Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 88.9% → 96.2%

Time: 13.2s

Alternatives: 10

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

C

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

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) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

C

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

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) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+284}:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \frac{t\_1}{z}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+248}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -1e+284)
     (/ y (* (+ x 1.0) (/ t_1 z)))
     (if (<= t_2 2e+248) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+284) {
		tmp = y / ((x + 1.0) * (t_1 / z));
	} else if (t_2 <= 2e+248) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-1d+284)) then
        tmp = y / ((x + 1.0d0) * (t_1 / z))
    else if (t_2 <= 2d+248) then
        tmp = t_2
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+284) {
		tmp = y / ((x + 1.0) * (t_1 / z));
	} else if (t_2 <= 2e+248) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -1e+284:
		tmp = y / ((x + 1.0) * (t_1 / z))
	elif t_2 <= 2e+248:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e+284)
		tmp = Float64(y / Float64(Float64(x + 1.0) * Float64(t_1 / z)));
	elseif (t_2 <= 2e+248)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e+284)
		tmp = y / ((x + 1.0) * (t_1 / z));
	elseif (t_2 <= 2e+248)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+284], N[(y / N[(N[(x + 1.0), $MachinePrecision] * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+248], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1.00000000000000008e284

   1. Initial program 31.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 31.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 31.4%

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

      1. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{1}{\frac{z \cdot t - x}{x - y \cdot z}}\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(1, \left(\frac{z \cdot t - x}{x - y \cdot z}\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(z \cdot t - x\right), \left(x - y \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(z \cdot t\right), x\right), \left(x - y \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right), \left(x - y \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right), \mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

      7. *-lowering-*.f64 31.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right), \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

   6. Applied egg-rr 31.4%

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

   7. Taylor expanded in y around inf

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

      1. times-frac N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{1 + x}\right), \color{blue}{\left(\frac{z}{t \cdot z - x}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(1 + x\right)\right), \left(\frac{\color{blue}{z}}{t \cdot z - x}\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(x + 1\right)\right), \left(\frac{z}{t \cdot z - x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{+.f64}\left(x, 1\right)\right), \left(\frac{z}{t \cdot z - x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{+.f64}\left(x, 1\right)\right), \mathsf{/.f64}\left(z, \color{blue}{\left(t \cdot z - x\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{+.f64}\left(x, 1\right)\right), \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(\left(t \cdot z\right), \color{blue}{x}\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{+.f64}\left(x, 1\right)\right), \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right) \]

      9. *-lowering-*.f64 88.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{+.f64}\left(x, 1\right)\right), \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right) \]

   9. Simplified 88.8%

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

       1. *-commutative N/A

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

       2. clear-num N/A

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

       3. frac-times N/A

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

       4. *-lft-identity N/A

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

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

          \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{z \cdot t - x}{z} \cdot \left(x + 1\right)\right)}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{z \cdot t - x}{z}\right), \color{blue}{\left(x + 1\right)}\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t - x\right), z\right), \left(\color{blue}{x} + 1\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(z \cdot t\right), x\right), z\right), \left(x + 1\right)\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right), z\right), \left(x + 1\right)\right)\right) \]

       10. +-lowering-+.f64 89.1%

           \[\leadsto \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right), z\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right) \]

   11. Applied egg-rr 89.1%

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

   if -1.00000000000000008e284 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000009e248

   1. Initial program 99.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 2.00000000000000009e248 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 26.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 26.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 26.1%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y}{t}\right), \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{t} + x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{y}{t}\right), x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(1 + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(x + \color{blue}{1}\right)\right) \]

      6. +-lowering-+.f64 91.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 91.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -1 \cdot 10^{+284}:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot \frac{z \cdot t - x}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+248}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-79}:\\ \;\;\;\;\frac{x - \frac{y \cdot z - x}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -9e-111)
     t_1
     (if (<= z 5.3e-79) (/ (- x (/ (- (* y z) x) x)) (+ x 1.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -9e-111) {
		tmp = t_1;
	} else if (z <= 5.3e-79) {
		tmp = (x - (((y * z) - x) / x)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-9d-111)) then
        tmp = t_1
    else if (z <= 5.3d-79) then
        tmp = (x - (((y * z) - x) / x)) / (x + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -9e-111) {
		tmp = t_1;
	} else if (z <= 5.3e-79) {
		tmp = (x - (((y * z) - x) / x)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -9e-111:
		tmp = t_1
	elif z <= 5.3e-79:
		tmp = (x - (((y * z) - x) / x)) / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -9e-111)
		tmp = t_1;
	elseif (z <= 5.3e-79)
		tmp = Float64(Float64(x - Float64(Float64(Float64(y * z) - x) / x)) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -9e-111)
		tmp = t_1;
	elseif (z <= 5.3e-79)
		tmp = (x - (((y * z) - x) / x)) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e-111], t$95$1, If[LessEqual[z, 5.3e-79], N[(N[(x - N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999987e-111 or 5.2999999999999998e-79 < z

