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

Percentage Accurate: 89.3% → 96.2%

Time: 8.6s

Alternatives: 14

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, \frac{y}{t\_1}, \frac{x}{x - t \cdot z} + x\right)}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 (- INFINITY))
     (/ (fma z (/ y t_1) (+ (/ x (- x (* t z))) x)) (+ x 1.0))
     (if (<= t_2 1e+146) t_2 (/ (+ (/ y t) x) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(z, (y / t_1), ((x / (x - (t * z))) + x)) / (x + 1.0);
	} else if (t_2 <= 1e+146) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(fma(z, Float64(y / t_1), Float64(Float64(x / Float64(x - Float64(t * z))) + x)) / Float64(x + 1.0));
	elseif (t_2 <= 1e+146)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z * N[(y / t$95$1), $MachinePrecision] + N[(N[(x / N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+146], t$95$2, N[(N[(N[(y / t), $MachinePrecision] + x), $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))) < -inf.0

   1. Initial program 41.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

   4. Applied rewrites 99.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.99999999999999934e145

   1. Initial program 98.1%

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

   if 9.99999999999999934e145 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 31.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, \frac{y}{t \cdot z - x}, \frac{x}{x - t \cdot z} + x\right)}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{+146}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ t_2 := \mathsf{fma}\left(t, z, -x\right)\\ t_3 := \frac{y}{t\_2} \cdot \frac{z}{1 + x}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+41}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 10^{+146}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
        (t_2 (fma t z (- x)))
        (t_3 (* (/ y t_2) (/ z (+ 1.0 x)))))
   (if (<= t_1 -5e+41)
     t_3
     (if (<= t_1 5e-10)
       (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
       (if (<= t_1 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_1 1e+146) t_3 (/ (+ (/ y t) x) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double t_2 = fma(t, z, -x);
	double t_3 = (y / t_2) * (z / (1.0 + x));
	double tmp;
	if (t_1 <= -5e+41) {
		tmp = t_3;
	} else if (t_1 <= 5e-10) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else if (t_1 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_1 <= 1e+146) {
		tmp = t_3;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	t_2 = fma(t, z, Float64(-x))
	t_3 = Float64(Float64(y / t_2) * Float64(z / Float64(1.0 + x)))
	tmp = 0.0
	if (t_1 <= -5e+41)
		tmp = t_3;
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_1 <= 1e+146)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(t * z + (-x)), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y / t$95$2), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+41], t$95$3, If[LessEqual[t$95$1, 5e-10], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+146], t$95$3, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5.00000000000000022e41 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.99999999999999934e145

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if -5.00000000000000022e41 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000031e-10

   1. Initial program 93.9%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 98.5

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

   5. Applied rewrites 98.5%

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

   if 5.00000000000000031e-10 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if 9.99999999999999934e145 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 31.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

      \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{x + 1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -5 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{+146}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ t_2 := \frac{x + \frac{t\_1}{t \cdot z - x}}{x + 1}\\ t_3 := \mathsf{fma}\left(t, z, -x\right)\\ t_4 := \frac{y}{t\_3} \cdot \frac{z}{1 + x}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+30}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x + \frac{t\_1}{t \cdot z}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_3}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+146}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x))
        (t_2 (/ (+ x (/ t_1 (- (* t z) x))) (+ x 1.0)))
        (t_3 (fma t z (- x)))
        (t_4 (* (/ y t_3) (/ z (+ 1.0 x)))))
   (if (<= t_2 -2e+30)
     t_4
     (if (<= t_2 5e-10)
       (/ (+ x (/ t_1 (* t z))) (+ x 1.0))
       (if (<= t_2 2.0)
         (/ (- x (/ x t_3)) (+ x 1.0))
         (if (<= t_2 1e+146) t_4 (/ (+ (/ y t) x) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (x + (t_1 / ((t * z) - x))) / (x + 1.0);
	double t_3 = fma(t, z, -x);
	double t_4 = (y / t_3) * (z / (1.0 + x));
	double tmp;
	if (t_2 <= -2e+30) {
		tmp = t_4;
	} else if (t_2 <= 5e-10) {
		tmp = (x + (t_1 / (t * z))) / (x + 1.0);
	} else if (t_2 <= 2.0) {
		tmp = (x - (x / t_3)) / (x + 1.0);
	} else if (t_2 <= 1e+146) {
		tmp = t_4;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - x)
	t_2 = Float64(Float64(x + Float64(t_1 / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	t_3 = fma(t, z, Float64(-x))
	t_4 = Float64(Float64(y / t_3) * Float64(z / Float64(1.0 + x)))
	tmp = 0.0
	if (t_2 <= -2e+30)
		tmp = t_4;
	elseif (t_2 <= 5e-10)
		tmp = Float64(Float64(x + Float64(t_1 / Float64(t * z))) / Float64(x + 1.0));
	elseif (t_2 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_3)) / Float64(x + 1.0));
	elseif (t_2 <= 1e+146)
		tmp = t_4;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(t$95$1 / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * z + (-x)), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y / t$95$3), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+30], t$95$4, If[LessEqual[t$95$2, 5e-10], N[(N[(x + N[(t$95$1 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], N[(N[(x - N[(x / t$95$3), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+146], t$95$4, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -2e30 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.99999999999999934e145

