Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 93.1% → 99.1%

Time: 8.2s

Alternatives: 14

Speedup: 1.0×

• 24.6% 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: 93.1% 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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (<= t_1 (- INFINITY))
     (+ x (* z (/ (- y x) t)))
     (if (<= t_1 5e+304) t_1 (+ x (/ z (/ t (- y x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (z * ((y - x) / t));
	} else if (t_1 <= 5e+304) {
		tmp = t_1;
	} else {
		tmp = x + (z / (t / (y - x)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (z * ((y - x) / t));
	} else if (t_1 <= 5e+304) {
		tmp = t_1;
	} else {
		tmp = x + (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - x) * z) / t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (z * ((y - x) / t))
	elif t_1 <= 5e+304:
		tmp = t_1
	else:
		tmp = x + (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * z) / t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	elseif (t_1 <= 5e+304)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((y - x) * z) / t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (z * ((y - x) / t));
	elseif (t_1 <= 5e+304)
		tmp = t_1;
	else
		tmp = x + (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+304], t$95$1, N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -inf.0

   1. Initial program 85.5%

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

      1. associate-*l/ 100.0%

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

   3. Applied egg-rr 100.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < 4.9999999999999997e304

   1. Initial program 98.6%

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

   if 4.9999999999999997e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 79.4%

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

      1. associate-*l/ 100.0%

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

   3. Applied egg-rr 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \]

Alternative 2: 53.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(-z\right)}{t}\\ t_2 := y \cdot \frac{z}{t}\\ t_3 := z \cdot \frac{x}{-t}\\ \mathbf{if}\;t \leq -290000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-265}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+19}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- z)) t)) (t_2 (* y (/ z t))) (t_3 (* z (/ x (- t)))))
   (if (<= t -290000000.0)
     x
     (if (<= t -1.5e-253)
       t_2
       (if (<= t 1.05e-302)
         t_1
         (if (<= t 7e-286)
           t_2
           (if (<= t 3.1e-265)
             t_3
             (if (<= t 1.52e-158)
               t_1
               (if (<= t 4e-98) t_2 (if (<= t 2.35e+19) t_3 x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * -z) / t;
	double t_2 = y * (z / t);
	double t_3 = z * (x / -t);
	double tmp;
	if (t <= -290000000.0) {
		tmp = x;
	} else if (t <= -1.5e-253) {
		tmp = t_2;
	} else if (t <= 1.05e-302) {
		tmp = t_1;
	} else if (t <= 7e-286) {
		tmp = t_2;
	} else if (t <= 3.1e-265) {
		tmp = t_3;
	} else if (t <= 1.52e-158) {
		tmp = t_1;
	} else if (t <= 4e-98) {
		tmp = t_2;
	} else if (t <= 2.35e+19) {
		tmp = t_3;
	} else {
		tmp = x;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (x * -z) / t
    t_2 = y * (z / t)
    t_3 = z * (x / -t)
    if (t <= (-290000000.0d0)) then
        tmp = x
    else if (t <= (-1.5d-253)) then
        tmp = t_2
    else if (t <= 1.05d-302) then
        tmp = t_1
    else if (t <= 7d-286) then
        tmp = t_2
    else if (t <= 3.1d-265) then
        tmp = t_3
    else if (t <= 1.52d-158) then
        tmp = t_1
    else if (t <= 4d-98) then
        tmp = t_2
    else if (t <= 2.35d+19) then
        tmp = t_3
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * -z) / t;
	double t_2 = y * (z / t);
	double t_3 = z * (x / -t);
	double tmp;
	if (t <= -290000000.0) {
		tmp = x;
	} else if (t <= -1.5e-253) {
		tmp = t_2;
	} else if (t <= 1.05e-302) {
		tmp = t_1;
	} else if (t <= 7e-286) {
		tmp = t_2;
	} else if (t <= 3.1e-265) {
		tmp = t_3;
	} else if (t <= 1.52e-158) {
		tmp = t_1;
	} else if (t <= 4e-98) {
		tmp = t_2;
	} else if (t <= 2.35e+19) {
		tmp = t_3;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * -z) / t
	t_2 = y * (z / t)
	t_3 = z * (x / -t)
	tmp = 0
	if t <= -290000000.0:
		tmp = x
	elif t <= -1.5e-253:
		tmp = t_2
	elif t <= 1.05e-302:
		tmp = t_1
	elif t <= 7e-286:
		tmp = t_2
	elif t <= 3.1e-265:
		tmp = t_3
	elif t <= 1.52e-158:
		tmp = t_1
	elif t <= 4e-98:
		tmp = t_2
	elif t <= 2.35e+19:
		tmp = t_3
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(-z)) / t)
	t_2 = Float64(y * Float64(z / t))
	t_3 = Float64(z * Float64(x / Float64(-t)))
	tmp = 0.0
	if (t <= -290000000.0)
		tmp = x;
	elseif (t <= -1.5e-253)
		tmp = t_2;
	elseif (t <= 1.05e-302)
		tmp = t_1;
	elseif (t <= 7e-286)
		tmp = t_2;
	elseif (t <= 3.1e-265)
		tmp = t_3;
	elseif (t <= 1.52e-158)
		tmp = t_1;
	elseif (t <= 4e-98)
		tmp = t_2;
	elseif (t <= 2.35e+19)
		tmp = t_3;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * -z) / t;
	t_2 = y * (z / t);
	t_3 = z * (x / -t);
	tmp = 0.0;
	if (t <= -290000000.0)
		tmp = x;
	elseif (t <= -1.5e-253)
		tmp = t_2;
	elseif (t <= 1.05e-302)
		tmp = t_1;
	elseif (t <= 7e-286)
		tmp = t_2;
	elseif (t <= 3.1e-265)
		tmp = t_3;
	elseif (t <= 1.52e-158)
		tmp = t_1;
	elseif (t <= 4e-98)
		tmp = t_2;
	elseif (t <= 2.35e+19)
		tmp = t_3;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -290000000.0], x, If[LessEqual[t, -1.5e-253], t$95$2, If[LessEqual[t, 1.05e-302], t$95$1, If[LessEqual[t, 7e-286], t$95$2, If[LessEqual[t, 3.1e-265], t$95$3, If[LessEqual[t, 1.52e-158], t$95$1, If[LessEqual[t, 4e-98], t$95$2, If[LessEqual[t, 2.35e+19], t$95$3, x]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9e8 or 2.35e19 < t

