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

Percentage Accurate: 88.8% → 94.3%

Time: 9.4s

Alternatives: 10

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.8% 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: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+260}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 5e+260) t_1 (/ (+ x (/ 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 <= 5e+260) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= 5d+260) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+260) {
		tmp = t_1;
	} else {
		tmp = (x + (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 <= 5e+260:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 5e+260)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 5e+260)
		tmp = t_1;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(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, 5e+260], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 4.9999999999999996e260

   1. Initial program 96.9%

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

   if 4.9999999999999996e260 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 9.7%

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

      1. *-commutative 9.7%

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

   3. Simplified 9.7%

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

   4. Taylor expanded in z around inf 81.6%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+260}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{z \cdot t}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-93}:\\ \;\;\;\;\frac{-y \cdot z}{x}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ x (* z t)))))
   (if (<= x -2.6e-13)
     (/ x (+ x 1.0))
     (if (<= x -5.8e-43)
       (/ y (* t (+ x 1.0)))
       (if (<= x -3.1e-71)
         t_1
         (if (<= x -3e-93)
           (/ (- (* y z)) x)
           (if (<= x -3.7e-190)
             t_1
             (if (<= x 5e-102) (/ y t) (if (<= x 2.25e-35) t_1 1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (x / (z * t));
	double tmp;
	if (x <= -2.6e-13) {
		tmp = x / (x + 1.0);
	} else if (x <= -5.8e-43) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= -3.1e-71) {
		tmp = t_1;
	} else if (x <= -3e-93) {
		tmp = -(y * z) / x;
	} else if (x <= -3.7e-190) {
		tmp = t_1;
	} else if (x <= 5e-102) {
		tmp = y / t;
	} else if (x <= 2.25e-35) {
		tmp = t_1;
	} 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 / (z * t))
    if (x <= (-2.6d-13)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-5.8d-43)) then
        tmp = y / (t * (x + 1.0d0))
    else if (x <= (-3.1d-71)) then
        tmp = t_1
    else if (x <= (-3d-93)) then
        tmp = -(y * z) / x
    else if (x <= (-3.7d-190)) then
        tmp = t_1
    else if (x <= 5d-102) then
        tmp = y / t
    else if (x <= 2.25d-35) then
        tmp = t_1
    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 / (z * t));
	double tmp;
	if (x <= -2.6e-13) {
		tmp = x / (x + 1.0);
	} else if (x <= -5.8e-43) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= -3.1e-71) {
		tmp = t_1;
	} else if (x <= -3e-93) {
		tmp = -(y * z) / x;
	} else if (x <= -3.7e-190) {
		tmp = t_1;
	} else if (x <= 5e-102) {
		tmp = y / t;
	} else if (x <= 2.25e-35) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (x / (z * t))
	tmp = 0
	if x <= -2.6e-13:
		tmp = x / (x + 1.0)
	elif x <= -5.8e-43:
		tmp = y / (t * (x + 1.0))
	elif x <= -3.1e-71:
		tmp = t_1
	elif x <= -3e-93:
		tmp = -(y * z) / x
	elif x <= -3.7e-190:
		tmp = t_1
	elif x <= 5e-102:
		tmp = y / t
	elif x <= 2.25e-35:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(x / Float64(z * t)))
	tmp = 0.0
	if (x <= -2.6e-13)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -5.8e-43)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	elseif (x <= -3.1e-71)
		tmp = t_1;
	elseif (x <= -3e-93)
		tmp = Float64(Float64(-Float64(y * z)) / x);
	elseif (x <= -3.7e-190)
		tmp = t_1;
	elseif (x <= 5e-102)
		tmp = Float64(y / t);
	elseif (x <= 2.25e-35)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (x / (z * t));
	tmp = 0.0;
	if (x <= -2.6e-13)
		tmp = x / (x + 1.0);
	elseif (x <= -5.8e-43)
		tmp = y / (t * (x + 1.0));
	elseif (x <= -3.1e-71)
		tmp = t_1;
	elseif (x <= -3e-93)
		tmp = -(y * z) / x;
	elseif (x <= -3.7e-190)
		tmp = t_1;
	elseif (x <= 5e-102)
		tmp = y / t;
	elseif (x <= 2.25e-35)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e-13], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.8e-43], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.1e-71], t$95$1, If[LessEqual[x, -3e-93], N[((-N[(y * z), $MachinePrecision]) / x), $MachinePrecision], If[LessEqual[x, -3.7e-190], t$95$1, If[LessEqual[x, 5e-102], N[(y / t), $MachinePrecision], If[LessEqual[x, 2.25e-35], t$95$1, 1.0]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.6e-13