   1. Initial program 85.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 83.2

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

   5. Applied rewrites 83.2%

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

   if -2e30 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000031e-10

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 92.4

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

   5. Applied rewrites 92.4%

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

   if 5.00000000000000031e-10 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if 9.99999999999999934e145 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 31.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

      \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{x + 1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -2 \cdot 10^{+30}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{+146}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} + x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ t_3 := \mathsf{fma}\left(t, z, -x\right)\\ t_4 := \frac{y}{t\_3} \cdot \frac{z}{1 + x}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+41}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(x, x, -1\right)} \cdot \left(x - 1\right)\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_3}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+146}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y t) x))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
        (t_3 (fma t z (- x)))
        (t_4 (* (/ y t_3) (/ z (+ 1.0 x)))))
   (if (<= t_2 -5e+41)
     t_4
     (if (<= t_2 5e-10)
       (* (/ t_1 (fma x x -1.0)) (- x 1.0))
       (if (<= t_2 2.0)
         (/ (- x (/ x t_3)) (+ x 1.0))
         (if (<= t_2 1e+146) t_4 (/ t_1 (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / t) + x;
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double t_3 = fma(t, z, -x);
	double t_4 = (y / t_3) * (z / (1.0 + x));
	double tmp;
	if (t_2 <= -5e+41) {
		tmp = t_4;
	} else if (t_2 <= 5e-10) {
		tmp = (t_1 / fma(x, x, -1.0)) * (x - 1.0);
	} else if (t_2 <= 2.0) {
		tmp = (x - (x / t_3)) / (x + 1.0);
	} else if (t_2 <= 1e+146) {
		tmp = t_4;
	} else {
		tmp = t_1 / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / t) + x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	t_3 = fma(t, z, Float64(-x))
	t_4 = Float64(Float64(y / t_3) * Float64(z / Float64(1.0 + x)))
	tmp = 0.0
	if (t_2 <= -5e+41)
		tmp = t_4;
	elseif (t_2 <= 5e-10)
		tmp = Float64(Float64(t_1 / fma(x, x, -1.0)) * Float64(x - 1.0));
	elseif (t_2 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_3)) / Float64(x + 1.0));
	elseif (t_2 <= 1e+146)
		tmp = t_4;
	else
		tmp = Float64(t_1 / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(t * z + (-x)), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y / t$95$3), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+41], t$95$4, If[LessEqual[t$95$2, 5e-10], N[(N[(t$95$1 / N[(x * x + -1.0), $MachinePrecision]), $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], N[(N[(x - N[(x / t$95$3), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+146], t$95$4, N[(t$95$1 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5.00000000000000022e41 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.99999999999999934e145

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if -5.00000000000000022e41 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000031e-10

