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

Percentage Accurate: 89.3% → 97.4%

Time: 14.2s

Alternatives: 16

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: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+198}:\\ \;\;\;\;\frac{x + y \cdot \left(\frac{x}{y \cdot \left(x - z \cdot t\right)} + \frac{z}{t\_1}\right)}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+264}:\\ \;\;\;\;\frac{\left(x + \frac{y \cdot z}{t\_1}\right) - \frac{x}{t\_1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} - \frac{y}{x + 1}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -1e+198)
     (/ (+ x (* y (+ (/ x (* y (- x (* z t)))) (/ z t_1)))) (+ x 1.0))
     (if (<= t_2 1e+264)
       (/ (- (+ x (/ (* y z) t_1)) (/ x t_1)) (+ x 1.0))
       (- (/ x (+ x 1.0)) (/ (- (/ x (* z (+ x 1.0))) (/ y (+ x 1.0))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+198) {
		tmp = (x + (y * ((x / (y * (x - (z * t)))) + (z / t_1)))) / (x + 1.0);
	} else if (t_2 <= 1e+264) {
		tmp = ((x + ((y * z) / t_1)) - (x / t_1)) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / 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) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-1d+198)) then
        tmp = (x + (y * ((x / (y * (x - (z * t)))) + (z / t_1)))) / (x + 1.0d0)
    else if (t_2 <= 1d+264) then
        tmp = ((x + ((y * z) / t_1)) - (x / t_1)) / (x + 1.0d0)
    else
        tmp = (x / (x + 1.0d0)) - (((x / (z * (x + 1.0d0))) - (y / (x + 1.0d0))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+198) {
		tmp = (x + (y * ((x / (y * (x - (z * t)))) + (z / t_1)))) / (x + 1.0);
	} else if (t_2 <= 1e+264) {
		tmp = ((x + ((y * z) / t_1)) - (x / t_1)) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -1e+198:
		tmp = (x + (y * ((x / (y * (x - (z * t)))) + (z / t_1)))) / (x + 1.0)
	elif t_2 <= 1e+264:
		tmp = ((x + ((y * z) / t_1)) - (x / t_1)) / (x + 1.0)
	else:
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e+198)
		tmp = Float64(Float64(x + Float64(y * Float64(Float64(x / Float64(y * Float64(x - Float64(z * t)))) + Float64(z / t_1)))) / Float64(x + 1.0));
	elseif (t_2 <= 1e+264)
		tmp = Float64(Float64(Float64(x + Float64(Float64(y * z) / t_1)) - Float64(x / t_1)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(Float64(x / Float64(z * Float64(x + 1.0))) - Float64(y / Float64(x + 1.0))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e+198)
		tmp = (x + (y * ((x / (y * (x - (z * t)))) + (z / t_1)))) / (x + 1.0);
	elseif (t_2 <= 1e+264)
		tmp = ((x + ((y * z) / t_1)) - (x / t_1)) / (x + 1.0);
	else
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+198], N[(N[(x + N[(y * N[(N[(x / N[(y * N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+264], N[(N[(N[(x + N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1.00000000000000002e198

   1. Initial program 70.8%

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

      1. *-commutative 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in y around inf 99.9%

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

   if -1.00000000000000002e198 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000004e264

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

   3. Simplified 99.4%

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

      1. div-sub 99.4%

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

      2. associate-+r- 99.4%

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

   6. Applied egg-rr 99.4%

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

   if 1.00000000000000004e264 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 28.3%