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in t around inf 91.8%

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

      1. +-commutative 91.8%

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

   6. Simplified 91.8%

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

   if -2.6e-13 < x < -5.8000000000000003e-43

   1. Initial program 68.0%

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

      1. *-commutative 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in y around inf 68.0%

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

      1. times-frac 99.7%

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

      2. +-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in t around inf 68.4%

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

   if -5.8000000000000003e-43 < x < -3.10000000000000002e-71 or -3.0000000000000001e-93 < x < -3.7000000000000002e-190 or 5.00000000000000026e-102 < x < 2.25000000000000005e-35

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in y around 0 69.1%

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

      1. +-commutative 69.1%

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

   6. Simplified 69.1%

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

      1. clear-num 69.1%

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

      2. inv-pow 69.1%

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

   8. Applied egg-rr 69.1%

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

      1. unpow-1 69.1%

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

      2. div-sub 69.1%

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

      3. sub-neg 69.1%

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

      4. associate-/l* 69.0%

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

      5. *-inverses 69.0%

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

      6. metadata-eval 69.0%

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

   10. Simplified 69.0%

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

   11. Taylor expanded in x around 0 52.4%

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

       1. *-commutative 52.4%

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

       2. sub-neg 52.4%

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

       3. distribute-neg-frac 52.4%

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

       4. metadata-eval 52.4%

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

       5. distribute-rgt-in 52.4%

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

       6. *-lft-identity 52.4%

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

       7. associate-*l/ 52.5%

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

       8. associate-*r/ 52.5%

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

       9. mul-1-neg 52.5%

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

       10. unsub-neg 52.5%

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

   13. Simplified 52.5%

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

   if -3.10000000000000002e-71 < x < -3.0000000000000001e-93

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in y around inf 63.2%

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

      1. times-frac 63.4%

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

      2. +-commutative 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in x around 0 63.4%

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

   8. Taylor expanded in t around 0 63.6%

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

      1. associate-*r/ 63.6%

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

      2. mul-1-neg 63.6%

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

      3. distribute-rgt-neg-out 63.6%

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

   10. Simplified 63.6%

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

   if -3.7000000000000002e-190 < x < 5.00000000000000026e-102

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 60.2%

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

      1. times-frac 48.9%

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

      2. +-commutative 48.9%

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

   6. Simplified 48.9%

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

   7. Taylor expanded in x around 0 54.5%

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

   if 2.25000000000000005e-35 < x

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around 0 92.6%

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

      1. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in x around inf 88.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-71}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-93}:\\ \;\;\;\;\frac{-y \cdot z}{x}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-190}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-35}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-228}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+46}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -1.3e-44)
     t_1
     (if (<= z 1.75e-228)
       (/ (+ 1.0 (- x (/ y (/ x z)))) (+ x 1.0))
       (if (<= z 1.1e+46) (/ (- 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 (z <= -1.3e-44) {
		tmp = t_1;
	} else if (z <= 1.75e-228) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else if (z <= 1.1e+46) {
		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 (z <= (-1.3d-44)) then
        tmp = t_1
    else if (z <= 1.75d-228) then
        tmp = (1.0d0 + (x - (y / (x / z)))) / (x + 1.0d0)
    else if (z <= 1.1d+46) 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 (z <= -1.3e-44) {
		tmp = t_1;
	} else if (z <= 1.75e-228) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else if (z <= 1.1e+46) {
		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 z <= -1.3e-44:
		tmp = t_1
	elif z <= 1.75e-228:
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0)
	elif z <= 1.1e+46:
		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 (z <= -1.3e-44)
		tmp = t_1;
	elseif (z <= 1.75e-228)
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	elseif (z <= 1.1e+46)
		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 (z <= -1.3e-44)
		tmp = t_1;
	elseif (z <= 1.75e-228)
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	elseif (z <= 1.1e+46)
		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[z, -1.3e-44], t$95$1, If[LessEqual[z, 1.75e-228], N[(N[(1.0 + N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+46], 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 z < -1.2999999999999999e-44 or 1.1e46 < z