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 63.5%

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

   if -2.9e8 < t < -1.5000000000000001e-253 or 1.05000000000000006e-302 < t < 6.99999999999999977e-286 or 1.52e-158 < t < 3.99999999999999976e-98

   1. Initial program 98.4%

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

   2. Taylor expanded in t around 0 89.2%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. associate-*r/ 72.9%

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

   5. Simplified 72.9%

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

   if -1.5000000000000001e-253 < t < 1.05000000000000006e-302 or 3.09999999999999988e-265 < t < 1.52e-158

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 64.8%

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

      1. *-commutative 64.8%

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

      2. distribute-lft-in 64.8%

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

      3. *-rgt-identity 64.8%

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

      4. mul-1-neg 64.8%

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

      5. distribute-rgt-neg-in 64.8%

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

      6. unsub-neg 64.8%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in x around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*l/ 55.2%

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

      3. *-commutative 55.2%

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

   7. Simplified 55.2%

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

      1. clear-num 55.2%

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

      2. un-div-inv 57.8%

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

   9. Applied egg-rr 57.8%

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

   10. Taylor expanded in z around inf 60.7%

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

       1. associate-*r/ 60.7%

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

       2. neg-mul-1 60.7%

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

       3. distribute-rgt-neg-in 60.7%

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

   12. Simplified 60.7%

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

   if 6.99999999999999977e-286 < t < 3.09999999999999988e-265 or 3.99999999999999976e-98 < t < 2.35e19

   1. Initial program 96.8%

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

   2. Taylor expanded in x around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. distribute-lft-in 69.2%

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

      3. *-rgt-identity 69.2%

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

      4. mul-1-neg 69.2%

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

      5. distribute-rgt-neg-in 69.2%

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

      6. unsub-neg 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in x around 0 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*l/ 72.1%

