Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 83.9% → 96.2%

Time: 10.3s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 83.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 9 \cdot 10^{+56}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, x\_m, x\_m \cdot y\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 9e+56)
    (/ (fma (- z) x_m (* x_m y)) (- t z))
    (* (/ x_m (- t z)) (- y z)))))

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) {
	double tmp;
	if (x_m <= 9e+56) {
		tmp = fma(-z, x_m, (x_m * y)) / (t - z);
	} else {
		tmp = (x_m / (t - z)) * (y - z);
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 9e+56)
		tmp = Float64(fma(Float64(-z), x_m, Float64(x_m * y)) / Float64(t - z));
	else
		tmp = Float64(Float64(x_m / Float64(t - z)) * Float64(y - z));
	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_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 9e+56], N[(N[((-z) * x$95$m + N[(x$95$m * y), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 9.0000000000000006e56

   1. Initial program 92.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 92.5

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

   4. Applied egg-rr 92.5%

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

   if 9.0000000000000006e56 < x

   1. Initial program 59.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 98.2

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

   4. Applied egg-rr 98.2%

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

Alternative 2: 86.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{t - z} \cdot \left(y - z\right)\\ t_2 := \frac{x\_m \cdot \left(y - z\right)}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-176}:\\ \;\;\;\;\frac{x\_m \cdot z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (/ x_m (- t z)) (- y z))) (t_2 (/ (* x_m (- y z)) (- t z))))
   (*
    x_s
    (if (<= t_2 -2e-175) t_1 (if (<= t_2 4e-176) (/ (* x_m z) (- z t)) t_1)))))

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) {
	double t_1 = (x_m / (t - z)) * (y - z);
	double t_2 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -2e-175) {
		tmp = t_1;
	} else if (t_2 <= 4e-176) {
		tmp = (x_m * z) / (z - t);
	} else {
		tmp = t_1;
	}
	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, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x_m / (t - z)) * (y - z)
    t_2 = (x_m * (y - z)) / (t - z)
    if (t_2 <= (-2d-175)) then
        tmp = t_1
    else if (t_2 <= 4d-176) then
        tmp = (x_m * z) / (z - t)
    else
        tmp = t_1
    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) {
	double t_1 = (x_m / (t - z)) * (y - z);
	double t_2 = (x_m * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -2e-175) {
		tmp = t_1;
	} else if (t_2 <= 4e-176) {
		tmp = (x_m * z) / (z - t);
	} else {
		tmp = t_1;
	}
	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):
	t_1 = (x_m / (t - z)) * (y - z)
	t_2 = (x_m * (y - z)) / (t - z)
	tmp = 0
	if t_2 <= -2e-175:
		tmp = t_1
	elif t_2 <= 4e-176:
		tmp = (x_m * z) / (z - t)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / Float64(t - z)) * Float64(y - z))
	t_2 = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_2 <= -2e-175)
		tmp = t_1;
	elseif (t_2 <= 4e-176)
		tmp = Float64(Float64(x_m * z) / Float64(z - t));
	else
		tmp = t_1;
	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)
	t_1 = (x_m / (t - z)) * (y - z);
	t_2 = (x_m * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_2 <= -2e-175)
		tmp = t_1;
	elseif (t_2 <= 4e-176)
		tmp = (x_m * z) / (z - t);
	else
		tmp = t_1;
	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_, t_] := Block[{t$95$1 = N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$2, -2e-175], t$95$1, If[LessEqual[t$95$2, 4e-176], N[(N[(x$95$m * z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -2e-175 or 4e-176 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 80.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 95.1

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

   4. Applied egg-rr 95.1%

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

   if -2e-175 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 4e-176

   1. Initial program 99.8%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 94.3

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

   4. Applied egg-rr 94.3%

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

      1. frac-2neg N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

      5. neg-sub0 N/A

         \[\leadsto \frac{x}{\color{blue}{0 - \left(t - z\right)}} \cdot \left(\mathsf{neg}\left(\left(y - z\right)\right)\right) \]