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

      1. *-commutative 28.3%

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

   3. Simplified 28.3%

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

   5. Taylor expanded in t around -inf 74.3%

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

      1. +-commutative 74.3%

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

      2. mul-1-neg 74.3%

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

      3. unsub-neg 74.3%

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

      4. +-commutative 74.3%

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

      5. sub-neg 74.3%

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

      6. mul-1-neg 74.3%

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

      7. distribute-neg-frac2 74.3%

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

      8. distribute-neg-in 74.3%

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

      9. metadata-eval 74.3%

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

      10. unsub-neg 74.3%

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

      11. mul-1-neg 74.3%

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

      12. remove-double-neg 74.3%

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

      13. +-commutative 74.3%

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

   7. Simplified 74.3%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -1 \cdot 10^{+198}:\\ \;\;\;\;\frac{x + y \cdot \left(\frac{x}{y \cdot \left(x - z \cdot t\right)} + \frac{z}{z \cdot t - x}\right)}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 10^{+264}:\\ \;\;\;\;\frac{\left(x + \frac{y \cdot z}{z \cdot t - x}\right) - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} - \frac{y}{x + 1}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+264}:\\ \;\;\;\;\frac{\left(x + \frac{y \cdot z}{t\_1}\right) - \frac{x}{t\_1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} - \frac{y}{x + 1}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 (- INFINITY))
     (/ (+ x (* z (/ y t_1))) (+ x 1.0))
     (if (<= t_2 1e+264)
       (/ (- (+ x (/ (* y z) t_1)) (/ x t_1)) (+ x 1.0))
       (- (/ x (+ x 1.0)) (/ (- (/ x (* z (+ x 1.0))) (/ y (+ x 1.0))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else if (t_2 <= 1e+264) {
		tmp = ((x + ((y * z) / t_1)) - (x / t_1)) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else if (t_2 <= 1e+264) {
		tmp = ((x + ((y * z) / t_1)) - (x / t_1)) / (x + 1.0);
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (x + (z * (y / t_1))) / (x + 1.0)
	elif t_2 <= 1e+264:
		tmp = ((x + ((y * z) / t_1)) - (x / t_1)) / (x + 1.0)
	else:
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t_1))) / Float64(x + 1.0));
	elseif (t_2 <= 1e+264)
		tmp = Float64(Float64(Float64(x + Float64(Float64(y * z) / t_1)) - Float64(x / t_1)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(Float64(x / Float64(z * Float64(x + 1.0))) - Float64(y / Float64(x + 1.0))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	elseif (t_2 <= 1e+264)
		tmp = ((x + ((y * z) / t_1)) - (x / t_1)) / (x + 1.0);
	else
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(x + N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+264], N[(N[(N[(x + N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $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 62.0%

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

      1. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in y around inf 62.0%

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

      1. *-commutative 62.0%

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

   7. Simplified 62.0%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   9. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000004e264

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

   3. Simplified 99.4%

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

      1. div-sub 99.4%

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

      2. associate-+r- 99.4%

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

   6. Applied egg-rr 99.4%

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

   if 1.00000000000000004e264 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 28.3%

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

      1. *-commutative 28.3%

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

   3. Simplified 28.3%

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

   5. Taylor expanded in t around -inf 74.3%

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

      1. +-commutative 74.3%

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

      2. mul-1-neg 74.3%

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

      3. unsub-neg 74.3%

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

      4. +-commutative 74.3%

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

      5. sub-neg 74.3%

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

      6. mul-1-neg 74.3%

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

      7. distribute-neg-frac2 74.3%

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

      8. distribute-neg-in 74.3%

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

      9. metadata-eval 74.3%

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

      10. unsub-neg 74.3%

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

      11. mul-1-neg 74.3%

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

      12. remove-double-neg 74.3%

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

      13. +-commutative 74.3%

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

   7. Simplified 74.3%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 10^{+264}:\\ \;\;\;\;\frac{\left(x + \frac{y \cdot z}{z \cdot t - x}\right) - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} - \frac{y}{x + 1}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+264}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} - \frac{y}{x + 1}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 (- INFINITY))
     (/ (+ x (* z (/ y t_1))) (+ x 1.0))
     (if (<= t_2 1e+264)
       t_2
       (- (/ x (+ x 1.0)) (/ (- (/ x (* z (+ x 1.0))) (/ y (+ x 1.0))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else if (t_2 <= 1e+264) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else if (t_2 <= 1e+264) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (x + (z * (y / t_1))) / (x + 1.0)
	elif t_2 <= 1e+264:
		tmp = t_2
	else:
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t_1))) / Float64(x + 1.0));
	elseif (t_2 <= 1e+264)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(Float64(x / Float64(z * Float64(x + 1.0))) - Float64(y / Float64(x + 1.0))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	elseif (t_2 <= 1e+264)
		tmp = t_2;
	else
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(x + N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+264], t$95$2, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $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 62.0%

