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

Percentage Accurate: 89.8% → 97.0%

Time: 12.5s

Alternatives: 11

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: 89.8% 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: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+232}:\\ \;\;\;\;\frac{x - y \cdot \left(\frac{x}{y \cdot t\_1} - \frac{z}{t\_1}\right)}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+171}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{\frac{x}{z}}{x + 1} - \frac{y}{x + 1}}{t}\\ \end{array} \end{array} \]

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 -5e+232)
     (/ (- x (* y (- (/ x (* y t_1)) (/ z t_1)))) (+ x 1.0))
     (if (<= t_2 4e+171)
       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 <= -5e+232) {
		tmp = (x - (y * ((x / (y * t_1)) - (z / t_1)))) / (x + 1.0);
	} else if (t_2 <= 4e+171) {
		tmp = t_2;
	} 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 <= (-5d+232)) then
        tmp = (x - (y * ((x / (y * t_1)) - (z / t_1)))) / (x + 1.0d0)
    else if (t_2 <= 4d+171) then
        tmp = t_2
    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 <= -5e+232) {
		tmp = (x - (y * ((x / (y * t_1)) - (z / t_1)))) / (x + 1.0);
	} else if (t_2 <= 4e+171) {
		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 <= -5e+232:
		tmp = (x - (y * ((x / (y * t_1)) - (z / t_1)))) / (x + 1.0)
	elif t_2 <= 4e+171:
		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 <= -5e+232)
		tmp = Float64(Float64(x - Float64(y * Float64(Float64(x / Float64(y * t_1)) - Float64(z / t_1)))) / Float64(x + 1.0));
	elseif (t_2 <= 4e+171)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(Float64(Float64(x / 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 <= -5e+232)
		tmp = (x - (y * ((x / (y * t_1)) - (z / t_1)))) / (x + 1.0);
	elseif (t_2 <= 4e+171)
		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, -5e+232], N[(N[(x - N[(y * N[(N[(x / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+171], t$95$2, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(x / z), $MachinePrecision] / N[(x + 1.0), $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))) < -4.99999999999999987e232

   1. Initial program 64.0%

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

      1. *-commutative 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in y around inf 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 -4.99999999999999987e232 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.99999999999999982e171

   1. Initial program 99.4%

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

   if 3.99999999999999982e171 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 40.7%

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

      1. *-commutative 40.7%

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

   3. Simplified 40.7%

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

   5. Taylor expanded in t around -inf 86.2%

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

      1. +-commutative 86.2%

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

      2. mul-1-neg 86.2%

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

      3. unsub-neg 86.2%

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

      4. +-commutative 86.2%

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

      5. sub-neg 86.2%

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

      6. mul-1-neg 86.2%

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

      7. distribute-neg-frac2 86.2%

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

      8. distribute-neg-in 86.2%

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

      9. metadata-eval 86.2%

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

      10. unsub-neg 86.2%

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

      11. mul-1-neg 86.2%

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

      12. remove-double-neg 86.2%

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

      13. associate-/r* 86.2%

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

      14. +-commutative 86.2%

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

   7. Simplified 86.2%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+232}:\\ \;\;\;\;\frac{x - y \cdot \left(\frac{x}{y \cdot \left(z \cdot t - x\right)} - \frac{z}{z \cdot t - x}\right)}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 4 \cdot 10^{+171}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{\frac{x}{z}}{x + 1} - \frac{y}{x + 1}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{y}}}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{\frac{x}{z}}{x + 1} - \frac{y}{x + 1}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 (- INFINITY))
     (/ (+ x (/ 1.0 (/ t y))) (+ x 1.0))
     (if (<= t_1 4e+171)
       t_1
       (- (/ 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 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x + (1.0 / (t / y))) / (x + 1.0);
	} else if (t_1 <= 4e+171) {
		tmp = t_1;
	} 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 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (1.0 / (t / y))) / (x + 1.0);
	} else if (t_1 <= 4e+171) {
		tmp = t_1;
	} 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 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x + (1.0 / (t / y))) / (x + 1.0)
	elif t_1 <= 4e+171:
		tmp = t_1
	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(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(1.0 / Float64(t / y))) / Float64(x + 1.0));
	elseif (t_1 <= 4e+171)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(Float64(Float64(x / 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 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x + (1.0 / (t / y))) / (x + 1.0);
	elseif (t_1 <= 4e+171)
		tmp = t_1;
	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[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x + N[(1.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+171], t$95$1, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(x / z), $MachinePrecision] / N[(x + 1.0), $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 48.0%