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. associate--r+ N/A

         \[\leadsto \frac{x}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t}} \cdot \left(\mathsf{neg}\left(\left(y - z\right)\right)\right) \]

      9. neg-sub0 N/A

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

      10. remove-double-neg N/A

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

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

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

      12. neg-sub0 N/A

          \[\leadsto \frac{x}{z - t} \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. associate--r+ N/A

          \[\leadsto \frac{x}{z - t} \cdot \color{blue}{\left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - y\right)} \]

      16. neg-sub0 N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 58.1

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

   6. Applied egg-rr 58.1%

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

   7. Taylor expanded in z around inf

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

   9. Simplified 52.4%

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

       1. *-commutative N/A

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

       2. associate-*r/ N/A

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

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

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

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

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

       5. --lowering--.f64 82.8

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

   11. Applied egg-rr 82.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -2 \cdot 10^{-175}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 4 \cdot 10^{-176}:\\ \;\;\;\;\frac{x \cdot z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-39}:\\ \;\;\;\;x\_m \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+26}:\\ \;\;\;\;x\_m \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x\_m, \frac{t}{z}, x\_m\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -3.4e+44)
    x_m
    (if (<= z 3.5e-39)
      (* x_m (/ y t))
      (if (<= z 5.4e+26) (* x_m (/ y (- z))) (fma x_m (/ t 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 t) {
	double tmp;
	if (z <= -3.4e+44) {
		tmp = x_m;
	} else if (z <= 3.5e-39) {
		tmp = x_m * (y / t);
	} else if (z <= 5.4e+26) {
		tmp = x_m * (y / -z);
	} else {
		tmp = fma(x_m, (t / 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, t)
	tmp = 0.0
	if (z <= -3.4e+44)
		tmp = x_m;
	elseif (z <= 3.5e-39)
		tmp = Float64(x_m * Float64(y / t));
	elseif (z <= 5.4e+26)
		tmp = Float64(x_m * Float64(y / Float64(-z)));
	else
		tmp = fma(x_m, Float64(t / z), 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_, t_] := N[(x$95$s * If[LessEqual[z, -3.4e+44], x$95$m, If[LessEqual[z, 3.5e-39], N[(x$95$m * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+26], N[(x$95$m * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(t / z), $MachinePrecision] + x$95$m), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -3.4e44

   1. Initial program 73.6%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 57.5%

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

   if -3.4e44 < z < 3.5e-39

   1. Initial program 93.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 94.9

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 63.8

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

   7. Simplified 63.8%

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

   if 3.5e-39 < z < 5.4e26

   1. Initial program 90.3%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - \frac{x \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* N/A

         \[\leadsto 0 - \color{blue}{x \cdot \frac{y - z}{z}} \]

      4. div-sub N/A

         \[\leadsto 0 - x \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg N/A

         \[\leadsto 0 - x \cdot \color{blue}{\left(\frac{y}{z} + \left(\mathsf{neg}\left(\frac{z}{z}\right)\right)\right)} \]

      6. *-inverses N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      8. distribute-rgt-in N/A

         \[\leadsto 0 - \color{blue}{\left(\frac{y}{z} \cdot x + -1 \cdot x\right)} \]

      9. *-commutative N/A

         \[\leadsto 0 - \left(\color{blue}{x \cdot \frac{y}{z}} + -1 \cdot x\right) \]

      10. associate-/l* N/A

          \[\leadsto 0 - \left(\color{blue}{\frac{x \cdot y}{z}} + -1 \cdot x\right) \]

      11. mul-1-neg N/A

          \[\leadsto 0 - \left(\frac{x \cdot y}{z} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      12. unsub-neg N/A

          \[\leadsto 0 - \color{blue}{\left(\frac{x \cdot y}{z} - x\right)} \]

      13. associate-+l- N/A

          \[\leadsto \color{blue}{\left(0 - \frac{x \cdot y}{z}\right) + x} \]

