Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.0% → 97.7%

Time: 7.8s

Alternatives: 11

Speedup: 1.1×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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 - x) * z) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - x) * z) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{z}{t}, y - x, x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma (/ z t) (- y x) x))

C

double code(double x, double y, double z, double t) {
	return fma((z / t), (y - x), x);
}

Julia

function code(x, y, z, t)
	return fma(Float64(z / t), Float64(y - x), x)
end

Wolfram

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

Derivation

1. Initial program 92.1%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 96.4

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

4. Applied rewrites 96.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{t}, y - x, x\right)} \]
5. Add Preprocessing

Alternative 2: 84.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t} + x\\ t_2 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+266}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{elif}\;t\_1 \leq 10^{+303}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, -x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (* (- y x) z) t) x)) (t_2 (* (- y x) (/ z t))))
   (if (<= t_1 -2e+266)
     t_2
     (if (<= t_1 2e+102)
       (+ (/ (* y z) t) x)
       (if (<= t_1 1e+303) (fma (/ z t) (- x) x) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((y - x) * z) / t) + x;
	double t_2 = (y - x) * (z / t);
	double tmp;
	if (t_1 <= -2e+266) {
		tmp = t_2;
	} else if (t_1 <= 2e+102) {
		tmp = ((y * z) / t) + x;
	} else if (t_1 <= 1e+303) {
		tmp = fma((z / t), -x, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(y - x) * z) / t) + x)
	t_2 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (t_1 <= -2e+266)
		tmp = t_2;
	elseif (t_1 <= 2e+102)
		tmp = Float64(Float64(Float64(y * z) / t) + x);
	elseif (t_1 <= 1e+303)
		tmp = fma(Float64(z / t), Float64(-x), x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+266], t$95$2, If[LessEqual[t$95$1, 2e+102], N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+303], N[(N[(z / t), $MachinePrecision] * (-x) + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -2.0000000000000001e266 or 1e303 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 82.5%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 81.4

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

   5. Applied rewrites 81.4%

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

   7. Applied rewrites 95.7%

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

   if -2.0000000000000001e266 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 1.99999999999999995e102

   1. Initial program 96.5%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 88.4

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

   5. Applied rewrites 88.4%

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

   if 1.99999999999999995e102 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 1e303

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 92.3

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

   4. Applied rewrites 92.3%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 78.5

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

   7. Applied rewrites 78.5%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq -2 \cdot 10^{+266}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq 2 \cdot 10^{+102}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq 10^{+303}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, -x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t} + x\\ t_2 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+266}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+105}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (* (- y x) z) t) x)) (t_2 (* (- y x) (/ z t))))
   (if (<= t_1 -2e+266)
     t_2
     (if (<= t_1 1e+105)
       (+ (/ (* y z) t) x)
       (if (<= t_1 2e+300) (- x (* (/ x t) z)) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((y - x) * z) / t) + x;
	double t_2 = (y - x) * (z / t);
	double tmp;
	if (t_1 <= -2e+266) {
		tmp = t_2;
	} else if (t_1 <= 1e+105) {
		tmp = ((y * z) / t) + x;
	} else if (t_1 <= 2e+300) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (((y - x) * z) / t) + x
    t_2 = (y - x) * (z / t)
    if (t_1 <= (-2d+266)) then
        tmp = t_2
    else if (t_1 <= 1d+105) then
        tmp = ((y * z) / t) + x
    else if (t_1 <= 2d+300) then
        tmp = x - ((x / t) * z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((y - x) * z) / t) + x;
	double t_2 = (y - x) * (z / t);
	double tmp;
	if (t_1 <= -2e+266) {
		tmp = t_2;
	} else if (t_1 <= 1e+105) {
		tmp = ((y * z) / t) + x;
	} else if (t_1 <= 2e+300) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((y - x) * z) / t) + x
	t_2 = (y - x) * (z / t)
	tmp = 0
	if t_1 <= -2e+266:
		tmp = t_2
	elif t_1 <= 1e+105:
		tmp = ((y * z) / t) + x
	elif t_1 <= 2e+300:
		tmp = x - ((x / t) * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(y - x) * z) / t) + x)
	t_2 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (t_1 <= -2e+266)
		tmp = t_2;
	elseif (t_1 <= 1e+105)
		tmp = Float64(Float64(Float64(y * z) / t) + x);
	elseif (t_1 <= 2e+300)
		tmp = Float64(x - Float64(Float64(x / t) * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((y - x) * z) / t) + x;
	t_2 = (y - x) * (z / t);
	tmp = 0.0;
	if (t_1 <= -2e+266)
		tmp = t_2;
	elseif (t_1 <= 1e+105)
		tmp = ((y * z) / t) + x;
	elseif (t_1 <= 2e+300)
		tmp = x - ((x / t) * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+266], t$95$2, If[LessEqual[t$95$1, 1e+105], N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+300], N[(x - N[(N[(x / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -2.0000000000000001e266 or 2.0000000000000001e300 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 82.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 80.5

