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

Percentage Accurate: 88.9% → 97.1%

Time: 12.3s

Alternatives: 10

Speedup: 0.4×

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: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ t_2 := \frac{x + \frac{x - y \cdot z}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+139}:\\ \;\;\;\;\frac{x + y \cdot \left(\frac{\frac{x}{y}}{t\_1} - \frac{z}{t\_1}\right)}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+278}:\\ \;\;\;\;\frac{x + \frac{\frac{1}{z}}{t - \frac{x}{z}} \cdot \left(y \cdot z - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))) (t_2 (/ (+ x (/ (- x (* y z)) t_1)) (+ x 1.0))))
   (if (<= t_2 -1e+139)
     (/ (+ x (* y (- (/ (/ x y) t_1) (/ z t_1)))) (+ x 1.0))
     (if (<= t_2 2e+278)
       (/ (+ x (* (/ (/ 1.0 z) (- t (/ x z))) (- (* y z) x))) (+ x 1.0))
       (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double t_2 = (x + ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+139) {
		tmp = (x + (y * (((x / y) / t_1) - (z / t_1)))) / (x + 1.0);
	} else if (t_2 <= 2e+278) {
		tmp = (x + (((1.0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0);
	} 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 = x - (z * t)
    t_2 = (x + ((x - (y * z)) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-1d+139)) then
        tmp = (x + (y * (((x / y) / t_1) - (z / t_1)))) / (x + 1.0d0)
    else if (t_2 <= 2d+278) then
        tmp = (x + (((1.0d0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0d0)
    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 = x - (z * t);
	double t_2 = (x + ((x - (y * z)) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+139) {
		tmp = (x + (y * (((x / y) / t_1) - (z / t_1)))) / (x + 1.0);
	} else if (t_2 <= 2e+278) {
		tmp = (x + (((1.0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	t_2 = (x + ((x - (y * z)) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -1e+139:
		tmp = (x + (y * (((x / y) / t_1) - (z / t_1)))) / (x + 1.0)
	elif t_2 <= 2e+278:
		tmp = (x + (((1.0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	t_2 = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e+139)
		tmp = Float64(Float64(x + Float64(y * Float64(Float64(Float64(x / y) / t_1) - Float64(z / t_1)))) / Float64(x + 1.0));
	elseif (t_2 <= 2e+278)
		tmp = Float64(Float64(x + Float64(Float64(Float64(1.0 / z) / Float64(t - Float64(x / z))) * Float64(Float64(y * z) - x))) / Float64(x + 1.0));
	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 = x - (z * t);
	t_2 = (x + ((x - (y * z)) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e+139)
		tmp = (x + (y * (((x / y) / t_1) - (z / t_1)))) / (x + 1.0);
	elseif (t_2 <= 2e+278)
		tmp = (x + (((1.0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+139], N[(N[(x + N[(y * N[(N[(N[(x / y), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+278], N[(N[(x + N[(N[(N[(1.0 / z), $MachinePrecision] / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 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))) < -1.00000000000000003e139

   1. Initial program 77.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in y around inf

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

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

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

      6. associate-/r* N/A

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

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

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

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

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

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

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

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

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

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

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

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

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

      13. *-lowering-*.f64 99.8%

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

   7. Simplified 99.8%

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

   if -1.00000000000000003e139 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999993e278

   1. Initial program 98.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in z around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

      5. /-lowering-/.f64 98.9%

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

   7. Simplified 98.9%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 99.1%

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

   9. Applied egg-rr 99.1%

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

   if 1.99999999999999993e278 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 13.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 13.9%