      14. neg-sub0 N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. --lowering--.f64 N/A

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

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

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

      23. /-lowering-/.f64 69.2

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

   5. Simplified 69.2%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. distribute-neg-frac2 N/A

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

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

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

      9. neg-lowering-neg.f64 49.4

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

   8. Simplified 49.4%

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

   if 5.4e26 < z

   1. Initial program 73.9%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 60.8

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 60.6

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

   8. Simplified 60.6%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{y - z}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -11200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, x\_m, x\_m\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ (- y z) t))))
   (*
    x_s
    (if (<= t -11200000000000.0)
      t_1
      (if (<= t 7.2e+98) (fma (/ y (- z)) x_m x_m) t_1)))))

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) {
	double t_1 = x_m * ((y - z) / t);
	double tmp;
	if (t <= -11200000000000.0) {
		tmp = t_1;
	} else if (t <= 7.2e+98) {
		tmp = fma((y / -z), x_m, x_m);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -11200000000000.0)
		tmp = t_1;
	elseif (t <= 7.2e+98)
		tmp = fma(Float64(y / Float64(-z)), x_m, x_m);
	else
		tmp = t_1;
	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_, t_] := Block[{t$95$1 = N[(x$95$m * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -11200000000000.0], t$95$1, If[LessEqual[t, 7.2e+98], N[(N[(y / (-z)), $MachinePrecision] * x$95$m + x$95$m), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.12e13 or 7.19999999999999962e98 < t

   1. Initial program 82.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 94.9

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 84.4%

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

   if -1.12e13 < t < 7.19999999999999962e98

   1. Initial program 85.6%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - \frac{x \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* N/A

         \[\leadsto 0 - \color{blue}{x \cdot \frac{y - z}{z}} \]

      4. div-sub N/A

         \[\leadsto 0 - x \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg N/A

         \[\leadsto 0 - x \cdot \color{blue}{\left(\frac{y}{z} + \left(\mathsf{neg}\left(\frac{z}{z}\right)\right)\right)} \]

      6. *-inverses N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      8. distribute-rgt-in N/A

         \[\leadsto 0 - \color{blue}{\left(\frac{y}{z} \cdot x + -1 \cdot x\right)} \]

      9. *-commutative N/A

         \[\leadsto 0 - \left(\color{blue}{x \cdot \frac{y}{z}} + -1 \cdot x\right) \]

      10. associate-/l* N/A

          \[\leadsto 0 - \left(\color{blue}{\frac{x \cdot y}{z}} + -1 \cdot x\right) \]

      11. mul-1-neg N/A

          \[\leadsto 0 - \left(\frac{x \cdot y}{z} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      12. unsub-neg N/A

          \[\leadsto 0 - \color{blue}{\left(\frac{x \cdot y}{z} - x\right)} \]

      13. associate-+l- N/A

          \[\leadsto \color{blue}{\left(0 - \frac{x \cdot y}{z}\right) + x} \]

      14. neg-sub0 N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. --lowering--.f64 N/A

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

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

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

      23. /-lowering-/.f64 79.0

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

   5. Simplified 79.0%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. clear-num N/A

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

      5. associate-*r/ N/A

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

      6. div-inv N/A

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

      7. times-frac N/A

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

      8. clear-num N/A

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

      9. /-rgt-identity N/A

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

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

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

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

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

      12. neg-lowering-neg.f64 81.3

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

   7. Applied egg-rr 81.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -11200000000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{-z}, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{y - z}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.34 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x\_m}{-z}, y, x\_m\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ (- y z) t))))
   (*
    x_s
    (if (<= t -1.34e+14)
      t_1
      (if (<= t 9e+98) (fma (/ x_m (- z)) y x_m) t_1)))))