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

   5. Applied rewrites 80.5%

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

   7. Applied rewrites 94.7%

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

   if -2.0000000000000001e266 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 9.9999999999999994e104

   1. Initial program 96.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if 9.9999999999999994e104 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 2.0000000000000001e300

   1. Initial program 99.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   5. Applied rewrites 77.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq -2 \cdot 10^{+266}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq 10^{+105}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq 2 \cdot 10^{+300}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - x\right) \cdot z}{t} + x\\ t_2 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+266}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+105}:\\ \;\;\;\;y \cdot \frac{z}{t} + x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (* (- y x) z) t) x)) (t_2 (* (- y x) (/ z t))))
   (if (<= t_1 -2e+266)
     t_2
     (if (<= t_1 1e+105)
       (+ (* y (/ z t)) x)
       (if (<= t_1 2e+300) (- x (* (/ x t) z)) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((y - x) * z) / t) + x;
	double t_2 = (y - x) * (z / t);
	double tmp;
	if (t_1 <= -2e+266) {
		tmp = t_2;
	} else if (t_1 <= 1e+105) {
		tmp = (y * (z / t)) + x;
	} else if (t_1 <= 2e+300) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (((y - x) * z) / t) + x
    t_2 = (y - x) * (z / t)
    if (t_1 <= (-2d+266)) then
        tmp = t_2
    else if (t_1 <= 1d+105) then
        tmp = (y * (z / t)) + x
    else if (t_1 <= 2d+300) then
        tmp = x - ((x / t) * z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((y - x) * z) / t) + x;
	double t_2 = (y - x) * (z / t);
	double tmp;
	if (t_1 <= -2e+266) {
		tmp = t_2;
	} else if (t_1 <= 1e+105) {
		tmp = (y * (z / t)) + x;
	} else if (t_1 <= 2e+300) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((y - x) * z) / t) + x
	t_2 = (y - x) * (z / t)
	tmp = 0
	if t_1 <= -2e+266:
		tmp = t_2
	elif t_1 <= 1e+105:
		tmp = (y * (z / t)) + x
	elif t_1 <= 2e+300:
		tmp = x - ((x / t) * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(y - x) * z) / t) + x)
	t_2 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (t_1 <= -2e+266)
		tmp = t_2;
	elseif (t_1 <= 1e+105)
		tmp = Float64(Float64(y * Float64(z / t)) + x);
	elseif (t_1 <= 2e+300)
		tmp = Float64(x - Float64(Float64(x / t) * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((y - x) * z) / t) + x;
	t_2 = (y - x) * (z / t);
	tmp = 0.0;
	if (t_1 <= -2e+266)
		tmp = t_2;
	elseif (t_1 <= 1e+105)
		tmp = (y * (z / t)) + x;
	elseif (t_1 <= 2e+300)
		tmp = x - ((x / t) * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+266], t$95$2, If[LessEqual[t$95$1, 1e+105], N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+300], N[(x - N[(N[(x / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -2.0000000000000001e266 or 2.0000000000000001e300 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 82.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 80.5

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

   5. Applied rewrites 80.5%

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

   7. Applied rewrites 94.7%

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

   if -2.0000000000000001e266 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 9.9999999999999994e104

   1. Initial program 96.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 94.1

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 86.4

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

   7. Applied rewrites 86.4%

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

   if 9.9999999999999994e104 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 2.0000000000000001e300