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

      1. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in y around inf 62.0%

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

      1. *-commutative 62.0%

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

   7. Simplified 62.0%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   9. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000004e264

   1. Initial program 99.4%

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

   if 1.00000000000000004e264 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 28.3%

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

      1. *-commutative 28.3%

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

   3. Simplified 28.3%

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

   5. Taylor expanded in t around -inf 74.3%

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

      1. +-commutative 74.3%

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

      2. mul-1-neg 74.3%

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

      3. unsub-neg 74.3%

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

      4. +-commutative 74.3%

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

      5. sub-neg 74.3%

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

      6. mul-1-neg 74.3%

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

      7. distribute-neg-frac2 74.3%

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

      8. distribute-neg-in 74.3%

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

      9. metadata-eval 74.3%

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

      10. unsub-neg 74.3%

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

      11. mul-1-neg 74.3%

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

      12. remove-double-neg 74.3%

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

      13. +-commutative 74.3%

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

   7. Simplified 74.3%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 10^{+264}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} - \frac{y}{x + 1}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 10^{+264}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 (- INFINITY))
     (/ (+ x (* z (/ y t_1))) (+ x 1.0))
     (if (<= t_2 1e+264) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else if (t_2 <= 1e+264) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else if (t_2 <= 1e+264) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (x + (z * (y / t_1))) / (x + 1.0)
	elif t_2 <= 1e+264:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t_1))) / Float64(x + 1.0));
	elseif (t_2 <= 1e+264)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	elseif (t_2 <= 1e+264)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(x + N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+264], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 62.0%

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

      1. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in y around inf 62.0%

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

      1. *-commutative 62.0%

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

   7. Simplified 62.0%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   9. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000004e264

   1. Initial program 99.4%

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

   if 1.00000000000000004e264 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 28.3%

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

      1. *-commutative 28.3%

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

   3. Simplified 28.3%

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

   5. Taylor expanded in z around inf 74.2%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 10^{+264}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-60}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-149}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.2e-60)
   1.0
   (if (<= x -2.5e-149)
     x
     (if (<= x 2.5e-120)
       (/ y t)
       (if (<= x 4.8e-66) x (if (<= x 5.2e-48) (/ y t) 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e-60) {
		tmp = 1.0;
	} else if (x <= -2.5e-149) {
		tmp = x;
	} else if (x <= 2.5e-120) {
		tmp = y / t;
	} else if (x <= 4.8e-66) {
		tmp = x;
	} else if (x <= 5.2e-48) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.2d-60)) then
        tmp = 1.0d0
    else if (x <= (-2.5d-149)) then
        tmp = x
    else if (x <= 2.5d-120) then
        tmp = y / t
    else if (x <= 4.8d-66) then
        tmp = x
    else if (x <= 5.2d-48) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e-60) {
		tmp = 1.0;
	} else if (x <= -2.5e-149) {
		tmp = x;
	} else if (x <= 2.5e-120) {
		tmp = y / t;
	} else if (x <= 4.8e-66) {
		tmp = x;
	} else if (x <= 5.2e-48) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.2e-60:
		tmp = 1.0
	elif x <= -2.5e-149:
		tmp = x
	elif x <= 2.5e-120:
		tmp = y / t
	elif x <= 4.8e-66:
		tmp = x
	elif x <= 5.2e-48:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.2e-60)
		tmp = 1.0;
	elseif (x <= -2.5e-149)
		tmp = x;
	elseif (x <= 2.5e-120)
		tmp = Float64(y / t);
	elseif (x <= 4.8e-66)
		tmp = x;
	elseif (x <= 5.2e-48)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.2e-60)
		tmp = 1.0;
	elseif (x <= -2.5e-149)
		tmp = x;
	elseif (x <= 2.5e-120)
		tmp = y / t;
	elseif (x <= 4.8e-66)
		tmp = x;
	elseif (x <= 5.2e-48)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.2e-60], 1.0, If[LessEqual[x, -2.5e-149], x, If[LessEqual[x, 2.5e-120], N[(y / t), $MachinePrecision], If[LessEqual[x, 4.8e-66], x, If[LessEqual[x, 5.2e-48], N[(y / t), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.19999999999999976e-60 or 5.19999999999999975e-48 < x