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

   3. Simplified 13.9%

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

   5. Taylor expanded in z around 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 87.7%

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

   7. Simplified 87.7%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1} \leq -1 \cdot 10^{+139}:\\ \;\;\;\;\frac{x + y \cdot \left(\frac{\frac{x}{y}}{x - z \cdot t} - \frac{z}{x - z \cdot t}\right)}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1} \leq 2 \cdot 10^{+278}:\\ \;\;\;\;\frac{x + \frac{\frac{1}{z}}{t - \frac{x}{z}} \cdot \left(y \cdot z - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1} \leq 2 \cdot 10^{+278}:\\ \;\;\;\;\frac{x + \frac{\frac{1}{z}}{t - \frac{x}{z}} \cdot \left(y \cdot z - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (+ x (/ (- x (* y z)) (- x (* z t)))) (+ x 1.0)) 2e+278)
   (/ (+ x (* (/ (/ 1.0 z) (- t (/ x z))) (- (* y z) x))) (+ x 1.0))
   (/ (+ x (/ y t)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0)) <= 2e+278) {
		tmp = (x + (((1.0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0);
	} 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) :: tmp
    if (((x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0d0)) <= 2d+278) then
        tmp = (x + (((1.0d0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0d0)
    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 tmp;
	if (((x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0)) <= 2e+278) {
		tmp = (x + (((1.0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0)) <= 2e+278:
		tmp = (x + (((1.0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / Float64(x - Float64(z * t)))) / Float64(x + 1.0)) <= 2e+278)
		tmp = Float64(Float64(x + Float64(Float64(Float64(1.0 / z) / Float64(t - Float64(x / z))) * Float64(Float64(y * z) - x))) / Float64(x + 1.0));
	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)
	tmp = 0.0;
	if (((x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0)) <= 2e+278)
		tmp = (x + (((1.0 / z) / (t - (x / z))) * ((y * z) - x))) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 2e+278], N[(N[(x + N[(N[(N[(1.0 / z), $MachinePrecision] / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999993e278

   1. Initial program 96.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

      5. /-lowering-/.f64 96.9%

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

   7. Simplified 96.9%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. associate-/r* N/A

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

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

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

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

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

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

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

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

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

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

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

      10. *-commutative N/A

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

      11. *-lowering-*.f64 97.0%

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

   9. Applied egg-rr 97.0%

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

   if 1.99999999999999993e278 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 13.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 13.9%

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

   3. Simplified 13.9%

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

   5. Taylor expanded in z around 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 87.7%

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

   7. Simplified 87.7%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1} \leq 2 \cdot 10^{+278}:\\ \;\;\;\;\frac{x + \frac{\frac{1}{z}}{t - \frac{x}{z}} \cdot \left(y \cdot z - x\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+278}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- x (* y z)) (- x (* z t)))) (+ x 1.0))))
   (if (<= t_1 2e+278) t_1 (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= 2e+278) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0d0)
    if (t_1 <= 2d+278) then
        tmp = t_1
    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 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= 2e+278) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0)
	tmp = 0
	if t_1 <= 2e+278:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / Float64(x - Float64(z * t)))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 2e+278)
		tmp = t_1;
	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 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 2e+278)
		tmp = t_1;
	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[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+278], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999993e278

   1. Initial program 96.9%

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

   if 1.99999999999999993e278 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 13.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 13.9%

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

   3. Simplified 13.9%

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

   5. Taylor expanded in z around 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 87.7%

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

   7. Simplified 87.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1} \leq 2 \cdot 10^{+278}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-126}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+19}:\\ \;\;\;\;\frac{1 + \left(x - y \cdot \frac{z}{x}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -1.7e+168)
     t_1
     (if (<= z 3.5e-126)
       (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))
       (if (<= z 6e+19) (/ (+ 1.0 (- x (* y (/ z 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 <= -1.7e+168) {
		tmp = t_1;
	} else if (z <= 3.5e-126) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else if (z <= 6e+19) {
		tmp = (1.0 + (x - (y * (z / 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 <= (-1.7d+168)) then
        tmp = t_1
    else if (z <= 3.5d-126) then
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    else if (z <= 6d+19) then
        tmp = (1.0d0 + (x - (y * (z / 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 <= -1.7e+168) {
		tmp = t_1;
	} else if (z <= 3.5e-126) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else if (z <= 6e+19) {
		tmp = (1.0 + (x - (y * (z / 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 <= -1.7e+168:
		tmp = t_1
	elif z <= 3.5e-126:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	elif z <= 6e+19:
		tmp = (1.0 + (x - (y * (z / 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 <= -1.7e+168)
		tmp = t_1;
	elseif (z <= 3.5e-126)
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	elseif (z <= 6e+19)
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y * Float64(z / 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 <= -1.7e+168)
		tmp = t_1;
	elseif (z <= 3.5e-126)
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	elseif (z <= 6e+19)
		tmp = (1.0 + (x - (y * (z / 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, -1.7e+168], t$95$1, If[LessEqual[z, 3.5e-126], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+19], N[(N[(1.0 + N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.70000000000000001e168 or 6e19 < z