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

      3. *-commutative 72.1%

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

   7. Simplified 72.1%

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

      1. clear-num 72.0%

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

      2. un-div-inv 72.1%

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

   9. Applied egg-rr 72.1%

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

   10. Taylor expanded in z around inf 56.5%

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

       1. mul-1-neg 56.5%

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

       2. *-lft-identity 56.5%

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

       3. metadata-eval 56.5%

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

       4. times-frac 56.5%

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

       5. neg-mul-1 56.5%

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

       6. distribute-lft-neg-in 56.5%

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

       7. neg-mul-1 56.5%

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

       8. associate-/l* 57.4%

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

       9. distribute-frac-neg 57.4%

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

       10. remove-double-neg 57.4%

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

       11. *-lft-identity 57.4%

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

       12. *-commutative 57.4%

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

       13. associate-*r/ 57.4%

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

       14. associate-/r/ 57.4%

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

       15. associate-*l/ 57.4%

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

       16. *-lft-identity 57.4%

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

   12. Simplified 57.4%

       \[\leadsto \color{blue}{z \cdot \frac{x}{-t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -290000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-302}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-158}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{-t}\\ t_2 := y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x (- t)))) (t_2 (* y (/ z t))))
   (if (<= t -5.6e+15)
     x
     (if (<= t -7.5e-284)
       t_2
       (if (<= t 6.5e-305)
         t_1
         (if (<= t 4.8e-94) t_2 (if (<= t 2.15e+21) t_1 x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / -t);
	double t_2 = y * (z / t);
	double tmp;
	if (t <= -5.6e+15) {
		tmp = x;
	} else if (t <= -7.5e-284) {
		tmp = t_2;
	} else if (t <= 6.5e-305) {
		tmp = t_1;
	} else if (t <= 4.8e-94) {
		tmp = t_2;
	} else if (t <= 2.15e+21) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x / -t)
    t_2 = y * (z / t)
    if (t <= (-5.6d+15)) then
        tmp = x
    else if (t <= (-7.5d-284)) then
        tmp = t_2
    else if (t <= 6.5d-305) then
        tmp = t_1
    else if (t <= 4.8d-94) then
        tmp = t_2
    else if (t <= 2.15d+21) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / -t);
	double t_2 = y * (z / t);
	double tmp;
	if (t <= -5.6e+15) {
		tmp = x;
	} else if (t <= -7.5e-284) {
		tmp = t_2;
	} else if (t <= 6.5e-305) {
		tmp = t_1;
	} else if (t <= 4.8e-94) {
		tmp = t_2;
	} else if (t <= 2.15e+21) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / -t)
	t_2 = y * (z / t)
	tmp = 0
	if t <= -5.6e+15:
		tmp = x
	elif t <= -7.5e-284:
		tmp = t_2
	elif t <= 6.5e-305:
		tmp = t_1
	elif t <= 4.8e-94:
		tmp = t_2
	elif t <= 2.15e+21:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / Float64(-t)))
	t_2 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (t <= -5.6e+15)
		tmp = x;
	elseif (t <= -7.5e-284)
		tmp = t_2;
	elseif (t <= 6.5e-305)
		tmp = t_1;
	elseif (t <= 4.8e-94)
		tmp = t_2;
	elseif (t <= 2.15e+21)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / -t);
	t_2 = y * (z / t);
	tmp = 0.0;
	if (t <= -5.6e+15)
		tmp = x;
	elseif (t <= -7.5e-284)
		tmp = t_2;
	elseif (t <= 6.5e-305)
		tmp = t_1;
	elseif (t <= 4.8e-94)
		tmp = t_2;
	elseif (t <= 2.15e+21)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+15], x, If[LessEqual[t, -7.5e-284], t$95$2, If[LessEqual[t, 6.5e-305], t$95$1, If[LessEqual[t, 4.8e-94], t$95$2, If[LessEqual[t, 2.15e+21], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6e15 or 2.15e21 < t

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 63.5%

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

   if -5.6e15 < t < -7.4999999999999999e-284 or 6.49999999999999991e-305 < t < 4.8e-94

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 87.2%

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

   3. Taylor expanded in y around inf 55.8%

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

      1. associate-*r/ 59.6%

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

   5. Simplified 59.6%

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

   if -7.4999999999999999e-284 < t < 6.49999999999999991e-305 or 4.8e-94 < t < 2.15e21