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around inf 97.2%

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

   6. Taylor expanded in x around inf 85.2%

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

   if -6.19999999999999976e-60 < x < -2.49999999999999984e-149 or 2.50000000000000003e-120 < x < 4.80000000000000052e-66

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around inf 49.0%

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

      1. +-commutative 49.0%

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

   7. Simplified 49.0%

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

   8. Taylor expanded in x around 0 49.0%

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

   if -2.49999999999999984e-149 < x < 2.50000000000000003e-120 or 4.80000000000000052e-66 < x < 5.19999999999999975e-48

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 85.8%

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

   6. Taylor expanded in x around 0 58.8%

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

Alternative 6: 85.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-131} \lor \neg \left(y \leq 3.9 \cdot 10^{-227}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e-131) (not (<= y 3.9e-227)))
   (/ (+ x (* z (/ y (- (* z t) x)))) (+ x 1.0))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e-131) || !(y <= 3.9e-227)) {
		tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.4d-131)) .or. (.not. (y <= 3.9d-227))) then
        tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0d0)
    else
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e-131) || !(y <= 3.9e-227)) {
		tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.4e-131) or not (y <= 3.9e-227):
		tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0)
	else:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4e-131) || !(y <= 3.9e-227))
		tmp = Float64(Float64(x + Float64(z * Float64(y / Float64(Float64(z * t) - x)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.4e-131) || ~((y <= 3.9e-227)))
		tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0);
	else
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4e-131], N[Not[LessEqual[y, 3.9e-227]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999995e-131 or 3.8999999999999999e-227 < y

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around inf 83.5%

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

      1. *-commutative 83.5%

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

   7. Simplified 83.5%

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

      1. associate-/l* 86.1%

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

      2. *-commutative 86.1%

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

   9. Applied egg-rr 86.1%

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

   if -3.39999999999999995e-131 < y < 3.8999999999999999e-227

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 94.6%

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

      1. +-commutative 94.6%

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

   7. Simplified 94.6%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-131} \lor \neg \left(y \leq 3.9 \cdot 10^{-227}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(1 + \frac{\frac{-1}{t}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.2e-149)
   (/ x (+ x 1.0))
   (if (<= x 3.1e-161)
     (/ y t)
     (if (<= x 6.5e-69) (* x (+ 1.0 (/ (/ -1.0 t) z))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-149) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.1e-161) {
		tmp = y / t;
	} else if (x <= 6.5e-69) {
		tmp = x * (1.0 + ((-1.0 / t) / z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.2d-149)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 3.1d-161) then
        tmp = y / t
    else if (x <= 6.5d-69) then
        tmp = x * (1.0d0 + (((-1.0d0) / t) / z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-149) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.1e-161) {
		tmp = y / t;
	} else if (x <= 6.5e-69) {
		tmp = x * (1.0 + ((-1.0 / t) / z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.2e-149:
		tmp = x / (x + 1.0)
	elif x <= 3.1e-161:
		tmp = y / t
	elif x <= 6.5e-69:
		tmp = x * (1.0 + ((-1.0 / t) / z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.2e-149)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 3.1e-161)
		tmp = Float64(y / t);
	elseif (x <= 6.5e-69)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(-1.0 / t) / z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.2e-149)
		tmp = x / (x + 1.0);
	elseif (x <= 3.1e-161)
		tmp = y / t;
	elseif (x <= 6.5e-69)
		tmp = x * (1.0 + ((-1.0 / t) / z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.2e-149], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-161], N[(y / t), $MachinePrecision], If[LessEqual[x, 6.5e-69], N[(x * N[(1.0 + N[(N[(-1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1999999999999998e-149