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) {
	double t_1 = x_m * ((y - z) / t);
	double tmp;
	if (t <= -1.34e+14) {
		tmp = t_1;
	} else if (t <= 9e+98) {
		tmp = fma((x_m / -z), y, x_m);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -1.34e+14)
		tmp = t_1;
	elseif (t <= 9e+98)
		tmp = fma(Float64(x_m / Float64(-z)), y, x_m);
	else
		tmp = t_1;
	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_, t_] := Block[{t$95$1 = N[(x$95$m * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -1.34e+14], t$95$1, If[LessEqual[t, 9e+98], N[(N[(x$95$m / (-z)), $MachinePrecision] * y + x$95$m), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.34e14 or 9.0000000000000004e98 < t

   1. Initial program 82.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 94.9

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 84.4%

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

   if -1.34e14 < t < 9.0000000000000004e98

   1. Initial program 85.6%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - \frac{x \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* N/A

         \[\leadsto 0 - \color{blue}{x \cdot \frac{y - z}{z}} \]

      4. div-sub N/A

         \[\leadsto 0 - x \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg N/A

         \[\leadsto 0 - x \cdot \color{blue}{\left(\frac{y}{z} + \left(\mathsf{neg}\left(\frac{z}{z}\right)\right)\right)} \]

      6. *-inverses N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      8. distribute-rgt-in N/A

         \[\leadsto 0 - \color{blue}{\left(\frac{y}{z} \cdot x + -1 \cdot x\right)} \]

      9. *-commutative N/A

         \[\leadsto 0 - \left(\color{blue}{x \cdot \frac{y}{z}} + -1 \cdot x\right) \]

      10. associate-/l* N/A

          \[\leadsto 0 - \left(\color{blue}{\frac{x \cdot y}{z}} + -1 \cdot x\right) \]

      11. mul-1-neg N/A

          \[\leadsto 0 - \left(\frac{x \cdot y}{z} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      12. unsub-neg N/A

          \[\leadsto 0 - \color{blue}{\left(\frac{x \cdot y}{z} - x\right)} \]

      13. associate-+l- N/A

          \[\leadsto \color{blue}{\left(0 - \frac{x \cdot y}{z}\right) + x} \]

      14. neg-sub0 N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. --lowering--.f64 N/A

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

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

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

      23. /-lowering-/.f64 79.0

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

   5. Simplified 79.0%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. distribute-frac-neg2 N/A

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

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

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

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

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

      8. neg-lowering-neg.f64 79.0

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

   7. Applied egg-rr 79.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.34 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{-z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{y - z}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2150000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+98}:\\ \;\;\;\;x\_m - y \cdot \frac{x\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ (- y z) t))))
   (*
    x_s
    (if (<= t -2150000000000.0)
      t_1
      (if (<= t 7.2e+98) (- x_m (* y (/ x_m z))) t_1)))))

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) {
	double t_1 = x_m * ((y - z) / t);
	double tmp;
	if (t <= -2150000000000.0) {
		tmp = t_1;
	} else if (t <= 7.2e+98) {
		tmp = x_m - (y * (x_m / z));
	} else {
		tmp = t_1;
	}
	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, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * ((y - z) / t)
    if (t <= (-2150000000000.0d0)) then
        tmp = t_1
    else if (t <= 7.2d+98) then
        tmp = x_m - (y * (x_m / z))
    else
        tmp = t_1
    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) {
	double t_1 = x_m * ((y - z) / t);
	double tmp;
	if (t <= -2150000000000.0) {
		tmp = t_1;
	} else if (t <= 7.2e+98) {
		tmp = x_m - (y * (x_m / z));
	} else {
		tmp = t_1;
	}
	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):
	t_1 = x_m * ((y - z) / t)
	tmp = 0
	if t <= -2150000000000.0:
		tmp = t_1
	elif t <= 7.2e+98:
		tmp = x_m - (y * (x_m / z))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -2150000000000.0)
		tmp = t_1;
	elseif (t <= 7.2e+98)
		tmp = Float64(x_m - Float64(y * Float64(x_m / z)));
	else
		tmp = t_1;
	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)
	t_1 = x_m * ((y - z) / t);
	tmp = 0.0;
	if (t <= -2150000000000.0)
		tmp = t_1;
	elseif (t <= 7.2e+98)
		tmp = x_m - (y * (x_m / z));
	else
		tmp = t_1;
	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_, t_] := Block[{t$95$1 = N[(x$95$m * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -2150000000000.0], t$95$1, If[LessEqual[t, 7.2e+98], N[(x$95$m - N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.15e12 or 7.19999999999999962e98 < t