   1. Initial program 98.9%

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

   2. Taylor expanded in x around inf 77.7%

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

      1. *-commutative 77.7%

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

      2. distribute-lft-in 77.7%

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

      3. *-rgt-identity 77.7%

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

      4. mul-1-neg 77.7%

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

      5. distribute-rgt-neg-in 77.7%

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

      6. unsub-neg 77.7%

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

   4. Simplified 77.7%

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

   5. Taylor expanded in x around 0 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l/ 71.9%

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

      3. *-commutative 71.9%

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

   7. Simplified 71.9%

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

      1. clear-num 71.9%

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

      2. un-div-inv 72.0%

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

   9. Applied egg-rr 72.0%

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

   10. Taylor expanded in z around inf 63.0%

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

       1. mul-1-neg 63.0%

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

       2. *-lft-identity 63.0%

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

       3. metadata-eval 63.0%

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

       4. times-frac 63.0%

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

       5. neg-mul-1 63.0%

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

       6. distribute-lft-neg-in 63.0%

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

       7. neg-mul-1 63.0%

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

       8. associate-/l* 60.9%

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

       9. distribute-frac-neg 60.9%

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

       10. remove-double-neg 60.9%

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

       11. *-lft-identity 60.9%

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

       12. *-commutative 60.9%

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

       13. associate-*r/ 60.8%

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

       14. associate-/r/ 60.7%

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

       15. associate-*l/ 60.8%

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

       16. *-lft-identity 60.8%

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

   12. Simplified 60.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-94} \lor \neg \left(z \leq 7.5 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e-94) (not (<= z 7.5e-5))) (* z (/ (- y x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-94) || !(z <= 7.5e-5)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	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 <= (-1.8d-94)) .or. (.not. (z <= 7.5d-5))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-94) || !(z <= 7.5e-5)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e-94) or not (z <= 7.5e-5):
		tmp = z * ((y - x) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e-94) || !(z <= 7.5e-5))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e-94) || ~((z <= 7.5e-5)))
		tmp = z * ((y - x) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e-94], N[Not[LessEqual[z, 7.5e-5]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e-94 or 7.49999999999999934e-5 < z

   1. Initial program 91.8%

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

   2. Taylor expanded in t around 0 71.0%

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

      1. associate-*l/ 98.1%

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

   4. Applied egg-rr 76.0%

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

   if -1.8e-94 < z < 7.49999999999999934e-5

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 61.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-94} \lor \neg \left(z \leq 7.5 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 79.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-11} \lor \neg \left(t \leq 6.3 \cdot 10^{+18}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e-11) (not (<= t 6.3e+18)))
   (+ x (* y (/ z t)))
   (* z (/ (- y x) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-11) || !(t <= 6.3e+18)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-8.5d-11)) .or. (.not. (t <= 6.3d+18))) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-11) || !(t <= 6.3e+18)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e-11) or not (t <= 6.3e+18):
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e-11) || !(t <= 6.3e+18))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e-11) || ~((t <= 6.3e+18)))
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e-11], N[Not[LessEqual[t, 6.3e+18]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000037e-11 or 6.3e18 < t

   1. Initial program 89.6%

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

   2. Taylor expanded in y around inf 84.3%

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

      1. associate-*r/ 28.5%

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

   4. Simplified 88.0%

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

   if -8.50000000000000037e-11 < t < 6.3e18

   1. Initial program 98.2%

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

   2. Taylor expanded in t around 0 85.4%

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

      1. associate-*l/ 85.4%

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

   4. Applied egg-rr 76.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-11} \lor \neg \left(t \leq 6.3 \cdot 10^{+18}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 6: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-14} \lor \neg \left(x \leq 2.05 \cdot 10^{+47}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3e-14) (not (<= x 2.05e+47)))
   (- x (* x (/ z t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3e-14) || !(x <= 2.05e+47)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3d-14)) .or. (.not. (x <= 2.05d+47))) then
        tmp = x - (x * (z / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3e-14) || !(x <= 2.05e+47)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3e-14) or not (x <= 2.05e+47):
		tmp = x - (x * (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3e-14) || !(x <= 2.05e+47))
		tmp = Float64(x - Float64(x * Float64(z / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3e-14) || ~((x <= 2.05e+47)))
		tmp = x - (x * (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3e-14], N[Not[LessEqual[x, 2.05e+47]], $MachinePrecision]], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9999999999999998e-14 or 2.05000000000000005e47 < x