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in t around inf 78.5%

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

      1. +-commutative 78.5%

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

   7. Simplified 78.5%

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

   if -2.1999999999999998e-149 < x < 3.0999999999999999e-161

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in y around inf 85.4%

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

   6. Taylor expanded in x around 0 60.3%

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

   if 3.0999999999999999e-161 < x < 6.49999999999999951e-69

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around -inf 81.9%

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

      1. mul-1-neg 81.9%

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

      2. unsub-neg 81.9%

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

      3. cancel-sign-sub-inv 81.9%

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

      4. metadata-eval 81.9%

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

      5. *-lft-identity 81.9%

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

      6. +-commutative 81.9%

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

      7. mul-1-neg 81.9%

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

      8. unsub-neg 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in y around 0 59.6%

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

      1. associate-/l/ 59.7%

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

      2. +-commutative 59.7%

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

   10. Simplified 59.7%

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

   11. Taylor expanded in x around 0 59.7%

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

       1. associate-/r* 59.8%

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

   13. Simplified 59.8%

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

   if 6.49999999999999951e-69 < x

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around inf 96.3%

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

   6. Taylor expanded in x around inf 79.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(1 + \frac{\frac{-1}{t}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -2.5e-149)
     t_1
     (if (<= x 1.25e-120)
       (/ y t)
       (if (<= x 1.45e-62) t_1 (if (<= x 9.5e-48) (/ y t) 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.5e-149) {
		tmp = t_1;
	} else if (x <= 1.25e-120) {
		tmp = y / t;
	} else if (x <= 1.45e-62) {
		tmp = t_1;
	} else if (x <= 9.5e-48) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (x <= (-2.5d-149)) then
        tmp = t_1
    else if (x <= 1.25d-120) then
        tmp = y / t
    else if (x <= 1.45d-62) then
        tmp = t_1
    else if (x <= 9.5d-48) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.5e-149) {
		tmp = t_1;
	} else if (x <= 1.25e-120) {
		tmp = y / t;
	} else if (x <= 1.45e-62) {
		tmp = t_1;
	} else if (x <= 9.5e-48) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -2.5e-149:
		tmp = t_1
	elif x <= 1.25e-120:
		tmp = y / t
	elif x <= 1.45e-62:
		tmp = t_1
	elif x <= 9.5e-48:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -2.5e-149)
		tmp = t_1;
	elseif (x <= 1.25e-120)
		tmp = Float64(y / t);
	elseif (x <= 1.45e-62)
		tmp = t_1;
	elseif (x <= 9.5e-48)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -2.5e-149)
		tmp = t_1;
	elseif (x <= 1.25e-120)
		tmp = y / t;
	elseif (x <= 1.45e-62)
		tmp = t_1;
	elseif (x <= 9.5e-48)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e-149], t$95$1, If[LessEqual[x, 1.25e-120], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.45e-62], t$95$1, If[LessEqual[x, 9.5e-48], N[(y / t), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.49999999999999984e-149 or 1.25000000000000002e-120 < x < 1.44999999999999993e-62

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around inf 74.5%

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

      1. +-commutative 74.5%

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

   7. Simplified 74.5%

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

   if -2.49999999999999984e-149 < x < 1.25000000000000002e-120 or 1.44999999999999993e-62 < x < 9.50000000000000036e-48

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 85.8%

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

   6. Taylor expanded in x around 0 58.8%

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

   if 9.50000000000000036e-48 < x

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 96.2%

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

   6. Taylor expanded in x around inf 83.7%

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

Alternative 9: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-149} \lor \neg \left(x \leq 4.3 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.5e-149) (not (<= x 4.3e-48)))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))
   (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.5e-149) || !(x <= 4.3e-48)) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.5d-149)) .or. (.not. (x <= 4.3d-48))) then
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    else
        tmp = (x + ((y - (x / z)) / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.5e-149) || !(x <= 4.3e-48)) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.5e-149) or not (x <= 4.3e-48):
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	else:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.5e-149) || !(x <= 4.3e-48))
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.5e-149) || ~((x <= 4.3e-48)))
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	else
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.5e-149], N[Not[LessEqual[x, 4.3e-48]], $MachinePrecision]], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.49999999999999995e-149 or 4.3e-48 < x

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. +-commutative 88.3%

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

   7. Simplified 88.3%

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

   if -7.49999999999999995e-149 < x < 4.3e-48

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around -inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. cancel-sign-sub-inv 76.4%