   1. Initial program 76.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 76.3%

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

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   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 91.3%

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

   7. Simplified 91.3%

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

   if -1.70000000000000001e168 < z < 3.5e-126

   1. Initial program 96.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 85.3%

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

   if 3.5e-126 < z < 6e19

   1. Initial program 99.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   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 76.2%

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

   7. Simplified 76.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-126}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+19}:\\ \;\;\;\;\frac{1 + \left(x - y \cdot \frac{z}{x}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-15}:\\ \;\;\;\;\frac{1 + \left(x - y \cdot \frac{z}{x}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -3.4e-91)
     t_1
     (if (<= t 2.75e-15) (/ (+ 1.0 (- x (* y (/ z 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 (t <= -3.4e-91) {
		tmp = t_1;
	} else if (t <= 2.75e-15) {
		tmp = (1.0 + (x - (y * (z / 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 (t <= (-3.4d-91)) then
        tmp = t_1
    else if (t <= 2.75d-15) then
        tmp = (1.0d0 + (x - (y * (z / 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 (t <= -3.4e-91) {
		tmp = t_1;
	} else if (t <= 2.75e-15) {
		tmp = (1.0 + (x - (y * (z / 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 t <= -3.4e-91:
		tmp = t_1
	elif t <= 2.75e-15:
		tmp = (1.0 + (x - (y * (z / 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 (t <= -3.4e-91)
		tmp = t_1;
	elseif (t <= 2.75e-15)
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y * Float64(z / 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 (t <= -3.4e-91)
		tmp = t_1;
	elseif (t <= 2.75e-15)
		tmp = (1.0 + (x - (y * (z / 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[t, -3.4e-91], t$95$1, If[LessEqual[t, 2.75e-15], N[(N[(1.0 + N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.40000000000000027e-91 or 2.7500000000000001e-15 < t

   1. Initial program 84.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 84.6%

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

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   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 88.2%

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

   7. Simplified 88.2%

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

   if -3.40000000000000027e-91 < t < 2.7500000000000001e-15

   1. Initial program 95.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around 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 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-15}:\\ \;\;\;\;\frac{1 + \left(x - y \cdot \frac{z}{x}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y - \frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.9e-13) 1.0 (if (<= x 3.35e-12) (+ x (/ (- y (/ x z)) t)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.9e-13) {
		tmp = 1.0;
	} else if (x <= 3.35e-12) {
		tmp = x + ((y - (x / z)) / 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 <= (-3.9d-13)) then
        tmp = 1.0d0
    else if (x <= 3.35d-12) then
        tmp = x + ((y - (x / z)) / 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 <= -3.9e-13) {
		tmp = 1.0;
	} else if (x <= 3.35e-12) {
		tmp = x + ((y - (x / z)) / t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.9e-13:
		tmp = 1.0
	elif x <= 3.35e-12:
		tmp = x + ((y - (x / z)) / t)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.9e-13)
		tmp = 1.0;
	elseif (x <= 3.35e-12)
		tmp = Float64(x + Float64(Float64(y - Float64(x / z)) / t));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.9e-13)
		tmp = 1.0;
	elseif (x <= 3.35e-12)
		tmp = x + ((y - (x / z)) / t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.9e-13], 1.0, If[LessEqual[x, 3.35e-12], N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.90000000000000004e-13 or 3.3500000000000001e-12 < x

   1. Initial program 89.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 89.9%

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

   if -3.90000000000000004e-13 < x < 3.3500000000000001e-12

   1. Initial program 89.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in t around -inf

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

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

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

      2. associate-*r/ N/A

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

      3. cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. distribute-lft-in N/A

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

      7. neg-mul-1 N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

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

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

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

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

      14. /-lowering-/.f64 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in x around 0