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

      1. *-commutative 48.0%

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

   3. Simplified 48.0%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. +-commutative 99.9%

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

   7. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. unpow-1 100.0%

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

   11. Simplified 100.0%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.99999999999999982e171

   1. Initial program 99.4%

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

   if 3.99999999999999982e171 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 40.7%

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

      1. *-commutative 40.7%

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

   3. Simplified 40.7%

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

   5. Taylor expanded in t around -inf 86.2%

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

      1. +-commutative 86.2%

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

      2. mul-1-neg 86.2%

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

      3. unsub-neg 86.2%

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

      4. +-commutative 86.2%

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

      5. sub-neg 86.2%

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

      6. mul-1-neg 86.2%

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

      7. distribute-neg-frac2 86.2%

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

      8. distribute-neg-in 86.2%

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

      9. metadata-eval 86.2%

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

      10. unsub-neg 86.2%

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

      11. mul-1-neg 86.2%

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

      12. remove-double-neg 86.2%

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

      13. associate-/r* 86.2%

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

      14. +-commutative 86.2%

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

   7. Simplified 86.2%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{y}}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 4 \cdot 10^{+171}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{\frac{x}{z}}{x + 1} - \frac{y}{x + 1}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{y}}}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 (- INFINITY))
     (/ (+ x (/ 1.0 (/ t y))) (+ x 1.0))
     (if (<= t_1 4e+171) t_1 (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x + (1.0 / (t / y))) / (x + 1.0);
	} else if (t_1 <= 4e+171) {
		tmp = t_1;
	} else {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (1.0 / (t / y))) / (x + 1.0);
	} else if (t_1 <= 4e+171) {
		tmp = t_1;
	} else {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x + (1.0 / (t / y))) / (x + 1.0)
	elif t_1 <= 4e+171:
		tmp = t_1
	else:
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(1.0 / Float64(t / y))) / Float64(x + 1.0));
	elseif (t_1 <= 4e+171)
		tmp = t_1;
	else
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x + (1.0 / (t / y))) / (x + 1.0);
	elseif (t_1 <= 4e+171)
		tmp = t_1;
	else
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x + N[(1.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+171], t$95$1, N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / 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 48.0%

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

      1. *-commutative 48.0%

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

   3. Simplified 48.0%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. +-commutative 99.9%

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

   7. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. unpow-1 100.0%

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

   11. Simplified 100.0%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.99999999999999982e171

   1. Initial program 99.4%

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

   if 3.99999999999999982e171 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 40.7%

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

      1. *-commutative 40.7%

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

   3. Simplified 40.7%

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

   5. Taylor expanded in t around -inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. distribute-lft-out-- 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{y}}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 4 \cdot 10^{+171}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-143}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+38}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -2.5e-122)
     t_1
     (if (<= t 4.3e-143)
       (/ (+ (- x (* y (/ z x))) 1.0) (+ x 1.0))
       (if (<= t 2.65e+38) (/ (- x (/ x (- (* z t) x))) (+ x 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -2.5e-122) {
		tmp = t_1;
	} else if (t <= 4.3e-143) {
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	} else if (t <= 2.65e+38) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-2.5d-122)) then
        tmp = t_1
    else if (t <= 4.3d-143) then
        tmp = ((x - (y * (z / x))) + 1.0d0) / (x + 1.0d0)
    else if (t <= 2.65d+38) then
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -2.5e-122) {
		tmp = t_1;
	} else if (t <= 4.3e-143) {
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	} else if (t <= 2.65e+38) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -2.5e-122:
		tmp = t_1
	elif t <= 4.3e-143:
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0)
	elif t <= 2.65e+38:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -2.5e-122)
		tmp = t_1;
	elseif (t <= 4.3e-143)
		tmp = Float64(Float64(Float64(x - Float64(y * Float64(z / x))) + 1.0) / Float64(x + 1.0));
	elseif (t <= 2.65e+38)
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -2.5e-122)
		tmp = t_1;
	elseif (t <= 4.3e-143)
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	elseif (t <= 2.65e+38)
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e-122], t$95$1, If[LessEqual[t, 4.3e-143], N[(N[(N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+38], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4999999999999999e-122 or 2.65000000000000012e38 < t

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in z around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. +-commutative 88.6%