   1. Initial program 93.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

   4. Applied rewrites 92.4%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 82.7

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

   7. Applied rewrites 82.7%

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

      1. lift-/.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. flip-+ N/A

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

      4. associate-/r/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 82.7

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

   9. Applied rewrites 82.7%

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

   if 5.00000000000000031e-10 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if 9.99999999999999934e145 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 31.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

      \[\leadsto \frac{\color{blue}{\frac{y}{t} + x}}{x + 1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -5 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{\mathsf{fma}\left(x, x, -1\right)} \cdot \left(x - 1\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{+146}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x + 1}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ t_3 := \mathsf{fma}\left(t, z, -x\right)\\ t_4 := \frac{y}{t\_3} \cdot \frac{z}{1 + x}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+41}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_3}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+146}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (+ x 1.0)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
        (t_3 (fma t z (- x)))
        (t_4 (* (/ y t_3) (/ z (+ 1.0 x)))))
   (if (<= t_2 -5e+41)
     t_4
     (if (<= t_2 5e-10)
       t_1
       (if (<= t_2 2.0)
         (/ (- x (/ x t_3)) (+ x 1.0))
         (if (<= t_2 1e+146) t_4 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double t_3 = fma(t, z, -x);
	double t_4 = (y / t_3) * (z / (1.0 + x));
	double tmp;
	if (t_2 <= -5e+41) {
		tmp = t_4;
	} else if (t_2 <= 5e-10) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = (x - (x / t_3)) / (x + 1.0);
	} else if (t_2 <= 1e+146) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	t_3 = fma(t, z, Float64(-x))
	t_4 = Float64(Float64(y / t_3) * Float64(z / Float64(1.0 + x)))
	tmp = 0.0
	if (t_2 <= -5e+41)
		tmp = t_4;
	elseif (t_2 <= 5e-10)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_3)) / Float64(x + 1.0));
	elseif (t_2 <= 1e+146)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(t * z + (-x)), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y / t$95$3), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+41], t$95$4, If[LessEqual[t$95$2, 5e-10], t$95$1, If[LessEqual[t$95$2, 2.0], N[(N[(x - N[(x / t$95$3), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+146], t$95$4, t$95$1]]]]]]]]

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))) < -5.00000000000000022e41 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.99999999999999934e145

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if -5.00000000000000022e41 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000031e-10 or 9.99999999999999934e145 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 87.8

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

   5. Applied rewrites 87.8%

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

   if 5.00000000000000031e-10 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 98.9

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

   5. Applied rewrites 98.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -5 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{+146}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t}}{x + 1}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0.9999999990698063:\\ \;\;\;\;\frac{x}{1 + x}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ y t) (+ x 1.0)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_2 -2e-21)
     t_1
     (if (<= t_2 0.9999999990698063)
       (/ x (+ 1.0 x))
       (if (<= t_2 2.0) 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / t) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e-21) {
		tmp = t_1;
	} else if (t_2 <= 0.9999999990698063) {
		tmp = x / (1.0 + x);
	} else if (t_2 <= 2.0) {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = (y / t) / (x + 1.0d0)
    t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_2 <= (-2d-21)) then
        tmp = t_1
    else if (t_2 <= 0.9999999990698063d0) then
        tmp = x / (1.0d0 + x)
    else if (t_2 <= 2.0d0) then
        tmp = 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 = (y / t) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e-21) {
		tmp = t_1;
	} else if (t_2 <= 0.9999999990698063) {
		tmp = x / (1.0 + x);
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / t) / (x + 1.0)
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= -2e-21:
		tmp = t_1
	elif t_2 <= 0.9999999990698063:
		tmp = x / (1.0 + x)
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / t) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -2e-21)
		tmp = t_1;
	elseif (t_2 <= 0.9999999990698063)
		tmp = Float64(x / Float64(1.0 + x));
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / t) / (x + 1.0);
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -2e-21)
		tmp = t_1;
	elseif (t_2 <= 0.9999999990698063)
		tmp = x / (1.0 + x);
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, If[LessEqual[t$95$2, -2e-21], t$95$1, If[LessEqual[t$95$2, 0.9999999990698063], N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]]

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))) < -1.99999999999999982e-21 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 71.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

   4. Applied rewrites 85.4%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 61.5

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

   7. Applied rewrites 61.5%

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

   if -1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.9999999990698063

   1. Initial program 93.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 50.8

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

   5. Applied rewrites 50.8%

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

   if 0.9999999990698063 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 97.6%