   1. Initial program 77.3%

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

      1. *-commutative 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in z around inf 89.6%

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

   if -1.2999999999999999e-44 < z < 1.74999999999999987e-228

   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. Taylor expanded in t around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. mul-1-neg 91.3%

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

      3. unsub-neg 91.3%

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

      4. associate-/l* 91.3%

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

      5. +-commutative 91.3%

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

   6. Simplified 91.3%

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

   if 1.74999999999999987e-228 < z < 1.1e46

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in y around 0 82.3%

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

      1. +-commutative 82.3%

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

   6. Simplified 82.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-228}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+46}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 4: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x}{z \cdot t}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-97}:\\ \;\;\;\;\frac{-y \cdot z}{x}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ x (* z t)))))
   (if (<= x -9.5e-67)
     (/ x (+ x 1.0))
     (if (<= x -3.55e-97)
       (/ (- (* y z)) x)
       (if (<= x -2.2e-190)
         t_1
         (if (<= x 5.8e-102) (/ y t) (if (<= x 2.4e-34) t_1 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (x / (z * t));
	double tmp;
	if (x <= -9.5e-67) {
		tmp = x / (x + 1.0);
	} else if (x <= -3.55e-97) {
		tmp = -(y * z) / x;
	} else if (x <= -2.2e-190) {
		tmp = t_1;
	} else if (x <= 5.8e-102) {
		tmp = y / t;
	} else if (x <= 2.4e-34) {
		tmp = t_1;
	} 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 / (z * t))
    if (x <= (-9.5d-67)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-3.55d-97)) then
        tmp = -(y * z) / x
    else if (x <= (-2.2d-190)) then
        tmp = t_1
    else if (x <= 5.8d-102) then
        tmp = y / t
    else if (x <= 2.4d-34) then
        tmp = t_1
    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 / (z * t));
	double tmp;
	if (x <= -9.5e-67) {
		tmp = x / (x + 1.0);
	} else if (x <= -3.55e-97) {
		tmp = -(y * z) / x;
	} else if (x <= -2.2e-190) {
		tmp = t_1;
	} else if (x <= 5.8e-102) {
		tmp = y / t;
	} else if (x <= 2.4e-34) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (x / (z * t))
	tmp = 0
	if x <= -9.5e-67:
		tmp = x / (x + 1.0)
	elif x <= -3.55e-97:
		tmp = -(y * z) / x
	elif x <= -2.2e-190:
		tmp = t_1
	elif x <= 5.8e-102:
		tmp = y / t
	elif x <= 2.4e-34:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(x / Float64(z * t)))
	tmp = 0.0
	if (x <= -9.5e-67)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -3.55e-97)
		tmp = Float64(Float64(-Float64(y * z)) / x);
	elseif (x <= -2.2e-190)
		tmp = t_1;
	elseif (x <= 5.8e-102)
		tmp = Float64(y / t);
	elseif (x <= 2.4e-34)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (x / (z * t));
	tmp = 0.0;
	if (x <= -9.5e-67)
		tmp = x / (x + 1.0);
	elseif (x <= -3.55e-97)
		tmp = -(y * z) / x;
	elseif (x <= -2.2e-190)
		tmp = t_1;
	elseif (x <= 5.8e-102)
		tmp = y / t;
	elseif (x <= 2.4e-34)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e-67], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.55e-97], N[((-N[(y * z), $MachinePrecision]) / x), $MachinePrecision], If[LessEqual[x, -2.2e-190], t$95$1, If[LessEqual[x, 5.8e-102], N[(y / t), $MachinePrecision], If[LessEqual[x, 2.4e-34], t$95$1, 1.0]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.4999999999999994e-67