   1. Initial program 93.0%

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

   2. Taylor expanded in x around inf 92.5%

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

      1. *-commutative 92.5%

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

      2. distribute-lft-in 92.5%

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

      3. *-rgt-identity 92.5%

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

      4. mul-1-neg 92.5%

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

      5. distribute-rgt-neg-in 92.5%

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

      6. unsub-neg 92.5%

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

   4. Simplified 92.5%

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

   if -2.9999999999999998e-14 < x < 2.05000000000000005e47

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 77.4%

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

      1. associate-*r/ 53.9%

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

   4. Simplified 81.9%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-14} \lor \neg \left(x \leq 2.05 \cdot 10^{+47}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-21} \lor \neg \left(x \leq 1.7 \cdot 10^{+47}\right):\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.7e-21) (not (<= x 1.7e+47)))
   (- x (/ x (/ t z)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e-21) || !(x <= 1.7e+47)) {
		tmp = x - (x / (t / z));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.7d-21)) .or. (.not. (x <= 1.7d+47))) then
        tmp = x - (x / (t / z))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e-21) || !(x <= 1.7e+47)) {
		tmp = x - (x / (t / z));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.7e-21) or not (x <= 1.7e+47):
		tmp = x - (x / (t / z))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.7e-21) || !(x <= 1.7e+47))
		tmp = Float64(x - Float64(x / Float64(t / z)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.7e-21) || ~((x <= 1.7e+47)))
		tmp = x - (x / (t / z));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.7e-21], N[Not[LessEqual[x, 1.7e+47]], $MachinePrecision]], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e-21 or 1.6999999999999999e47 < x

   1. Initial program 93.1%

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

   2. Taylor expanded in x around inf 91.8%

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

      1. *-commutative 91.8%

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

      2. distribute-lft-in 91.8%

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

      3. *-rgt-identity 91.8%

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

      4. mul-1-neg 91.8%

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

      5. distribute-rgt-neg-in 91.8%

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

      6. unsub-neg 91.8%

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

   4. Simplified 91.8%

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

      1. clear-num 91.8%

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

      2. un-div-inv 92.4%

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

   6. Applied egg-rr 92.4%

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

   if -1.7e-21 < x < 1.6999999999999999e47

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 77.7%

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

      1. associate-*r/ 54.6%

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

   4. Simplified 82.3%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-21} \lor \neg \left(x \leq 1.7 \cdot 10^{+47}\right):\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 8: 79.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.8e-15)
   (+ x (* y (/ z t)))
   (if (<= t 4.1e+16) (* z (/ (- y x) t)) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e-15) {
		tmp = x + (y * (z / t));
	} else if (t <= 4.1e+16) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y / (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 (t <= (-3.8d-15)) then
        tmp = x + (y * (z / t))
    else if (t <= 4.1d+16) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.8e-15) {
		tmp = x + (y * (z / t));
	} else if (t <= 4.1e+16) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.8e-15:
		tmp = x + (y * (z / t))
	elif t <= 4.1e+16:
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.8e-15)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 4.1e+16)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.8e-15)
		tmp = x + (y * (z / t));
	elseif (t <= 4.1e+16)
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.8e-15], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+16], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000002e-15