   1. Initial program 82.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 94.9

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 84.4%

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

   if -2.15e12 < t < 7.19999999999999962e98

   1. Initial program 85.6%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - \frac{x \cdot \left(y - z\right)}{z}} \]

      3. associate-/l* N/A

         \[\leadsto 0 - \color{blue}{x \cdot \frac{y - z}{z}} \]

      4. div-sub N/A

         \[\leadsto 0 - x \cdot \color{blue}{\left(\frac{y}{z} - \frac{z}{z}\right)} \]

      5. sub-neg N/A

         \[\leadsto 0 - x \cdot \color{blue}{\left(\frac{y}{z} + \left(\mathsf{neg}\left(\frac{z}{z}\right)\right)\right)} \]

      6. *-inverses N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      8. distribute-rgt-in N/A

         \[\leadsto 0 - \color{blue}{\left(\frac{y}{z} \cdot x + -1 \cdot x\right)} \]

      9. *-commutative N/A

         \[\leadsto 0 - \left(\color{blue}{x \cdot \frac{y}{z}} + -1 \cdot x\right) \]

      10. associate-/l* N/A

          \[\leadsto 0 - \left(\color{blue}{\frac{x \cdot y}{z}} + -1 \cdot x\right) \]

      11. mul-1-neg N/A

          \[\leadsto 0 - \left(\frac{x \cdot y}{z} + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right) \]

      12. unsub-neg N/A

          \[\leadsto 0 - \color{blue}{\left(\frac{x \cdot y}{z} - x\right)} \]

      13. associate-+l- N/A

          \[\leadsto \color{blue}{\left(0 - \frac{x \cdot y}{z}\right) + x} \]

      14. neg-sub0 N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. --lowering--.f64 N/A

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

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

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

      23. /-lowering-/.f64 79.0

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

   5. Simplified 79.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2150000000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+98}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{z}{z - t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -155000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ z (- z t)))))
   (*
    x_s
    (if (<= z -155000000.0)
      t_1
      (if (<= z 1.95e+34) (* x_m (/ y (- t z))) t_1)))))

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) {
	double t_1 = x_m * (z / (z - t));
	double tmp;
	if (z <= -155000000.0) {
		tmp = t_1;
	} else if (z <= 1.95e+34) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	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, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * (z / (z - t))
    if (z <= (-155000000.0d0)) then
        tmp = t_1
    else if (z <= 1.95d+34) then
        tmp = x_m * (y / (t - z))
    else
        tmp = t_1
    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) {
	double t_1 = x_m * (z / (z - t));
	double tmp;
	if (z <= -155000000.0) {
		tmp = t_1;
	} else if (z <= 1.95e+34) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	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):
	t_1 = x_m * (z / (z - t))
	tmp = 0
	if z <= -155000000.0:
		tmp = t_1
	elif z <= 1.95e+34:
		tmp = x_m * (y / (t - z))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -155000000.0)
		tmp = t_1;
	elseif (z <= 1.95e+34)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	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)
	t_1 = x_m * (z / (z - t));
	tmp = 0.0;
	if (z <= -155000000.0)
		tmp = t_1;
	elseif (z <= 1.95e+34)
		tmp = x_m * (y / (t - z));
	else
		tmp = t_1;
	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_, t_] := Block[{t$95$1 = N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -155000000.0], t$95$1, If[LessEqual[z, 1.95e+34], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e8 or 1.9500000000000001e34 < z