   1. Initial program 82.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 82.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y}{t}\right), \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{t} + x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{y}{t}\right), x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(1 + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(x + \color{blue}{1}\right)\right) \]

      6. +-lowering-+.f64 84.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 84.3%

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

   if -8.99999999999999987e-111 < z < 5.2999999999999998e-79

   1. Initial program 99.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \color{blue}{\left(-1 \cdot x\right)}\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(\mathsf{neg}\left(x\right)\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(0 - x\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

      3. --lowering--.f64 85.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(0, x\right)\right)\right), \mathsf{+.f64}\left(x, 1\right)\right) \]

   7. Simplified 85.0%

      \[\leadsto \frac{x - \frac{x - y \cdot z}{\color{blue}{0 - x}}}{x + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-111}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-79}:\\ \;\;\;\;\frac{x - \frac{y \cdot z - x}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-78}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -1.02e-112)
     t_1
     (if (<= z 1.55e-78) (/ (+ (- x (* y (/ z x))) 1.0) (+ x 1.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -1.02e-112) {
		tmp = t_1;
	} else if (z <= 1.55e-78) {
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-1.02d-112)) then
        tmp = t_1
    else if (z <= 1.55d-78) then
        tmp = ((x - (y * (z / x))) + 1.0d0) / (x + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -1.02e-112) {
		tmp = t_1;
	} else if (z <= 1.55e-78) {
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -1.02e-112:
		tmp = t_1
	elif z <= 1.55e-78:
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -1.02e-112)
		tmp = t_1;
	elseif (z <= 1.55e-78)
		tmp = Float64(Float64(Float64(x - Float64(y * Float64(z / x))) + 1.0) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -1.02e-112)
		tmp = t_1;
	elseif (z <= 1.55e-78)
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e-112], t$95$1, If[LessEqual[z, 1.55e-78], N[(N[(N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.01999999999999996e-112 or 1.55000000000000009e-78 < z

   1. Initial program 82.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 82.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y}{t}\right), \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{t} + x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{y}{t}\right), x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(1 + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(x + \color{blue}{1}\right)\right) \]

      6. +-lowering-+.f64 84.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 84.3%

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

   if -1.01999999999999996e-112 < z < 1.55000000000000009e-78

   1. Initial program 99.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \left(x + -1 \cdot \frac{y \cdot z}{x}\right)\right), \color{blue}{\left(1 + x\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(x + -1 \cdot \frac{y \cdot z}{x}\right)\right), \left(\color{blue}{1} + x\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(x + \left(\mathsf{neg}\left(\frac{y \cdot z}{x}\right)\right)\right)\right), \left(1 + x\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(x - \frac{y \cdot z}{x}\right)\right), \left(1 + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{\_.f64}\left(x, \left(\frac{y \cdot z}{x}\right)\right)\right), \left(1 + x\right)\right) \]

      6. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{\_.f64}\left(x, \left(y \cdot \frac{z}{x}\right)\right)\right), \left(1 + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \left(\frac{z}{x}\right)\right)\right)\right), \left(1 + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, x\right)\right)\right)\right), \left(1 + x\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, x\right)\right)\right)\right), \left(x + \color{blue}{1}\right)\right) \]