   1. Initial program 88.3%

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

   2. Taylor expanded in y around inf 83.7%

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

      1. associate-*r/ 27.0%

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

   4. Simplified 88.0%

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

   if -3.8000000000000002e-15 < t < 4.1e16

   1. Initial program 98.2%

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

   2. Taylor expanded in t around 0 85.4%

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

      1. associate-*l/ 85.4%

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

   4. Applied egg-rr 76.8%

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

   if 4.1e16 < t

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 85.0%

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

      1. associate-*r/ 30.1%

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

   4. Simplified 88.0%

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

      1. clear-num 87.9%

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

      2. un-div-inv 88.0%

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

   6. Applied egg-rr 88.0%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -660000:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -660000.0)
   (+ x (* y (/ z t)))
   (if (<= t 5.6e+17) (/ (* (- y x) z) t) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -660000.0) {
		tmp = x + (y * (z / t));
	} else if (t <= 5.6e+17) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = x + (y / (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 (t <= (-660000.0d0)) then
        tmp = x + (y * (z / t))
    else if (t <= 5.6d+17) then
        tmp = ((y - x) * z) / t
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -660000.0) {
		tmp = x + (y * (z / t));
	} else if (t <= 5.6e+17) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -660000.0:
		tmp = x + (y * (z / t))
	elif t <= 5.6e+17:
		tmp = ((y - x) * z) / t
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -660000.0)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 5.6e+17)
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -660000.0)
		tmp = x + (y * (z / t));
	elseif (t <= 5.6e+17)
		tmp = ((y - x) * z) / t;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -660000.0], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+17], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.6e5

   1. Initial program 87.9%

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

   2. Taylor expanded in y around inf 83.1%

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

      1. associate-*r/ 24.6%

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

   4. Simplified 87.6%

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

   if -6.6e5 < t < 5.6e17

   1. Initial program 98.2%

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

   2. Taylor expanded in t around 0 85.7%

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

   if 5.6e17 < t

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 85.0%

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

      1. associate-*r/ 30.1%

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

   4. Simplified 88.0%

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

      1. clear-num 87.9%

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

      2. un-div-inv 88.0%

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

   6. Applied egg-rr 88.0%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -660000:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 10: 92.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{+47}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 6.8e+47) (+ x (* z (/ (- y x) t))) (- x (/ x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 6.8e+47) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x - (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 <= 6.8d+47) then
        tmp = x + (z * ((y - x) / t))
    else
        tmp = x - (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 <= 6.8e+47) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x - (x / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 6.8e+47:
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x - (x / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 6.8e+47)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(x - Float64(x / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 6.8e+47)
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x - (x / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 6.8e+47], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.7999999999999996e47

   1. Initial program 94.2%

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

      1. associate-*l/ 92.4%

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

   3. Applied egg-rr 92.4%

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

   if 6.7999999999999996e47 < x

   1. Initial program 93.1%

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

   2. Taylor expanded in x around inf 96.1%

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

      1. *-commutative 96.1%

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

      2. distribute-lft-in 96.1%

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

      3. *-rgt-identity 96.1%

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

      4. mul-1-neg 96.1%

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

      5. distribute-rgt-neg-in 96.1%

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

      6. unsub-neg 96.1%

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

   4. Simplified 96.1%

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

      1. clear-num 96.1%

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

      2. un-div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{+47}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \]

Alternative 11: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -14000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -14000000000000.0) x (if (<= t 1.4e-102) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -14000000000000.0) {
		tmp = x;
	} else if (t <= 1.4e-102) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-14000000000000.0d0)) then
        tmp = x
    else if (t <= 1.4d-102) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -14000000000000.0) {
		tmp = x;
	} else if (t <= 1.4e-102) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -14000000000000.0:
		tmp = x
	elif t <= 1.4e-102:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -14000000000000.0)
		tmp = x;
	elseif (t <= 1.4e-102)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -14000000000000.0)
		tmp = x;
	elseif (t <= 1.4e-102)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -14000000000000.0], x, If[LessEqual[t, 1.4e-102], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e13 or 1.40000000000000006e-102 < t

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 57.2%

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

   if -1.4e13 < t < 1.40000000000000006e-102

   1. Initial program 97.8%

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

   2. Taylor expanded in t around 0 88.5%

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

   3. Taylor expanded in y around inf 52.8%

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

      1. associate-*r/ 57.3%

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

   5. Simplified 57.3%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -14000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (z / (t / (y - x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. associate-*l/ 91.4%

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

3. Applied egg-rr 91.4%

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

   1. *-commutative 91.4%

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

   2. clear-num 91.4%

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

   3. un-div-inv 91.8%

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

5. Applied egg-rr 91.8%

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

6. Final simplification 91.8%

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

Alternative 13: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) / (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 = x + ((y - x) / (t / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 14: 39.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

2. Taylor expanded in z around 0 37.4%

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

3. Final simplification 37.4%

   \[\leadsto x \]

Developer target: 97.9% accurate, 0.7× 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 2023176 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (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)))))

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