   1. Initial program 74.2%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 62.6

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

   5. Simplified 62.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. distribute-frac-neg N/A

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

      5. distribute-frac-neg2 N/A

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

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

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

      7. neg-sub0 N/A

         \[\leadsto \frac{z}{\color{blue}{0 - \left(t - z\right)}} \cdot x \]

      8. sub-neg N/A

         \[\leadsto \frac{z}{0 - \color{blue}{\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)}} \cdot x \]

      9. +-commutative N/A

         \[\leadsto \frac{z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + t\right)}} \cdot x \]

      10. associate--r+ N/A

          \[\leadsto \frac{z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t}} \cdot x \]

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 79.7

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

   7. Applied egg-rr 79.7%

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

   if -1.55e8 < z < 1.9500000000000001e34

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 76.7

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

   5. Simplified 76.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -155000000:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{y}{t - z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-97}:\\ \;\;\;\;z \cdot \frac{x\_m}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ y (- t z)))))
   (*
    x_s
    (if (<= y -1.4e-65) t_1 (if (<= y 2.1e-97) (* z (/ x_m (- z t))) t_1)))))

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) {
	double t_1 = x_m * (y / (t - z));
	double tmp;
	if (y <= -1.4e-65) {
		tmp = t_1;
	} else if (y <= 2.1e-97) {
		tmp = z * (x_m / (z - t));
	} else {
		tmp = t_1;
	}
	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, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * (y / (t - z))
    if (y <= (-1.4d-65)) then
        tmp = t_1
    else if (y <= 2.1d-97) then
        tmp = z * (x_m / (z - t))
    else
        tmp = t_1
    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) {
	double t_1 = x_m * (y / (t - z));
	double tmp;
	if (y <= -1.4e-65) {
		tmp = t_1;
	} else if (y <= 2.1e-97) {
		tmp = z * (x_m / (z - t));
	} else {
		tmp = t_1;
	}
	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):
	t_1 = x_m * (y / (t - z))
	tmp = 0
	if y <= -1.4e-65:
		tmp = t_1
	elif y <= 2.1e-97:
		tmp = z * (x_m / (z - t))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -1.4e-65)
		tmp = t_1;
	elseif (y <= 2.1e-97)
		tmp = Float64(z * Float64(x_m / Float64(z - t)));
	else
		tmp = t_1;
	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)
	t_1 = x_m * (y / (t - z));
	tmp = 0.0;
	if (y <= -1.4e-65)
		tmp = t_1;
	elseif (y <= 2.1e-97)
		tmp = z * (x_m / (z - t));
	else
		tmp = t_1;
	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_, t_] := Block[{t$95$1 = N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -1.4e-65], t$95$1, If[LessEqual[y, 2.1e-97], N[(z * N[(x$95$m / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-65 or 2.1000000000000001e-97 < y

   1. Initial program 82.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 70.2

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

   5. Simplified 70.2%

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

   if -1.4e-65 < y < 2.1000000000000001e-97

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 81.4

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

   5. Simplified 81.4%

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

      1. frac-2neg N/A

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

      2. div-inv N/A

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

      3. distribute-rgt-neg-out N/A

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

      4. remove-double-neg N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. div-inv N/A

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

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

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

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

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

      10. neg-sub0 N/A

          \[\leadsto z \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      11. sub-neg N/A

          \[\leadsto z \cdot \frac{x}{0 - \color{blue}{\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)}} \]

      12. +-commutative N/A

          \[\leadsto z \cdot \frac{x}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + t\right)}} \]

      13. associate--r+ N/A

          \[\leadsto z \cdot \frac{x}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t}} \]