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

   7. Simplified 88.6%

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

   if -2.4999999999999999e-122 < t < 4.29999999999999956e-143

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around 0 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

      3. associate-/l* 89.2%

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

      4. +-commutative 89.2%

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

   7. Simplified 89.2%

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

   if 4.29999999999999956e-143 < t < 2.65000000000000012e38

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in y around 0 71.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-122}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-143}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+38}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;x \leq 28000:\\ \;\;\;\;\frac{z}{x + 1} \cdot \frac{y}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.4e-26)
   1.0
   (if (<= x 7.5e-40)
     (/ (+ x (/ y t)) (+ x 1.0))
     (if (<= x 28000.0) (* (/ z (+ x 1.0)) (/ y (- (* z t) x))) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.4e-26) {
		tmp = 1.0;
	} else if (x <= 7.5e-40) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (x <= 28000.0) {
		tmp = (z / (x + 1.0)) * (y / ((z * t) - 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 <= (-3.4d-26)) then
        tmp = 1.0d0
    else if (x <= 7.5d-40) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (x <= 28000.0d0) then
        tmp = (z / (x + 1.0d0)) * (y / ((z * t) - 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 <= -3.4e-26) {
		tmp = 1.0;
	} else if (x <= 7.5e-40) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (x <= 28000.0) {
		tmp = (z / (x + 1.0)) * (y / ((z * t) - x));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.4e-26:
		tmp = 1.0
	elif x <= 7.5e-40:
		tmp = (x + (y / t)) / (x + 1.0)
	elif x <= 28000.0:
		tmp = (z / (x + 1.0)) * (y / ((z * t) - x))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.4e-26)
		tmp = 1.0;
	elseif (x <= 7.5e-40)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (x <= 28000.0)
		tmp = Float64(Float64(z / Float64(x + 1.0)) * Float64(y / Float64(Float64(z * t) - x)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.4e-26)
		tmp = 1.0;
	elseif (x <= 7.5e-40)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (x <= 28000.0)
		tmp = (z / (x + 1.0)) * (y / ((z * t) - x));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.4e-26], 1.0, If[LessEqual[x, 7.5e-40], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 28000.0], N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(y / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.40000000000000013e-26 or 28000 < 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 x around inf 90.0%

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

   if -3.40000000000000013e-26 < x < 7.50000000000000069e-40

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in z around inf 64.5%

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

      1. +-commutative 64.5%

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

      2. +-commutative 64.5%

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

   7. Simplified 64.5%

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

   if 7.50000000000000069e-40 < x < 28000

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 78.9%

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

      1. associate-/l/ 78.9%

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

      2. *-commutative 78.9%

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

      3. times-frac 78.9%

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

   7. Applied egg-rr 78.9%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-40}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;x \leq 28000:\\ \;\;\;\;\frac{z}{x + 1} \cdot \frac{y}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-122} \lor \neg \left(t \leq 6.5 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.6e-122) (not (<= t 6.5e+36)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ (- x (* y (/ z x))) 1.0) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.6e-122) || !(t <= 6.5e+36)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x - (y * (z / x))) + 1.0) / (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 ((t <= (-5.6d-122)) .or. (.not. (t <= 6.5d+36))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = ((x - (y * (z / x))) + 1.0d0) / (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 ((t <= -5.6e-122) || !(t <= 6.5e+36)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.6e-122) or not (t <= 6.5e+36):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.6e-122) || !(t <= 6.5e+36))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x - Float64(y * Float64(z / x))) + 1.0) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.6e-122) || ~((t <= 6.5e+36)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = ((x - (y * (z / x))) + 1.0) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.6e-122], N[Not[LessEqual[t, 6.5e+36]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5999999999999998e-122 or 6.4999999999999998e36 < t

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in z around inf 88.1%

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

      1. +-commutative 88.1%

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

      2. +-commutative 88.1%

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

   7. Simplified 88.1%

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

   if -5.5999999999999998e-122 < t < 6.4999999999999998e36

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. unsub-neg 77.2%

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

      3. associate-/l* 79.8%

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

      4. +-commutative 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-122} \lor \neg \left(t \leq 6.5 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y \cdot \frac{z}{x}\right) + 1}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3700000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.8e-26)
   1.0
   (if (<= x 3700000000.0) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.8e-26) {
		tmp = 1.0;
	} else if (x <= 3700000000.0) {
		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 <= (-7.8d-26)) then
        tmp = 1.0d0
    else if (x <= 3700000000.0d0) 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 <= -7.8e-26) {
		tmp = 1.0;
	} else if (x <= 3700000000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.8e-26:
		tmp = 1.0
	elif x <= 3700000000.0:
		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 <= -7.8e-26)
		tmp = 1.0;
	elseif (x <= 3700000000.0)
		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 <= -7.8e-26)
		tmp = 1.0;
	elseif (x <= 3700000000.0)
		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, -7.8e-26], 1.0, If[LessEqual[x, 3700000000.0], 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 < -7.79999999999999973e-26 or 3.7e9 < 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 x around inf 90.0%