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

Alternative 7: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999990698063:\\ \;\;\;\;\frac{x}{1 + x}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -2e-21)
     (/ y t)
     (if (<= t_1 0.9999999990698063)
       (/ x (+ 1.0 x))
       (if (<= t_1 2.0) 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999990698063) {
		tmp = x / (1.0 + x);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	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 * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= (-2d-21)) then
        tmp = y / t
    else if (t_1 <= 0.9999999990698063d0) then
        tmp = x / (1.0d0 + x)
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999990698063) {
		tmp = x / (1.0 + x);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -2e-21:
		tmp = y / t
	elif t_1 <= 0.9999999990698063:
		tmp = x / (1.0 + x)
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -2e-21)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999990698063)
		tmp = Float64(x / Float64(1.0 + x));
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -2e-21)
		tmp = y / t;
	elseif (t_1 <= 0.9999999990698063)
		tmp = x / (1.0 + x);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -2e-21], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999990698063], N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / t), $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))) < -1.99999999999999982e-21 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 71.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 58.7

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

   5. Applied rewrites 58.7%

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

   if -1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.9999999990698063

   1. Initial program 93.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 50.8

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

   5. Applied rewrites 50.8%

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

   if 0.9999999990698063 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 97.6%

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

Alternative 8: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{-18}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -2e-21)
     (/ y t)
     (if (<= t_1 1e-18) (/ x 1.0) (if (<= t_1 2.0) 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = y / t;
	} else if (t_1 <= 1e-18) {
		tmp = x / 1.0;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	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 * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= (-2d-21)) then
        tmp = y / t
    else if (t_1 <= 1d-18) then
        tmp = x / 1.0d0
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = y / t;
	} else if (t_1 <= 1e-18) {
		tmp = x / 1.0;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -2e-21:
		tmp = y / t
	elif t_1 <= 1e-18:
		tmp = x / 1.0
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -2e-21)
		tmp = Float64(y / t);
	elseif (t_1 <= 1e-18)
		tmp = Float64(x / 1.0);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -2e-21)
		tmp = y / t;
	elseif (t_1 <= 1e-18)
		tmp = x / 1.0;
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -2e-21], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 1e-18], N[(x / 1.0), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / t), $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))) < -1.99999999999999982e-21 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 71.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 58.7

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

   5. Applied rewrites 58.7%

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

   if -1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.0000000000000001e-18

   1. Initial program 92.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 50.7

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

   7. Applied rewrites 50.7%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{x}{1} \]
   9. Step-by-step derivation

   10. Applied rewrites 50.7%

       \[\leadsto \frac{x}{1} \]

   if 1.0000000000000001e-18 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 95.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{-18}:\\ \;\;\;\;\frac{x}{1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{-18}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -2e-21)
     (/ y t)
     (if (<= t_1 1e-18) (* (- 1.0 x) x) (if (<= t_1 2.0) 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = y / t;
	} else if (t_1 <= 1e-18) {
		tmp = (1.0 - x) * x;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	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 * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= (-2d-21)) then
        tmp = y / t
    else if (t_1 <= 1d-18) then
        tmp = (1.0d0 - x) * x
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -2e-21) {
		tmp = y / t;
	} else if (t_1 <= 1e-18) {
		tmp = (1.0 - x) * x;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -2e-21:
		tmp = y / t
	elif t_1 <= 1e-18:
		tmp = (1.0 - x) * x
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -2e-21)
		tmp = Float64(y / t);
	elseif (t_1 <= 1e-18)
		tmp = Float64(Float64(1.0 - x) * x);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -2e-21)
		tmp = y / t;
	elseif (t_1 <= 1e-18)
		tmp = (1.0 - x) * x;
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -2e-21], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 1e-18], N[(N[(1.0 - x), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / t), $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))) < -1.99999999999999982e-21 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 71.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 58.7

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

   5. Applied rewrites 58.7%

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

   if -1.99999999999999982e-21 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.0000000000000001e-18