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. --lowering--.f64 84.9

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

   7. Applied egg-rr 84.9%

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

Alternative 9: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+95}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+59}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x\_m, \frac{t}{z}, x\_m\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -2e+95)
    x_m
    (if (<= z 1.1e+59) (* x_m (/ y (- t z))) (fma x_m (/ t 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 t) {
	double tmp;
	if (z <= -2e+95) {
		tmp = x_m;
	} else if (z <= 1.1e+59) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = fma(x_m, (t / 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, t)
	tmp = 0.0
	if (z <= -2e+95)
		tmp = x_m;
	elseif (z <= 1.1e+59)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = fma(x_m, Float64(t / z), 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_, t_] := N[(x$95$s * If[LessEqual[z, -2e+95], x$95$m, If[LessEqual[z, 1.1e+59], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(t / z), $MachinePrecision] + x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000004e95

   1. Initial program 71.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 62.1%

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

   if -2.00000000000000004e95 < z < 1.1e59

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 73.3

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

   5. Simplified 73.3%

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

   if 1.1e59 < z

   1. Initial program 70.9%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 61.9

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

   5. Simplified 61.9%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 63.4

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

   8. Simplified 63.4%

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

Alternative 10: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 0.0005:\\ \;\;\;\;x\_m \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x\_m, \frac{t}{z}, x\_m\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -1.95e+43)
    x_m
    (if (<= z 0.0005) (* x_m (/ y t)) (fma x_m (/ t 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 t) {
	double tmp;
	if (z <= -1.95e+43) {
		tmp = x_m;
	} else if (z <= 0.0005) {
		tmp = x_m * (y / t);
	} else {
		tmp = fma(x_m, (t / 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, t)
	tmp = 0.0
	if (z <= -1.95e+43)
		tmp = x_m;
	elseif (z <= 0.0005)
		tmp = Float64(x_m * Float64(y / t));
	else
		tmp = fma(x_m, Float64(t / z), 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_, t_] := N[(x$95$s * If[LessEqual[z, -1.95e+43], x$95$m, If[LessEqual[z, 0.0005], N[(x$95$m * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(t / z), $MachinePrecision] + x$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e43

   1. Initial program 73.6%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 57.5%

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

   if -1.95e43 < z < 5.0000000000000001e-4

   1. Initial program 93.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 95.3

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 61.4

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

   7. Simplified 61.4%

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

   if 5.0000000000000001e-4 < z

   1. Initial program 76.1%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 57.5

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

   5. Simplified 57.5%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 55.8

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

   8. Simplified 55.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{t}{z}, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0005:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+43}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-31}:\\ \;\;\;\;x\_m \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -7.2e+43) x_m (if (<= z 3.6e-31) (* x_m (/ y t)) 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 t) {
	double tmp;
	if (z <= -7.2e+43) {
		tmp = x_m;
	} else if (z <= 3.6e-31) {
		tmp = x_m * (y / t);
	} 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, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.2d+43)) then
        tmp = x_m
    else if (z <= 3.6d-31) then
        tmp = x_m * (y / t)
    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 t) {
	double tmp;
	if (z <= -7.2e+43) {
		tmp = x_m;
	} else if (z <= 3.6e-31) {
		tmp = x_m * (y / t);
	} 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, t):
	tmp = 0
	if z <= -7.2e+43:
		tmp = x_m
	elif z <= 3.6e-31:
		tmp = x_m * (y / t)
	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, t)
	tmp = 0.0
	if (z <= -7.2e+43)
		tmp = x_m;
	elseif (z <= 3.6e-31)
		tmp = Float64(x_m * Float64(y / t));
	else
		tmp = 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, t)
	tmp = 0.0;
	if (z <= -7.2e+43)
		tmp = x_m;
	elseif (z <= 3.6e-31)
		tmp = x_m * (y / t);
	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_, t_] := N[(x$95$s * If[LessEqual[z, -7.2e+43], x$95$m, If[LessEqual[z, 3.6e-31], N[(x$95$m * N[(y / t), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000002e43 or 3.60000000000000004e-31 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 54.0%