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in t around inf 82.2%

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

      1. +-commutative 82.2%

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

   6. Simplified 82.2%

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

   if -9.4999999999999994e-67 < x < -3.55000000000000008e-97

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in y around inf 63.2%

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

      1. times-frac 63.4%

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

      2. +-commutative 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in x around 0 63.4%

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

   8. Taylor expanded in t around 0 63.6%

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

      1. associate-*r/ 63.6%

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

      2. mul-1-neg 63.6%

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

      3. distribute-rgt-neg-out 63.6%

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

   10. Simplified 63.6%

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

   if -3.55000000000000008e-97 < x < -2.20000000000000004e-190 or 5.79999999999999973e-102 < x < 2.39999999999999991e-34

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in y around 0 67.6%

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

      1. +-commutative 67.6%

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

   6. Simplified 67.6%

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

      1. clear-num 67.6%

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

      2. inv-pow 67.6%

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

   8. Applied egg-rr 67.6%

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

      1. unpow-1 67.6%

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

      2. div-sub 67.6%

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

      3. sub-neg 67.6%

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

      4. associate-/l* 67.6%

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

      5. *-inverses 67.6%

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

      6. metadata-eval 67.6%

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

   10. Simplified 67.6%

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

   11. Taylor expanded in x around 0 51.3%

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

       1. *-commutative 51.3%

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

       2. sub-neg 51.3%

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

       3. distribute-neg-frac 51.3%

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

       4. metadata-eval 51.3%

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

       5. distribute-rgt-in 51.3%

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

       6. *-lft-identity 51.3%

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

       7. associate-*l/ 51.4%

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

       8. associate-*r/ 51.4%

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

       9. mul-1-neg 51.4%

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

       10. unsub-neg 51.4%

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

   13. Simplified 51.4%

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

   if -2.20000000000000004e-190 < x < 5.79999999999999973e-102

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 60.2%

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

      1. times-frac 48.9%

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

      2. +-commutative 48.9%

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

   6. Simplified 48.9%

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

   7. Taylor expanded in x around 0 54.5%

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

   if 2.39999999999999991e-34 < x

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around 0 92.6%

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

      1. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in x around inf 88.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-97}:\\ \;\;\;\;\frac{-y \cdot z}{x}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-190}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-46} \lor \neg \left(z \leq 9.2 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e-46) (not (<= z 9.2e+33)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ 1.0 (- x (/ y (/ x z)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-46) || !(z <= 9.2e+33)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (y / (x / z)))) / (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 ((z <= (-5.2d-46)) .or. (.not. (z <= 9.2d+33))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (1.0d0 + (x - (y / (x / z)))) / (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 ((z <= -5.2e-46) || !(z <= 9.2e+33)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e-46) or not (z <= 9.2e+33):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e-46) || !(z <= 9.2e+33))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e-46) || ~((z <= 9.2e+33)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e-46], N[Not[LessEqual[z, 9.2e+33]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000004e-46 or 9.20000000000000042e33 < z

   1. Initial program 77.6%

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

      1. *-commutative 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in z around inf 89.2%

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

   if -5.2000000000000004e-46 < z < 9.20000000000000042e33

   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. Taylor expanded in t around 0 82.1%

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

      1. +-commutative 82.1%

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

      2. mul-1-neg 82.1%

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

      3. unsub-neg 82.1%

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

      4. associate-/l* 82.1%

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

      5. +-commutative 82.1%

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

   6. Simplified 82.1%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-46} \lor \neg \left(z \leq 9.2 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \]