   1. Initial program 92.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 50.7

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

   7. Applied rewrites 50.7%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 50.7%

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

   if 1.0000000000000001e-18 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 95.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{-18}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;t\_1 \leq 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 (- INFINITY))
     (* (/ y (fma t z (- x))) (/ z (+ 1.0 x)))
     (if (<= t_1 1e+146) t_1 (/ (+ (/ y t) x) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / fma(t, z, -x)) * (z / (1.0 + x));
	} else if (t_1 <= 1e+146) {
		tmp = t_1;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / fma(t, z, Float64(-x))) * Float64(z / Float64(1.0 + x)));
	elseif (t_1 <= 1e+146)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / N[(t * z + (-x)), $MachinePrecision]), $MachinePrecision] * N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+146], t$95$1, N[(N[(N[(y / t), $MachinePrecision] + x), $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))) < -inf.0

   1. Initial program 41.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.99999999999999934e145

   1. Initial program 98.1%

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

   if 9.99999999999999934e145 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 31.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(t, z, -x\right)} \cdot \frac{z}{1 + x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{+146}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-10} \lor \neg \left(t\_1 \leq 1.02\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{\mathsf{fma}\left(t, z, -x\right)}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (or (<= t_1 5e-10) (not (<= t_1 1.02)))
     (/ (+ (/ y t) x) (+ x 1.0))
     (/ (- x (/ x (fma t z (- x)))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= 5e-10) || !(t_1 <= 1.02)) {
		tmp = ((y / t) + x) / (x + 1.0);
	} else {
		tmp = (x - (x / fma(t, z, -x))) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if ((t_1 <= 5e-10) || !(t_1 <= 1.02))
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / fma(t, z, Float64(-x)))) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, 5e-10], N[Not[LessEqual[t$95$1, 1.02]], $MachinePrecision]], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(t * z + (-x)), $MachinePrecision]), $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))) < 5.00000000000000031e-10 or 1.02 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 79.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 73.6

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

   5. Applied rewrites 73.6%

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

   if 5.00000000000000031e-10 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.02

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 98.9

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

   5. Applied rewrites 98.9%

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

4. Final simplification 84.0%

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

Alternative 12: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 0.9999999990698063 \lor \neg \left(t\_1 \leq 1.02\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (or (<= t_1 0.9999999990698063) (not (<= t_1 1.02)))
     (/ (+ (/ y t) x) (+ x 1.0))
     1.0)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= 0.9999999990698063) || !(t_1 <= 1.02)) {
		tmp = ((y / t) + x) / (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) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if ((t_1 <= 0.9999999990698063d0) .or. (.not. (t_1 <= 1.02d0))) then
        tmp = ((y / t) + x) / (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 t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= 0.9999999990698063) || !(t_1 <= 1.02)) {
		tmp = ((y / t) + x) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if (t_1 <= 0.9999999990698063) or not (t_1 <= 1.02):
		tmp = ((y / t) + x) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if ((t_1 <= 0.9999999990698063) || !(t_1 <= 1.02))
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if ((t_1 <= 0.9999999990698063) || ~((t_1 <= 1.02)))
		tmp = ((y / t) + x) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, 0.9999999990698063], N[Not[LessEqual[t$95$1, 1.02]], $MachinePrecision]], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

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))) < 0.9999999990698063 or 1.02 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 79.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 74.0

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

   5. Applied rewrites 74.0%

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

   if 0.9999999990698063 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.02

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 98.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 0.9999999990698063 \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 1.02\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{-18}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) 1e-18)
   (* (- 1.0 x) x)
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)) <= 1e-18) {
		tmp = (1.0 - x) * x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)) <= 1d-18) then
        tmp = (1.0d0 - x) * x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)) <= 1e-18) {
		tmp = (1.0 - x) * x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)) <= 1e-18:
		tmp = (1.0 - x) * x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0)) <= 1e-18)
		tmp = Float64(Float64(1.0 - x) * x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)) <= 1e-18)
		tmp = (1.0 - x) * x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[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], 1e-18], N[(N[(1.0 - x), $MachinePrecision] * x), $MachinePrecision], 1.0]

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))) < 1.0000000000000001e-18

   1. Initial program 87.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. div-sub N/A

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

      6. sub-neg N/A

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

   4. Applied rewrites 90.5%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 30.2

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

   7. Applied rewrites 30.2%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 27.6%

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

   if 1.0000000000000001e-18 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 70.8%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 10^{-18}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.2% accurate, 45.0× 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 87.8%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 44.4%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.7× 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 2024318 
(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)))