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

   if -7.2000000000000002e43 < z < 3.60000000000000004e-31

   1. Initial program 93.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 94.9

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 64.1

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

   7. Simplified 64.1%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{x\_m}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -1.65e+43) x_m (if (<= z 6e-30) (* y (/ x_m t)) 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 t) {
	double tmp;
	if (z <= -1.65e+43) {
		tmp = x_m;
	} else if (z <= 6e-30) {
		tmp = y * (x_m / t);
	} 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, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.65d+43)) then
        tmp = x_m
    else if (z <= 6d-30) then
        tmp = y * (x_m / t)
    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 t) {
	double tmp;
	if (z <= -1.65e+43) {
		tmp = x_m;
	} else if (z <= 6e-30) {
		tmp = y * (x_m / t);
	} 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, t):
	tmp = 0
	if z <= -1.65e+43:
		tmp = x_m
	elif z <= 6e-30:
		tmp = y * (x_m / t)
	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, t)
	tmp = 0.0
	if (z <= -1.65e+43)
		tmp = x_m;
	elseif (z <= 6e-30)
		tmp = Float64(y * Float64(x_m / t));
	else
		tmp = 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, t)
	tmp = 0.0;
	if (z <= -1.65e+43)
		tmp = x_m;
	elseif (z <= 6e-30)
		tmp = y * (x_m / t);
	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_, t_] := N[(x$95$s * If[LessEqual[z, -1.65e+43], x$95$m, If[LessEqual[z, 6e-30], N[(y * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.6500000000000001e43 or 5.9999999999999998e-30 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 54.0%

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

   if -1.6500000000000001e43 < z < 5.9999999999999998e-30

   1. Initial program 93.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 94.9

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 64.1

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

   7. Simplified 64.1%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. /-lowering-/.f64 59.4

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

   9. Applied egg-rr 59.4%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 10^{+57}:\\ \;\;\;\;\frac{x\_m \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1e+57) (/ (* x_m (- y z)) (- t z)) (* (/ x_m (- t z)) (- y z)))))

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) {
	double tmp;
	if (x_m <= 1e+57) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (x_m / (t - z)) * (y - z);
	}
	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, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x_m <= 1d+57) then
        tmp = (x_m * (y - z)) / (t - z)
    else
        tmp = (x_m / (t - z)) * (y - z)
    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) {
	double tmp;
	if (x_m <= 1e+57) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (x_m / (t - z)) * (y - z);
	}
	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):
	tmp = 0
	if x_m <= 1e+57:
		tmp = (x_m * (y - z)) / (t - z)
	else:
		tmp = (x_m / (t - z)) * (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 1e+57)
		tmp = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(x_m / Float64(t - z)) * Float64(y - z));
	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)
	tmp = 0.0;
	if (x_m <= 1e+57)
		tmp = (x_m * (y - z)) / (t - z);
	else
		tmp = (x_m / (t - z)) * (y - z);
	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_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 1e+57], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000005e57

   1. Initial program 92.5%

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

   if 1.00000000000000005e57 < x

   1. Initial program 59.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 98.2

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

   4. Applied egg-rr 98.2%

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

Alternative 14: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

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) {
	return x_s * (x_m * ((y - z) / (t - z)));
}

Fortran

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

Python

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

Julia

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

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * (x_m * ((y - z) / (t - z)));
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_, t_] := N[(x$95$s * N[(x$95$m * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.4%

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

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

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

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

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

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

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

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

   6. --lowering--.f64 97.4

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

4. Applied egg-rr 97.4%

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

5. Final simplification 97.4%

   \[\leadsto x \cdot \frac{y - z}{t - z} \]
6. Add Preprocessing

Alternative 15: 35.3% accurate, 23.0× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t) :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, double t) {
	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, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    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, double t) {
	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, t):
	return x_s * x_m

Julia

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

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	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_, t_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 84.4%

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

3. Taylor expanded in z around inf

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

5. Simplified 32.1%

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

Developer Target 1: 97.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (/ (- t z) (- y z))))

C

double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - z));
}

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return x / ((t - z) / (y - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(t - z) / Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((t - z) / (y - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024198 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ (- t z) (- y z))))

  (/ (* x (- y z)) (- t z)))