m) z)
    (* (/ x_m z) (- (- y z) -1.0)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 1.3e-45) {
		tmp = fma((y - z), x_m, x_m) / z;
	} else {
		tmp = (x_m / z) * ((y - z) - -1.0);
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 1.3e-45)
		tmp = Float64(fma(Float64(y - z), x_m, x_m) / z);
	else
		tmp = Float64(Float64(x_m / z) * Float64(Float64(y - z) - -1.0));
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 1.3e-45], N[(N[(N[(y - z), $MachinePrecision] * x$95$m + x$95$m), $MachinePrecision] / z), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.29999999999999993e-45

   1. Initial program 91.0%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 91.0

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

   4. Applied rewrites 91.0%

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

   if 1.29999999999999993e-45 < x

   1. Initial program 73.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.9

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

      8. lift-+.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-+l- N/A

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

      13. associate--r+ N/A

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

      14. lift--.f64 N/A

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

      15. lower--.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 8: 64.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\_m\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= z -1.0) (- x_m) (if (<= z 1.0) (/ x_m z) (- x_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x_m;
	} else if (z <= 1.0) {
		tmp = x_m / z;
	} else {
		tmp = -x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = -x_m
    else if (z <= 1.0d0) then
        tmp = x_m / z
    else
        tmp = -x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x_m;
	} else if (z <= 1.0) {
		tmp = x_m / z;
	} else {
		tmp = -x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x_m
	elif z <= 1.0:
		tmp = x_m / z
	else:
		tmp = -x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x_m);
	elseif (z <= 1.0)
		tmp = Float64(x_m / z);
	else
		tmp = Float64(-x_m);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -x_m;
	elseif (z <= 1.0)
		tmp = x_m / z;
	else
		tmp = -x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, -1.0], (-x$95$m), If[LessEqual[z, 1.0], N[(x$95$m / z), $MachinePrecision], (-x$95$m)]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 70.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(x\right)} \]

      2. lower-neg.f64 72.7

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

   5. Applied rewrites 72.7%

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

   if -1 < z < 1

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. div-sub N/A

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

      4. associate-/l* N/A

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

      5. *-inverses N/A

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

      6. *-rgt-identity N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 53.8

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

   7. Applied rewrites 53.8%

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

   8. Taylor expanded in z around 0

      \[\leadsto \frac{x}{\color{blue}{z}} \]
   9. Step-by-step derivation

   10. Applied rewrites 53.0%

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

Alternative 9: 65.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(\frac{x\_m}{z} - x\_m\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (- (/ x_m z) x_m)))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * ((x_m / z) - x_m);
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * ((x_m / z) - x_m)
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * ((x_m / z) - x_m);
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * ((x_m / z) - x_m)

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(Float64(x_m / z) - x_m))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * ((x_m / z) - x_m);
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * N[(N[(x$95$m / z), $MachinePrecision] - x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.6%

   \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. associate-/l* N/A

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

   2. div-sub N/A

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

   3. sub-neg N/A

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

   4. *-inverses N/A

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

   5. metadata-eval N/A

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

   6. distribute-lft-in N/A

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

   7. associate-/l* N/A

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

   8. *-rgt-identity N/A

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

   9. *-commutative N/A

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

   10. mul-1-neg N/A

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

   11. unsub-neg N/A

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

   12. lower--.f64 N/A

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

   13. lower-/.f64 63.4

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

5. Applied rewrites 63.4%

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

Alternative 10: 38.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(-x\_m\right) \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (- x_m)))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * -x_m;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * -x_m
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * -x_m;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * -x_m

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(-x_m))
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * -x_m;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * (-x$95$m)), $MachinePrecision]

Derivation

1. Initial program 85.6%

   \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(x\right)} \]

   2. lower-neg.f64 37.3

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

5. Applied rewrites 37.3%

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

Developer Target 1: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ 1.0 y) (/ x z)) x)))
   (if (< x -2.71483106713436e-162)
     t_0
     (if (< x 3.874108816439546e-197)
       (* (* x (+ (- y z) 1.0)) (/ 1.0 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((1.0 + y) * (x / z)) - x
	tmp = 0
	if x < -2.71483106713436e-162:
		tmp = t_0
	elif x < 3.874108816439546e-197:
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x)
	tmp = 0.0
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) * Float64(1.0 / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((1.0 + y) * (x / z)) - x;
	tmp = 0.0;
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Less[x, -2.71483106713436e-162], t$95$0, If[Less[x, 3.874108816439546e-197], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024273 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -67870776678359/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (+ 1 y) (/ x z)) x) (if (< x 1937054408219773/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x))))

  (/ (* x (+ (- y z) 1.0)) z))