Alternative 6: 68.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-33}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.5e-10)
   (/ x (+ x 1.0))
   (if (<= x -1.76e-94)
     (* z (/ y (- (* z t) x)))
     (if (<= x 6.2e-102) (/ y t) (if (<= x 4e-33) (- x (/ x (* z t))) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e-10) {
		tmp = x / (x + 1.0);
	} else if (x <= -1.76e-94) {
		tmp = z * (y / ((z * t) - x));
	} else if (x <= 6.2e-102) {
		tmp = y / t;
	} else if (x <= 4e-33) {
		tmp = x - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-8.5d-10)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-1.76d-94)) then
        tmp = z * (y / ((z * t) - x))
    else if (x <= 6.2d-102) then
        tmp = y / t
    else if (x <= 4d-33) then
        tmp = x - (x / (z * t))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e-10) {
		tmp = x / (x + 1.0);
	} else if (x <= -1.76e-94) {
		tmp = z * (y / ((z * t) - x));
	} else if (x <= 6.2e-102) {
		tmp = y / t;
	} else if (x <= 4e-33) {
		tmp = x - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.5e-10:
		tmp = x / (x + 1.0)
	elif x <= -1.76e-94:
		tmp = z * (y / ((z * t) - x))
	elif x <= 6.2e-102:
		tmp = y / t
	elif x <= 4e-33:
		tmp = x - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.5e-10)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -1.76e-94)
		tmp = Float64(z * Float64(y / Float64(Float64(z * t) - x)));
	elseif (x <= 6.2e-102)
		tmp = Float64(y / t);
	elseif (x <= 4e-33)
		tmp = Float64(x - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.5e-10)
		tmp = x / (x + 1.0);
	elseif (x <= -1.76e-94)
		tmp = z * (y / ((z * t) - x));
	elseif (x <= 6.2e-102)
		tmp = y / t;
	elseif (x <= 4e-33)
		tmp = x - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.5e-10], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.76e-94], N[(z * N[(y / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e-102], N[(y / t), $MachinePrecision], If[LessEqual[x, 4e-33], N[(x - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.4999999999999996e-10

   1. Initial program 85.2%

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

      1. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around inf 93.2%

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

      1. +-commutative 93.2%

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

   6. Simplified 93.2%

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

   if -8.4999999999999996e-10 < x < -1.7599999999999999e-94

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in y around inf 56.6%

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

      1. times-frac 66.2%

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

      2. +-commutative 66.2%

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

   6. Simplified 66.2%

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

   7. Taylor expanded in x around 0 64.4%

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

   if -1.7599999999999999e-94 < x < 6.20000000000000026e-102

   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. Taylor expanded in y around inf 49.5%