      10. +-lowering-+.f64 85.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(z, x\right)\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 85.0%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-112}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-78}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{t - y}{x} + 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -4.5e-118)
     t_1
     (if (<= z 7.2e-80) (+ (* z (/ (- t y) x)) 1.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -4.5e-118) {
		tmp = t_1;
	} else if (z <= 7.2e-80) {
		tmp = (z * ((t - y) / x)) + 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-4.5d-118)) then
        tmp = t_1
    else if (z <= 7.2d-80) then
        tmp = (z * ((t - y) / x)) + 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -4.5e-118) {
		tmp = t_1;
	} else if (z <= 7.2e-80) {
		tmp = (z * ((t - y) / x)) + 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -4.5e-118:
		tmp = t_1
	elif z <= 7.2e-80:
		tmp = (z * ((t - y) / x)) + 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -4.5e-118)
		tmp = t_1;
	elseif (z <= 7.2e-80)
		tmp = Float64(Float64(z * Float64(Float64(t - y) / x)) + 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -4.5e-118)
		tmp = t_1;
	elseif (z <= 7.2e-80)
		tmp = (z * ((t - y) / x)) + 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e-118], t$95$1, If[LessEqual[z, 7.2e-80], N[(N[(z * N[(N[(t - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e-118 or 7.2e-80 < z

   1. Initial program 82.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 82.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y}{t}\right), \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{t} + x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{y}{t}\right), x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(1 + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(x + \color{blue}{1}\right)\right) \]

      6. +-lowering-+.f64 84.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 84.3%

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

   if -4.5e-118 < z < 7.2e-80

   1. Initial program 99.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(z \cdot \left(-1 \cdot \frac{y}{x \cdot \left(1 + x\right)} + \frac{t}{x \cdot \left(1 + x\right)}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \frac{y}{x \cdot \left(1 + x\right)} + \frac{t}{x \cdot \left(1 + x\right)}\right)}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\frac{t}{x \cdot \left(1 + x\right)} + \color{blue}{-1 \cdot \frac{y}{x \cdot \left(1 + x\right)}}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\frac{t}{x \cdot \left(1 + x\right)} + \left(\mathsf{neg}\left(\frac{y}{x \cdot \left(1 + x\right)}\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \left(\frac{t}{x \cdot \left(1 + x\right)} - \color{blue}{\frac{y}{x \cdot \left(1 + x\right)}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(\frac{t}{x \cdot \left(1 + x\right)}\right), \color{blue}{\left(\frac{y}{x \cdot \left(1 + x\right)}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, \left(x \cdot \left(1 + x\right)\right)\right), \left(\frac{\color{blue}{y}}{x \cdot \left(1 + x\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(x, \left(1 + x\right)\right)\right), \left(\frac{y}{x \cdot \left(1 + x\right)}\right)\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(x, \left(x + 1\right)\right)\right), \left(\frac{y}{x \cdot \left(1 + x\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, 1\right)\right)\right), \left(\frac{y}{x \cdot \left(1 + x\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, 1\right)\right)\right), \mathsf{/.f64}\left(y, \color{blue}{\left(x \cdot \left(1 + x\right)\right)}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, 1\right)\right)\right), \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(1 + x\right)}\right)\right)\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, 1\right)\right)\right), \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(x, \left(x + \color{blue}{1}\right)\right)\right)\right)\right)\right) \]

      14. +-lowering-+.f64 78.4%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, 1\right)\right)\right), \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right)\right)\right)\right)\right) \]

   7. Simplified 78.4%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{t - y}{x}\right)}\right)\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\left(t - y\right), \color{blue}{x}\right)\right)\right) \]

      2. --lowering--.f64 75.2%

         \[\leadsto \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, y\right), x\right)\right)\right) \]

   10. Simplified 75.2%

       \[\leadsto 1 + z \cdot \color{blue}{\frac{t - y}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-118}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{t - y}{x} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e-6) 1.0 (if (<= x 1.65e-20) (+ x (/ y t)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-6) {
		tmp = 1.0;
	} else if (x <= 1.65e-20) {
		tmp = x + (y / t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (x <= (-2.6d-6)) then
        tmp = 1.0d0
    else if (x <= 1.65d-20) then
        tmp = x + (y / t)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-6) {
		tmp = 1.0;
	} else if (x <= 1.65e-20) {
		tmp = x + (y / t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e-6:
		tmp = 1.0
	elif x <= 1.65e-20:
		tmp = x + (y / t)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e-6)
		tmp = 1.0;
	elseif (x <= 1.65e-20)
		tmp = Float64(x + Float64(y / t));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.6e-6)
		tmp = 1.0;
	elseif (x <= 1.65e-20)
		tmp = x + (y / t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e-6], 1.0, If[LessEqual[x, 1.65e-20], N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000009e-6 or 1.65e-20 < x