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

      4. metadata-eval 76.4%

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

      5. *-lft-identity 76.4%

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

      6. +-commutative 76.4%

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

      7. mul-1-neg 76.4%

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

      8. unsub-neg 76.4%

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

   7. Simplified 76.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-149} \lor \neg \left(x \leq 4.3 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-149} \lor \neg \left(x \leq 7.8 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.6e-149) (not (<= x 7.8e-48)))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))
   (/ (+ x (/ y t)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-149) || !(x <= 7.8e-48)) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.6d-149)) .or. (.not. (x <= 7.8d-48))) then
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-149) || !(x <= 7.8e-48)) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.6e-149) or not (x <= 7.8e-48):
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.6e-149) || !(x <= 7.8e-48))
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.6e-149) || ~((x <= 7.8e-48)))
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.6e-149], N[Not[LessEqual[x, 7.8e-48]], $MachinePrecision]], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000001e-149 or 7.800000000000001e-48 < x

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. +-commutative 88.3%

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

   7. Simplified 88.3%

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

   if -7.6000000000000001e-149 < x < 7.800000000000001e-48

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around inf 70.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-149} \lor \neg \left(x \leq 7.8 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-149}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-48}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.6e-149)
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))
   (if (<= x 5.1e-48)
     (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0))
     (/ (- (+ x 1.0) (* y (/ z x))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e-149) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else if (x <= 5.1e-48) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-7.6d-149)) then
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    else if (x <= 5.1d-48) then
        tmp = (x + ((y - (x / z)) / t)) / (x + 1.0d0)
    else
        tmp = ((x + 1.0d0) - (y * (z / x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e-149) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else if (x <= 5.1e-48) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.6e-149:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	elif x <= 5.1e-48:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	else:
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.6e-149)
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	elseif (x <= 5.1e-48)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.6e-149)
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	elseif (x <= 5.1e-48)
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	else
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.6e-149], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.1e-48], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.6000000000000001e-149

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in y around 0 89.1%

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

      1. +-commutative 89.1%

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

   7. Simplified 89.1%

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

   if -7.6000000000000001e-149 < x < 5.10000000000000011e-48

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around -inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. cancel-sign-sub-inv 76.4%

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

      4. metadata-eval 76.4%

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

      5. *-lft-identity 76.4%

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

      6. +-commutative 76.4%

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

      7. mul-1-neg 76.4%

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

      8. unsub-neg 76.4%

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

   7. Simplified 76.4%

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

   if 5.10000000000000011e-48 < x

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 85.0%

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

      1. associate-+r+ 85.0%

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

      2. mul-1-neg 85.0%

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

      3. unsub-neg 85.0%

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

      4. +-commutative 85.0%

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

      5. associate-/l* 88.9%

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

      6. +-commutative 88.9%

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

   7. Simplified 88.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-149}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-48}:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-53}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.18e-53)
   1.0
   (if (<= x 1.1e-29)
     (+ (/ x (+ x 1.0)) (/ y (* t (+ x 1.0))))
     (/ (- x (* y (/ z x))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.18e-53) {
		tmp = 1.0;
	} else if (x <= 1.1e-29) {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	} else {
		tmp = (x - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.18d-53)) then
        tmp = 1.0d0
    else if (x <= 1.1d-29) then
        tmp = (x / (x + 1.0d0)) + (y / (t * (x + 1.0d0)))
    else
        tmp = (x - (y * (z / x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.18e-53) {
		tmp = 1.0;
	} else if (x <= 1.1e-29) {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	} else {
		tmp = (x - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.18e-53:
		tmp = 1.0
	elif x <= 1.1e-29:
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)))
	else:
		tmp = (x - (y * (z / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.18e-53)
		tmp = 1.0;
	elseif (x <= 1.1e-29)
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(x + 1.0))));
	else
		tmp = Float64(Float64(x - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.18e-53)
		tmp = 1.0;
	elseif (x <= 1.1e-29)
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	else
		tmp = (x - (y * (z / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.18e-53], 1.0, If[LessEqual[x, 1.1e-29], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.18000000000000005e-53

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around inf 98.3%

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

   6. Taylor expanded in x around inf 86.8%

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

   if -1.18000000000000005e-53 < x < 1.09999999999999995e-29

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in y around inf 76.4%

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

      1. *-commutative 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in t around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. +-commutative 66.3%