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

      1. times-frac 42.7%

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

      2. +-commutative 42.7%

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

   6. Simplified 42.7%

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

   7. Taylor expanded in x around 0 49.2%

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

   if 6.20000000000000026e-102 < x < 4.0000000000000002e-33

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 73.2%

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

      1. +-commutative 73.2%

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

   6. Simplified 73.2%

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

      1. clear-num 73.2%

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

      2. inv-pow 73.2%

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

   8. Applied egg-rr 73.2%

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

      1. unpow-1 73.2%

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

      2. div-sub 73.2%

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

      3. sub-neg 73.2%

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

      4. associate-/l* 73.1%

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

      5. *-inverses 73.1%

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

      6. metadata-eval 73.1%

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

   10. Simplified 73.1%

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

   11. Taylor expanded in x around 0 51.1%

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

       1. *-commutative 51.1%

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

       2. sub-neg 51.1%

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

       3. distribute-neg-frac 51.1%

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

       4. metadata-eval 51.1%

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

       5. distribute-rgt-in 51.1%

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

       6. *-lft-identity 51.1%

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

       7. associate-*l/ 51.2%

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

       8. associate-*r/ 51.2%

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

       9. mul-1-neg 51.2%

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

       10. unsub-neg 51.2%

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

   13. Simplified 51.2%

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

   if 4.0000000000000002e-33 < x

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in y around 0 92.6%

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

      1. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in x around inf 88.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -1.76 \cdot 10^{-94}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-33}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 76.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.65 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{-35}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.65e+21)
   1.0
   (if (<= x 1.62e-35) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.65e+21) {
		tmp = 1.0;
	} else if (x <= 1.62e-35) {
		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 <= (-3.65d+21)) then
        tmp = 1.0d0
    else if (x <= 1.62d-35) 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 <= -3.65e+21) {
		tmp = 1.0;
	} else if (x <= 1.62e-35) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.65e+21:
		tmp = 1.0
	elif x <= 1.62e-35:
		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 <= -3.65e+21)
		tmp = 1.0;
	elseif (x <= 1.62e-35)
		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 <= -3.65e+21)
		tmp = 1.0;
	elseif (x <= 1.62e-35)
		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, -3.65e+21], 1.0, If[LessEqual[x, 1.62e-35], 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 < -3.65e21 or 1.62000000000000011e-35 < x

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in y around 0 93.7%

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

      1. +-commutative 93.7%

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

   6. Simplified 93.7%

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

   7. Taylor expanded in x around inf 91.5%

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

   if -3.65e21 < x < 1.62000000000000011e-35

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in z around inf 65.4%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.65 \cdot 10^{+21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.62 \cdot 10^{-35}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 67.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.028:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.028) 1.0 (if (<= x 2.7e-80) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.028) {
		tmp = 1.0;
	} else if (x <= 2.7e-80) {
		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 <= (-0.028d0)) then
        tmp = 1.0d0
    else if (x <= 2.7d-80) 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 <= -0.028) {
		tmp = 1.0;
	} else if (x <= 2.7e-80) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.028:
		tmp = 1.0
	elif x <= 2.7e-80:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.028)
		tmp = 1.0;
	elseif (x <= 2.7e-80)
		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 <= -0.028)
		tmp = 1.0;
	elseif (x <= 2.7e-80)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.028], 1.0, If[LessEqual[x, 2.7e-80], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0280000000000000006 or 2.7000000000000002e-80 < x

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in y around 0 91.8%

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

      1. +-commutative 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in x around inf 85.2%

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

   if -0.0280000000000000006 < x < 2.7000000000000002e-80

   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. Taylor expanded in y around inf 50.0%

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

      1. times-frac 46.7%

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

      2. +-commutative 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in x around 0 45.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.028:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 67.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.8e-13) (/ x (+ x 1.0)) (if (<= x 2.75e-80) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.8e-13) {
		tmp = x / (x + 1.0);
	} else if (x <= 2.75e-80) {
		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 <= (-8.8d-13)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 2.75d-80) 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 <= -8.8e-13) {
		tmp = x / (x + 1.0);
	} else if (x <= 2.75e-80) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.8e-13:
		tmp = x / (x + 1.0)
	elif x <= 2.75e-80:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.8e-13)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 2.75e-80)
		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 <= -8.8e-13)
		tmp = x / (x + 1.0);
	elseif (x <= 2.75e-80)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.8e-13], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.75e-80], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -8.79999999999999986e-13

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in t around inf 91.8%

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

      1. +-commutative 91.8%

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

   6. Simplified 91.8%

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

   if -8.79999999999999986e-13 < x < 2.7499999999999998e-80

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in y around inf 50.4%

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

      1. times-frac 47.0%

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

      2. +-commutative 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in x around 0 46.5%

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

   if 2.7499999999999998e-80 < x

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in y around 0 90.5%

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

      1. +-commutative 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in x around inf 79.6%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 52.8% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.0%

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

   1. *-commutative 88.0%

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

3. Simplified 88.0%

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

4. Taylor expanded in y around 0 71.3%

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

   1. +-commutative 71.3%

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

6. Simplified 71.3%

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

7. Taylor expanded in x around inf 56.7%

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

8. Final simplification 56.7%

   \[\leadsto 1 \]

Developer target: 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 2023257 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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