   1. Initial program 99.8%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   5. Applied rewrites 77.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq -2 \cdot 10^{+266}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq 10^{+105}:\\ \;\;\;\;y \cdot \frac{z}{t} + x\\ \mathbf{elif}\;\frac{\left(y - x\right) \cdot z}{t} + x \leq 2 \cdot 10^{+300}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot z + x\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-69}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+15}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ y t) z) x)))
   (if (<= t -1.26e-54)
     t_1
     (if (<= t 4.6e-69)
       (/ (* (- y x) z) t)
       (if (<= t 1.2e+15) (- x (* (/ x t) z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) * z) + x;
	double tmp;
	if (t <= -1.26e-54) {
		tmp = t_1;
	} else if (t <= 4.6e-69) {
		tmp = ((y - x) * z) / t;
	} else if (t <= 1.2e+15) {
		tmp = x - ((x / t) * z);
	} 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 = ((y / t) * z) + x
    if (t <= (-1.26d-54)) then
        tmp = t_1
    else if (t <= 4.6d-69) then
        tmp = ((y - x) * z) / t
    else if (t <= 1.2d+15) then
        tmp = x - ((x / t) * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) * z) + x;
	double tmp;
	if (t <= -1.26e-54) {
		tmp = t_1;
	} else if (t <= 4.6e-69) {
		tmp = ((y - x) * z) / t;
	} else if (t <= 1.2e+15) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) * z) + x
	tmp = 0
	if t <= -1.26e-54:
		tmp = t_1
	elif t <= 4.6e-69:
		tmp = ((y - x) * z) / t
	elif t <= 1.2e+15:
		tmp = x - ((x / t) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) * z) + x)
	tmp = 0.0
	if (t <= -1.26e-54)
		tmp = t_1;
	elseif (t <= 4.6e-69)
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	elseif (t <= 1.2e+15)
		tmp = Float64(x - Float64(Float64(x / t) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) * z) + x;
	tmp = 0.0;
	if (t <= -1.26e-54)
		tmp = t_1;
	elseif (t <= 4.6e-69)
		tmp = ((y - x) * z) / t;
	elseif (t <= 1.2e+15)
		tmp = x - ((x / t) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -1.26e-54], t$95$1, If[LessEqual[t, 4.6e-69], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.2e+15], N[(x - N[(N[(x / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2599999999999999e-54 or 1.2e15 < t

   1. Initial program 88.0%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 87.1

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

   5. Applied rewrites 87.1%

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

   if -1.2599999999999999e-54 < t < 4.6000000000000001e-69

   1. Initial program 96.1%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if 4.6000000000000001e-69 < t < 1.2e15

   1. Initial program 99.9%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 89.5

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

   5. Applied rewrites 89.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-54}:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-69}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+15}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;y \leq -0.65:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+108}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))))
   (if (<= y -0.65) t_1 (if (<= y 2.2e+108) (- x (* (/ x t) z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if (y <= -0.65) {
		tmp = t_1;
	} else if (y <= 2.2e+108) {
		tmp = x - ((x / t) * z);
	} 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 = (y - x) * (z / t)
    if (y <= (-0.65d0)) then
        tmp = t_1
    else if (y <= 2.2d+108) then
        tmp = x - ((x / t) * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double tmp;
	if (y <= -0.65) {
		tmp = t_1;
	} else if (y <= 2.2e+108) {
		tmp = x - ((x / t) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	tmp = 0
	if y <= -0.65:
		tmp = t_1
	elif y <= 2.2e+108:
		tmp = x - ((x / t) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	tmp = 0.0
	if (y <= -0.65)
		tmp = t_1;
	elseif (y <= 2.2e+108)
		tmp = Float64(x - Float64(Float64(x / t) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	tmp = 0.0;
	if (y <= -0.65)
		tmp = t_1;
	elseif (y <= 2.2e+108)
		tmp = x - ((x / t) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.65], t$95$1, If[LessEqual[y, 2.2e+108], N[(x - N[(N[(x / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.650000000000000022 or 2.2000000000000001e108 < y