   1. Initial program 86.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 86.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 83.1%

      \[\leadsto \color{blue}{1} \]

   if -2.60000000000000009e-6 < x < 1.65e-20

   1. Initial program 89.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 89.8%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y}{t}\right), \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{t} + x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{y}{t}\right), x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(1 + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(x + \color{blue}{1}\right)\right) \]

      6. +-lowering-+.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 72.3%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \color{blue}{1}\right) \]
   9. Step-by-step derivation

   10. Simplified 71.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + 1}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-84}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.2e-64)
   (/ 1.0 (+ (/ 1.0 x) 1.0))
   (if (<= x 4e-84) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-64) {
		tmp = 1.0 / ((1.0 / x) + 1.0);
	} else if (x <= 4e-84) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (x <= (-2.2d-64)) then
        tmp = 1.0d0 / ((1.0d0 / x) + 1.0d0)
    else if (x <= 4d-84) then
        tmp = y / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-64) {
		tmp = 1.0 / ((1.0 / x) + 1.0);
	} else if (x <= 4e-84) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.2e-64:
		tmp = 1.0 / ((1.0 / x) + 1.0)
	elif x <= 4e-84:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.2e-64)
		tmp = Float64(1.0 / Float64(Float64(1.0 / x) + 1.0));
	elseif (x <= 4e-84)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.2e-64)
		tmp = 1.0 / ((1.0 / x) + 1.0);
	elseif (x <= 4e-84)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.2e-64], N[(1.0 / N[(N[(1.0 / x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e-84], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2e-64

   1. Initial program 84.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 84.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y}{t}\right), \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{t} + x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{y}{t}\right), x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(1 + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(x + \color{blue}{1}\right)\right) \]

      6. +-lowering-+.f64 69.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 69.7%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \color{blue}{\left(x \cdot \left(1 + \frac{1}{x}\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{1}{x}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{1}{x}\right)}\right)\right)\right) \]

      3. /-lowering-/.f64 69.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right)\right) \]

   10. Simplified 69.7%

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

   11. Taylor expanded in y around 0

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

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

          \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(1 + \frac{1}{x}\right)}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

       3. /-lowering-/.f64 75.1%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   13. Simplified 75.1%

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

   if -2.2e-64 < x < 4.0000000000000001e-84

   1. Initial program 89.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 89.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 57.1%

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{t}\right) \]

   7. Simplified 57.1%

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

   if 4.0000000000000001e-84 < x

   1. Initial program 90.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 90.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(x + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 77.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 77.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{1}{\frac{1}{x} + 1}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-84}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -4.7e-64) t_1 (if (<= x 7e-82) (/ y t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -4.7e-64) {
		tmp = t_1;
	} else if (x <= 7e-82) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (x <= (-4.7d-64)) then
        tmp = t_1
    else if (x <= 7d-82) then
        tmp = y / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -4.7e-64) {
		tmp = t_1;
	} else if (x <= 7e-82) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -4.7e-64:
		tmp = t_1
	elif x <= 7e-82:
		tmp = y / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -4.7e-64)
		tmp = t_1;
	elseif (x <= 7e-82)
		tmp = Float64(y / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -4.7e-64)
		tmp = t_1;
	elseif (x <= 7e-82)
		tmp = y / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.7e-64], t$95$1, If[LessEqual[x, 7e-82], N[(y / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6999999999999998e-64 or 6.9999999999999997e-82 < x

   1. Initial program 87.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 87.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(x + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 76.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 76.4%

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

   if -4.6999999999999998e-64 < x < 6.9999999999999997e-82

   1. Initial program 89.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 89.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 57.1%

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{t}\right) \]

   7. Simplified 57.1%

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

Alternative 8: 67.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-32}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-78}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.8e-32) 1.0 (if (<= x 1.12e-78) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e-32) {
		tmp = 1.0;
	} else if (x <= 1.12e-78) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (x <= (-4.8d-32)) then
        tmp = 1.0d0
    else if (x <= 1.12d-78) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e-32) {
		tmp = 1.0;
	} else if (x <= 1.12e-78) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.8e-32:
		tmp = 1.0
	elif x <= 1.12e-78:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.8e-32)
		tmp = 1.0;
	elseif (x <= 1.12e-78)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.8e-32)
		tmp = 1.0;
	elseif (x <= 1.12e-78)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.8e-32], 1.0, If[LessEqual[x, 1.12e-78], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000003e-32 or 1.12000000000000005e-78 < x