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

   10. Simplified 72.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.35 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y - \frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+72}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.3e-14) 1.0 (if (<= x 3.15e+72) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e-14) {
		tmp = 1.0;
	} else if (x <= 3.15e+72) {
		tmp = (x + (y / t)) / (x + 1.0);
	} 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 <= (-1.3d-14)) then
        tmp = 1.0d0
    else if (x <= 3.15d+72) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    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 <= -1.3e-14) {
		tmp = 1.0;
	} else if (x <= 3.15e+72) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.3e-14:
		tmp = 1.0
	elif x <= 3.15e+72:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.3e-14)
		tmp = 1.0;
	elseif (x <= 3.15e+72)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.3e-14)
		tmp = 1.0;
	elseif (x <= 3.15e+72)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.3e-14], 1.0, If[LessEqual[x, 3.15e+72], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.29999999999999998e-14 or 3.14999999999999981e72 < x

   1. Initial program 91.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 95.5%

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

   if -1.29999999999999998e-14 < x < 3.14999999999999981e72

   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 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 65.3%

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

   7. Simplified 65.3%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+72}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-23}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-49}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.2e-23)
   1.0
   (if (<= x -3.3e-99) x (if (<= x 1.2e-49) (/ y t) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.2e-23) {
		tmp = 1.0;
	} else if (x <= -3.3e-99) {
		tmp = x;
	} else if (x <= 1.2e-49) {
		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 <= (-1.2d-23)) then
        tmp = 1.0d0
    else if (x <= (-3.3d-99)) then
        tmp = x
    else if (x <= 1.2d-49) 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 <= -1.2e-23) {
		tmp = 1.0;
	} else if (x <= -3.3e-99) {
		tmp = x;
	} else if (x <= 1.2e-49) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.2e-23:
		tmp = 1.0
	elif x <= -3.3e-99:
		tmp = x
	elif x <= 1.2e-49:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.2e-23)
		tmp = 1.0;
	elseif (x <= -3.3e-99)
		tmp = x;
	elseif (x <= 1.2e-49)
		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 <= -1.2e-23)
		tmp = 1.0;
	elseif (x <= -3.3e-99)
		tmp = x;
	elseif (x <= 1.2e-49)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.2e-23], 1.0, If[LessEqual[x, -3.3e-99], x, If[LessEqual[x, 1.2e-49], N[(y / t), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.19999999999999998e-23 or 1.19999999999999996e-49 < x

   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 inf

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

   7. Simplified 87.6%

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

   if -1.19999999999999998e-23 < x < -3.29999999999999986e-99

   1. Initial program 95.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 95.0%

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

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   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 56.9%

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

   7. Simplified 56.9%

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

   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 56.9%

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

   11. Taylor expanded in y around 0

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

   13. Simplified 45.7%

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

   if -3.29999999999999986e-99 < x < 1.19999999999999996e-49

   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 0

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

      1. /-lowering-/.f64 52.9%

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

   7. Simplified 52.9%

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

Alternative 9: 77.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e-22) 1.0 (if (<= x 3.4e-8) (+ x (/ y t)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e-22) {
		tmp = 1.0;
	} else if (x <= 3.4e-8) {
		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 <= (-1.55d-22)) then
        tmp = 1.0d0
    else if (x <= 3.4d-8) 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 <= -1.55e-22) {
		tmp = 1.0;
	} else if (x <= 3.4e-8) {
		tmp = x + (y / t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.55e-22:
		tmp = 1.0
	elif x <= 3.4e-8:
		tmp = x + (y / t)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e-22)
		tmp = 1.0;
	elseif (x <= 3.4e-8)
		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 <= -1.55e-22)
		tmp = 1.0;
	elseif (x <= 3.4e-8)
		tmp = x + (y / t);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.55e-22], 1.0, If[LessEqual[x, 3.4e-8], N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000006e-22 or 3.4e-8 < x

   1. Initial program 89.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 89.3%

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

   if -1.55000000000000006e-22 < x < 3.4e-8

   1. Initial program 89.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   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 89.1%

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

   3. Simplified 89.1%

      \[\leadsto \color{blue}{\frac{x - \frac{x - y \cdot z}{z \cdot t - x}}{x + 1}} \]
   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 64.6%

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

   7. Simplified 64.6%

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

   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 64.4%

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

       1. /-rgt-identity N/A

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

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

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

       3. /-lowering-/.f64 64.4%

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

   12. Applied egg-rr 64.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.9% 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 89.1%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
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 89.1%

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

3. Simplified 89.1%

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

5. Taylor expanded in x around inf

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

7. Simplified 55.9%

   \[\leadsto \color{blue}{1} \]
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 2024161 
(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)))