   1. Initial program 89.6%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 67.6

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

   5. Applied rewrites 67.6%

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

   7. Applied rewrites 73.5%

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

   if -0.650000000000000022 < y < 2.2000000000000001e108

   1. Initial program 93.7%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 79.9

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

   5. Applied rewrites 79.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.65:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+108}:\\ \;\;\;\;x - \frac{x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 46.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+143}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= y -3.5e-24) t_1 (if (<= y 2.4e+143) (* (- x) (/ z t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (y <= -3.5e-24) {
		tmp = t_1;
	} else if (y <= 2.4e+143) {
		tmp = -x * (z / t);
	} 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 = y * (z / t)
    if (y <= (-3.5d-24)) then
        tmp = t_1
    else if (y <= 2.4d+143) then
        tmp = -x * (z / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (y <= -3.5e-24) {
		tmp = t_1;
	} else if (y <= 2.4e+143) {
		tmp = -x * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if y <= -3.5e-24:
		tmp = t_1
	elif y <= 2.4e+143:
		tmp = -x * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (y <= -3.5e-24)
		tmp = t_1;
	elseif (y <= 2.4e+143)
		tmp = Float64(Float64(-x) * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (y <= -3.5e-24)
		tmp = t_1;
	elseif (y <= 2.4e+143)
		tmp = -x * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-24], t$95$1, If[LessEqual[y, 2.4e+143], N[((-x) * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999996e-24 or 2.3999999999999998e143 < y

   1. Initial program 90.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 96.9

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

   4. Applied rewrites 96.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 68.5

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

   7. Applied rewrites 68.5%

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

   if -3.4999999999999996e-24 < y < 2.3999999999999998e143

   1. Initial program 93.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 55.7

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

   5. Applied rewrites 55.7%

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

   7. Applied rewrites 57.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 45.2%

       \[\leadsto \frac{z}{t} \cdot \left(-x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+143}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= y -3.5e-24) t_1 (if (<= y 2.3e+143) (* (/ (- x) t) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (y <= -3.5e-24) {
		tmp = t_1;
	} else if (y <= 2.3e+143) {
		tmp = (-x / t) * z;
	} 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 = y * (z / t)
    if (y <= (-3.5d-24)) then
        tmp = t_1
    else if (y <= 2.3d+143) then
        tmp = (-x / t) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if (y <= -3.5e-24) {
		tmp = t_1;
	} else if (y <= 2.3e+143) {
		tmp = (-x / t) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if y <= -3.5e-24:
		tmp = t_1
	elif y <= 2.3e+143:
		tmp = (-x / t) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (y <= -3.5e-24)
		tmp = t_1;
	elseif (y <= 2.3e+143)
		tmp = Float64(Float64(Float64(-x) / t) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (y <= -3.5e-24)
		tmp = t_1;
	elseif (y <= 2.3e+143)
		tmp = (-x / t) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-24], t$95$1, If[LessEqual[y, 2.3e+143], N[(N[((-x) / t), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999996e-24 or 2.3e143 < y

   1. Initial program 90.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 96.9

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

   4. Applied rewrites 96.9%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 68.5

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

   7. Applied rewrites 68.5%

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

   if -3.4999999999999996e-24 < y < 2.3e143

   1. Initial program 93.3%

      \[x + \frac{\left(y - x\right) \cdot z}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 55.7

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

   5. Applied rewrites 55.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 44.1%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.4% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 = (y - x) * (z / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
2. Add Preprocessing

3. Taylor expanded in t around 0

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower--.f64 59.5

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

5. Applied rewrites 59.5%

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

7. Applied rewrites 62.6%

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

8. Final simplification 62.6%

   \[\leadsto \left(y - x\right) \cdot \frac{z}{t} \]
9. Add Preprocessing

Alternative 10: 40.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{z}{t} \end{array} \]

FPCore

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

C

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

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 = y * (z / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 96.4

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

4. Applied rewrites 96.4%

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

5. Taylor expanded in y around inf

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

   1. *-commutative N/A

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

   2. associate-*l/ N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 37.8

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

7. Applied rewrites 37.8%

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

8. Final simplification 37.8%

   \[\leadsto y \cdot \frac{z}{t} \]
9. Add Preprocessing

Alternative 11: 37.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{y}{t} \cdot z \end{array} \]

FPCore

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

C

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

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 = (y / t) * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.1%

   \[x + \frac{\left(y - x\right) \cdot z}{t} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 35.9

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

5. Applied rewrites 35.9%

   \[\leadsto \color{blue}{\frac{y}{t} \cdot z} \]
6. Add Preprocessing

Developer Target 1: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	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 < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024255 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1805102239106601/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (* (/ z t) (- x y))) (if (< x 855006432740143/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z))))))

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