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

   if -7.79999999999999973e-26 < x < 3.7e9

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in z around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. +-commutative 61.8%

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

   7. Simplified 61.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3700000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-43}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 28000:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.4e-43) 1.0 (if (<= x 28000.0) (* z (/ y (- (* z t) x))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e-43) {
		tmp = 1.0;
	} else if (x <= 28000.0) {
		tmp = z * (y / ((z * t) - x));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.4d-43)) then
        tmp = 1.0d0
    else if (x <= 28000.0d0) then
        tmp = z * (y / ((z * t) - x))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e-43) {
		tmp = 1.0;
	} else if (x <= 28000.0) {
		tmp = z * (y / ((z * t) - x));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.4e-43:
		tmp = 1.0
	elif x <= 28000.0:
		tmp = z * (y / ((z * t) - x))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.4e-43)
		tmp = 1.0;
	elseif (x <= 28000.0)
		tmp = Float64(z * Float64(y / Float64(Float64(z * t) - x)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.4e-43)
		tmp = 1.0;
	elseif (x <= 28000.0)
		tmp = z * (y / ((z * t) - x));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.4e-43], 1.0, If[LessEqual[x, 28000.0], N[(z * N[(y / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999e-43 or 28000 < 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 x around inf 88.2%

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

   if -1.3999999999999999e-43 < x < 28000

   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 y around inf 48.8%

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

      1. associate-/l/ 48.8%

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

      2. *-commutative 48.8%

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

      3. times-frac 48.8%

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

   7. Applied egg-rr 48.8%

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

   8. Taylor expanded in x around 0 47.6%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-43}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 28000:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-69}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.5e-69) 1.0 (if (<= x 5.9e-156) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-69) {
		tmp = 1.0;
	} else if (x <= 5.9e-156) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.5d-69)) then
        tmp = 1.0d0
    else if (x <= 5.9d-156) then
        tmp = y / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-69) {
		tmp = 1.0;
	} else if (x <= 5.9e-156) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.5e-69:
		tmp = 1.0
	elif x <= 5.9e-156:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.5e-69)
		tmp = 1.0;
	elseif (x <= 5.9e-156)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.5e-69)
		tmp = 1.0;
	elseif (x <= 5.9e-156)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.5e-69], 1.0, If[LessEqual[x, 5.9e-156], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.50000000000000017e-69

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in x around inf 80.8%

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

   if -2.50000000000000017e-69 < x < 5.8999999999999999e-156

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in x around 0 51.7%

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

   if 5.8999999999999999e-156 < x

   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 76.0%

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

      1. +-commutative 76.0%

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

   7. Simplified 76.0%

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

Alternative 10: 68.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-68}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.02 \cdot 10^{-112}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.6e-68) 1.0 (if (<= x 2.02e-112) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e-68) {
		tmp = 1.0;
	} else if (x <= 2.02e-112) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.6d-68)) then
        tmp = 1.0d0
    else if (x <= 2.02d-112) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e-68) {
		tmp = 1.0;
	} else if (x <= 2.02e-112) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.6e-68:
		tmp = 1.0
	elif x <= 2.02e-112:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.6e-68)
		tmp = 1.0;
	elseif (x <= 2.02e-112)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.6e-68)
		tmp = 1.0;
	elseif (x <= 2.02e-112)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.6e-68], 1.0, If[LessEqual[x, 2.02e-112], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5999999999999999e-68 or 2.02e-112 < 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 x around inf 78.1%

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

   if -1.5999999999999999e-68 < x < 2.02e-112

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in x around 0 49.1%

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

Alternative 11: 55.3% 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 90.8%

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

   1. *-commutative 90.8%

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

3. Simplified 90.8%

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

5. Taylor expanded in x around inf 55.9%

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

Developer Target 1: 99.5% 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 2024145 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1)))

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