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

   10. Simplified 66.3%

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

   if 1.09999999999999995e-29 < x

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around inf 85.3%

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

      1. *-commutative 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in t around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. unsub-neg 84.2%

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

      3. associate-/l* 88.3%

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

      4. +-commutative 88.3%

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

   10. Simplified 88.3%

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

Alternative 13: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-53}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-28}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.05e-53)
   1.0
   (if (<= x 1.85e-28)
     (/ (+ x (/ y t)) (+ x 1.0))
     (/ (- x (* y (/ z x))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.05e-53) {
		tmp = 1.0;
	} else if (x <= 1.85e-28) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.05d-53)) then
        tmp = 1.0d0
    else if (x <= 1.85d-28) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x - (y * (z / x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.05e-53) {
		tmp = 1.0;
	} else if (x <= 1.85e-28) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.05e-53:
		tmp = 1.0
	elif x <= 1.85e-28:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x - (y * (z / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.05e-53)
		tmp = 1.0;
	elseif (x <= 1.85e-28)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.05e-53)
		tmp = 1.0;
	elseif (x <= 1.85e-28)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x - (y * (z / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.05e-53], 1.0, If[LessEqual[x, 1.85e-28], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.04999999999999989e-53

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around inf 98.3%

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

   6. Taylor expanded in x around inf 86.8%

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

   if -1.04999999999999989e-53 < x < 1.8500000000000001e-28

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around inf 66.3%

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

   if 1.8500000000000001e-28 < x

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around inf 85.3%

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

      1. *-commutative 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in t around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. unsub-neg 84.2%

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

      3. associate-/l* 88.3%

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

      4. +-commutative 88.3%

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

   10. Simplified 88.3%

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

Alternative 14: 76.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-53}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.05e-53)
   1.0
   (if (<= x 1.02e-47) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.05e-53) {
		tmp = 1.0;
	} else if (x <= 1.02e-47) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.05d-53)) then
        tmp = 1.0d0
    else if (x <= 1.02d-47) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.05e-53) {
		tmp = 1.0;
	} else if (x <= 1.02e-47) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.05e-53:
		tmp = 1.0
	elif x <= 1.02e-47:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.05e-53)
		tmp = 1.0;
	elseif (x <= 1.02e-47)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.05e-53)
		tmp = 1.0;
	elseif (x <= 1.02e-47)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.05e-53], 1.0, If[LessEqual[x, 1.02e-47], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.04999999999999989e-53 or 1.02000000000000002e-47 < x

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around inf 97.2%

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

   6. Taylor expanded in x around inf 85.2%

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

   if -1.04999999999999989e-53 < x < 1.02000000000000002e-47

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around inf 67.8%

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

Alternative 15: 56.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-59}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.2e-59) 1.0 (if (<= x 4.8e-68) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.2e-59) {
		tmp = 1.0;
	} else if (x <= 4.8e-68) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-8.2d-59)) then
        tmp = 1.0d0
    else if (x <= 4.8d-68) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.2e-59) {
		tmp = 1.0;
	} else if (x <= 4.8e-68) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.2e-59:
		tmp = 1.0
	elif x <= 4.8e-68:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.2e-59)
		tmp = 1.0;
	elseif (x <= 4.8e-68)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.2e-59)
		tmp = 1.0;
	elseif (x <= 4.8e-68)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.2e-59], 1.0, If[LessEqual[x, 4.8e-68], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999991e-59 or 4.79999999999999982e-68 < x

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 97.2%

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

   6. Taylor expanded in x around inf 83.1%

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

   if -8.1999999999999991e-59 < x < 4.79999999999999982e-68

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around inf 26.1%

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

      1. +-commutative 26.1%

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

   7. Simplified 26.1%

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

   8. Taylor expanded in x around 0 26.1%

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

Alternative 16: 54.0% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 92.2%

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

   1. *-commutative 92.2%

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

3. Simplified 92.2%

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

5. Taylor expanded in y around inf 93.0%

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

6. Taylor expanded in x around inf 53.6%

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

Developer target: 99.6% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024081 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

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