   1. Initial program 87.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 87.6%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 77.3%

      \[\leadsto \color{blue}{1} \]

   if -4.8000000000000003e-32 < x < 1.12000000000000005e-78

   1. Initial program 89.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 89.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 55.8%

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{t}\right) \]

   7. Simplified 55.8%

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

Alternative 9: 56.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-29}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.35e-29) 1.0 (if (<= x 1.6e-67) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-29) {
		tmp = 1.0;
	} else if (x <= 1.6e-67) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (x <= (-1.35d-29)) then
        tmp = 1.0d0
    else if (x <= 1.6d-67) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-29) {
		tmp = 1.0;
	} else if (x <= 1.6e-67) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e-29:
		tmp = 1.0
	elif x <= 1.6e-67:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e-29)
		tmp = 1.0;
	elseif (x <= 1.6e-67)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.35e-29)
		tmp = 1.0;
	elseif (x <= 1.6e-67)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.35e-29], 1.0, If[LessEqual[x, 1.6e-67], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35000000000000011e-29 or 1.60000000000000011e-67 < x

   1. Initial program 87.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 87.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 78.7%

      \[\leadsto \color{blue}{1} \]

   if -1.35000000000000011e-29 < x < 1.60000000000000011e-67

   1. Initial program 89.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      5. associate-+l- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

      7. distribute-frac-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

      16. +-lowering-+.f64 89.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y}{t}\right), \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{t} + x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{y}{t}\right), x\right), \left(\color{blue}{1} + x\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(1 + x\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \left(x + \color{blue}{1}\right)\right) \]

      6. +-lowering-+.f64 75.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 75.5%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \color{blue}{\left(x \cdot \left(1 + \frac{1}{x}\right)\right)}\right) \]
   9. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{*.f64}\left(x, \color{blue}{\left(1 + \frac{1}{x}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{1}{x}\right)}\right)\right)\right) \]

      3. /-lowering-/.f64 75.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right)\right) \]

   10. Simplified 75.3%

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

   11. Taylor expanded in y around 0

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

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

          \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(1 + \frac{1}{x}\right)}\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{1}{x}\right)}\right)\right) \]

       3. /-lowering-/.f64 24.3%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

   13. Simplified 24.3%

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

   14. Taylor expanded in x around 0

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

   16. Simplified 24.4%

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

Alternative 10: 54.4% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

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 = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 88.2%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
2. Step-by-step derivation

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

      \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right), \color{blue}{\left(x + 1\right)}\right) \]

   2. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{y \cdot z + \left(\mathsf{neg}\left(x\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

   3. +-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(\mathsf{neg}\left(x\right)\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

   4. neg-sub0 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\left(0 - x\right) + y \cdot z}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

   5. associate-+l- N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{0 - \left(x - y \cdot z\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

   6. sub0-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x + \frac{\mathsf{neg}\left(\left(x - y \cdot z\right)\right)}{t \cdot z - x}\right), \left(x + 1\right)\right) \]

   7. distribute-frac-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x + \left(\mathsf{neg}\left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right)\right), \left(x + 1\right)\right) \]

   8. sub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x - \frac{x - y \cdot z}{t \cdot z - x}\right), \left(\color{blue}{x} + 1\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(\frac{x - y \cdot z}{t \cdot z - x}\right)\right), \left(\color{blue}{x} + 1\right)\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(x - y \cdot z\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \left(y \cdot z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \left(t \cdot z - x\right)\right)\right), \left(x + 1\right)\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(t \cdot z\right), x\right)\right)\right), \left(x + 1\right)\right) \]

   14. *-commutative N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\left(z \cdot t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \left(x + 1\right)\right) \]

   16. +-lowering-+.f64 88.2%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, t\right), x\right)\right)\right), \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

3. Simplified 88.2%

   \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
6. Step-by-step derivation

7. Simplified 51.5%

   \[\leadsto \color{blue}{1} \]
8. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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 / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1)))

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